SIX SIGMA AND THE UNIVERSITY: TEACHING, RESEARCH, AND MESO-ANALYSIS DISSERTATION Presented in Partial Fulfillment of the Requirements for The Degree Doctor of Philosophy In the Graduate School of The Ohio State University By James E. Brady, B.S., M.S., MBA, P.E.

The Ohio State University 2005

Dissertation Committee:

Approved by

Dr. Theodore T. Allen, Adviser Dr. Allen R. Miller Dr. Clark A. Mount-Campbell

Graduate Program in Industrial and Systems Engineering

ABSTRACT

Six Sigma was introduced by industry practitioners and consultants as a means to improve any given company’s competitive position. Its acceptance by industry has been widespread over the past two decades, yet academic research on Six Sigma has been surprisingly limited. Further, most of the research has been focused on the tools and statistical techniques used in Six Sigma. Its relationship with university activities including teaching, research, and service is not clear. The purpose of this dissertation is to explore selected aspects of the relationship between Six Sigma and universities more fully. In doing so, there is an attempt to answer these fundamental questions: (i) What is Six Sigma? (ii) What roles can academics usefully play in relation to Six Sigma? and (iii) How can academia help companies to better use the new project related data sources created by Six Sigma. Results here divide into three chapters. First, the literature on Six Sigma is reviewed and synthesized. This includes detailed descriptions of research trends with an emphasis on establishing its relationship to quality management theory and topics for future research. Secondly, case base training is examined as a method to improve Six Sigma education and increase usage on the job among university student learners. Third, with Six Sigma’s emphasis on management by data and project based data collection, industry is starting to ii

accumulate many large databases of “meta-data” concerning the successes or failures of individual quality improvement projects. We propose methods specifically for making use of the project data and illustrate their application using 39 case studies form a mid-western manufacturing firm.

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ACKNOWLEDGMENTS

Reflecting on my long and continuing education process, I find it difficult to adequately acknowledge the incredible support I have received form so many people I am sincerely grateful to my advisor, Dr. Allen, for all of his continuous assistance and direction. I would like to thank my other committee members: Dr. MountCampbell, and Dr. Miller as well as Chaitanya Joshi who helped in the early formulation of some of the goals. I appreciate Lucent Technologies, Inc. and LaBarge, Inc for the support they provided during my recent studies. I owe a debt to my Aunt Joan for instilling in me the value and love of learning, my children and grandchildren for the sacrifice of their time. Finally, I would like to thank my wife. This dissertation is dedicated to her endless encouragement and support over these many years.

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VITA 1951 ……………………………………………… Born – Tucson, Arizona 1974 ……………………………………………… BS Aeronautical Engineering Wichita State University Wichita, Kansas 1974-1976 ……………………………………….. US Air Force W-PAFB, Ohio 1977 ……………………………………………… MS Mechanical Engineering University of Kansas Lawrence, Kansas 1977 -2001………………………………………… Lucent Technologies Bell Labs, AT&T, Sandia National Labs, Western Electric Various locations and subsidiaries 1980 ……………………………………………… MBA Marketing Avila College Kansas City, Missouri 1997 - Present …………………………………… Ohio State University Columbus, Ohio 2001-Present ……………………………………… LaBarge, Inc Joplin, Missouri

FIELDS OF STUDY Major Field: Industrial and Systems Engineering Minor Field: Computational Methods v

TABLE OF CONTENTS Abstract ………………………………………………………………………………. i Acknowledgements ………………………………………………………………….. ii VITA …………………………………………………………………………………. v List of Tables ………………………………………………………………………. viii List of Figures ……………………………………………………………………….. x Chapter 1 Introduction ................................................................................................ 1 1.1 Overview .............................................................................................................. 1 1.2 Plan of Study ........................................................................................................ 3 Chapter 2 Six Sigma Overview and History .............................................................. 5 2.1 Overview of Six Sigma ........................................................................................ 5 2.2 History of Six Sigma .......................................................................................... 12 Chapter 3 Literature Review..................................................................................... 19 3.1 Introduction ........................................................................................................ 19 3.2 Literature Review Methods and List of Articles ................................................ 19 3.3 The Classification Scheme ................................................................................. 22 3.4 Literature Trends ................................................................................................ 24 3.5 Literature Research Topics and Methods ........................................................... 28 3.6 Success Factors................................................................................................... 35 3.7 Six Sigma in the context of Management Theory.............................................. 36 3.8 The Academic Contribution of Six Sigma ......................................................... 37 3.9 Defining Six Sigma ............................................................................................ 39 3.10 The Quality Performance Model ...................................................................... 42 3.11 Review of Empirical Evaluations of Six Sigma ............................................... 44 3.12 Synthesis and Future Research......................................................................... 46 3.13 Literature Review Summary ............................................................................ 50 Chapter 4 Case Study Based Training ..................................................................... 53 4.1 Introduction ........................................................................................................ 54 4.2 Case Study Exercises.......................................................................................... 58 4.3 Sample Case Study “Improving the Yields of Printed Circuit Boards”............. 59 4.4 The Problem Statement ...................................................................................... 60 vi

4.5 Background Information .................................................................................... 60 4.6 In-class Exercise for PCB Study ........................................................................ 63 4.7 The Team Actions and Results........................................................................... 64 4.8 Student Feedback ............................................................................................... 68 Chapter 5 The challenge of Six Sigma Project Meso-Analysis............................... 70 5.1 Introduction ........................................................................................................ 70 5.2 Potential Use of Database................................................................................... 72 5.3 Database Example .............................................................................................. 73 5.4 General Procedure .............................................................................................. 74 5.5 Data Collection................................................................................................... 75 5.6 Statistical Process Control.................................................................................. 79 5.7 Regression .......................................................................................................... 84 5.8 Regression Data Analysis................................................................................... 87 5.9 Regression Results ............................................................................................. 94 5.10 Markov Decision Processes.............................................................................. 96 5.11 Markov Decision Process Analysis................................................................ 103 5.12 Sample MDP Example ................................................................................... 115 5.13 Conclusions .................................................................................................... 122 Chapter 6 Conclusions and Future Research ........................................................ 126 6.1 Overview .......................................................................................................... 126 6.2 Summary of Findings ....................................................................................... 127 6.3 Limitations and Future Research...................................................................... 130 Appendix A The Article Database.………………………………………………. 133 Appendix B Project Database……………………………………………………. 140 Bibliography………………………………………………………………………. 143

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LIST OF TABLES Table 1 List of journals or proceedings with at least one article in the study. ............. 21 Table 2 Descriptors used to classify articles. ............................................................... 24 Table 3 Tabulations of articles by focus and authorship.............................................. 30 Table 4 Literature pertinent to evaluation of Six Sigma’s effects on firm performance. (BP – Business Performance, C – Core, SSC – Six Sigma Core, SSI – Six Sigma Infrastructure, OP – Operational Performance, QP – Quality Performance) ....... 45 Table 5 The yields achieved for 16 weeks prior to the initial teams activities. ........... 61 Table 6 The initial team's predicted yield improvements by adjusting each factor. .... 62 Table 7 The performance after the implementation of the initial team's recommendations.................................................................................................. 62 Table 8 The yields for the 5 weeks subsequent to the initial intervention. .................. 65 Table 9 The data for a Pareto chart of the data from week 1 to week 16..................... 66 Table 10 The data from the fractional factorial design in four factors......................... 67 Table 11 The confirmation runs establishing the process shift/improvement.............. 68 Table 12 Definition of variables................................................................................... 77 Table 13 Summary statistics for the 39 projects, duration team memberrs and profits78 Table 14 Characteristics of the Study Variables .......................................................... 79 Table 15 Summary statistics for model. ....................................................................... 89 Table 16 Coefficient estimates ..................................................................................... 89 Table 17 Regression Checklist. .................................................................................... 91 Table 18 Summary statistics for Simple model............................................................ 94 Table 19 Coefficients for Simple model. ..................................................................... 94 Table 20 Costs and rewards (in $K), rt(st,a), of applying actions (a) in different states (st).Coefficient estimates .................................................................................... 104 Table 21 Assumed transition probabilities for applying DOE, pt(st+1= j|st= i,a = $$ DOE)................................................................................................................... 105 Table 22 Optimal decision policy for five decision periods....................................... 106 Table 23 The expected reward, ERt*(st = i), in $K as a function of period and state. 106 Table 24 Component Method of Six Sigma. .............................................................. 108 Table 25 State Description Mapped to DMAIC for Sample MDP. ........................... 115 Table 26 Actions and Rewards for Sample MDP. ..................................................... 115 Table 27 Tabulation of State Transitions for Sample MDP. ...................................... 117 Table 28 Bayesian Estimate of State Transitions for Sample MDP........................... 118 Table 29 State Transitions for Sample MDP.............................................................. 120 Table 30 Optimal Policy for Sample MDP. ............................................................... 121 viii

Table 31 Comparison of strengths and limitations for meso-analysis methods used. 124

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LIST OF FIGURES Figure 1 The yearly number of Six Sigma related articles and their authorship. ......... 26 Figure 2 The percentage of articles focused on manufacturing tropics........................ 27 Figure 3 Percentages of articles sponsored by difference societies or areas................ 28 Figure 4 Pareto chart of articles by research approach ................................................ 31 Figure 5 Journal impact factors associated with articles by different types of authors.32 Figure 6 Journal impact factors of publications pertinent to business sectors. ............ 33 Figure 7 Journal impact factors associated with articles focusing on people (Pe), Tools and Techniques (To), Systems (Sy), or a combination of these. .......................... 34 Figure 8 Journal impact factors associated with articles focusing on philosophy (Ph), practices (Pr), Tools and Techniques (To), or a combination of these................. 35 Figure 9 Percentages of articles mentioning each of 14 success factors...................... 36 Figure 10 Extended quality performance model of Garvin.......................................... 43 Figure 11 Control chart for the entire study period...................................................... 65 Figure 12 Normal Probability Chart for Six Sigma Projects........................................ 80 Figure 13 EWMA Control Chart for first 25 Six Sigma Projects. ............................... 82 Figure 14 EWMA Control Chart for Six Sigma Projects............................................. 83 Figure 15 Main Effects Plot of Regression Model. ...................................................... 88 Figure 16 3-D plot of the results.................................................................................. 90 Figure 17 Normal sores vs. residuals. .......................................................................... 91 Figure 18 Main Effects Plot of Simple Regression Model........................................... 93 Figure 19 Flow Chart of DMAIC Six Sigma Project. ................................................ 110 Figure 20 Morkov Decision Process for Six Sigma. .................................................. 114

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CHAPTER 1 INTRODUCTION

1.1 Overview Six Sigma was born approximately two decades ago as a process improvement philosophy to help improve business financial performance. It was developed in industry and spread largely by professional consultants. Since its introduction it has found its way into most sectors of today’s business society. Mostly led by practitioners Six Sigma has acquired a strong prescriptive stance with practices often being advocated as universally applicable, “one size fits all”. Yet, Six Sigma has already spawned a large number of published articles in pier reviewed journals. One of the main objectives of this dissertation is to review this information and identify opportunities for additional contributions for the academy. While Six Sigma has made a big impact on industry, the relationship between the university, industry and Six Sigma has not been studied. University-industry partnerships are expected to contribute to the advancement of knowledge and innovation in the production of competitive products, processes and services and ultimately contribute to the welfare of society.

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The major problems addressed in this dissertation are: 1.

With reference to past academic contributions, what is Six Sigma? Also, what are the on-going research trends?

2.

What are the implications of Six Sigma philosophy and methods for university education?

3.

What methods should be used to mine the new databases about project financial results? Also, what insights can be gained form studying data at a real company? This dissertation addresses these three aspects of the university-industry

relationship with Six Sigma. For the first question, the literature covering a fourteen year timeframe describing the trends, sources, and findings of Six Sigma is reviewed. The aim is to provide a description of the Six Sigma literature with an emphasis on establishing its relationship to quality management theory and to business practices in general and to identify topics for future research. Secondly, case base training is examined as a method to improve Six Sigma education and increase usage on the job among university student learners. From the literature review, one of the major themes and “success factors” identified by authors of Six Sigma articles is education of practitioners in the use of statistical tools. Six Sigma differs form most quality management systems by its emphases on training what people need to know to implement improvement programs effectively. A subset of this topic is the education of non-statisticians in the use of statistical tools. A major

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concept than becomes how to effectively educate participants in the necessary tools and techniques of Six Sigma. Third, with Six Sigma’s emphasis on management by data and project based data collection, industry is starting to accumulate a large database on quality improvement programs. Quality/cost improvement project data was collected over a 30 month period at a U.S. based mid-west manufacturing firm. A study was undertaken to look at this database in a way that could help management decisionmaking applied to improvement projects. Three levels of decision-making are defined as: Micro – related to the use of individual statistical methods. Meso – supervisor level decision-making about method selection and timing. Macro – dealing with overall quality programs and stock performance. This study investigates the use of Six Sigma databases in Meso-Analysis for decisionmaking.

1.2 Plan of Study The remainder of the study is organized as follows: •

Chapter 2 is an overview and history of Six Sigma. It describes how financial accountability for each project is established by the literature as a key component of Six Sigma philosophy and methods. As a result, databases about the financial successes or failures of individual projects have been generated in many companies for the first time. 3

•

Chapter 3 covers a review of the literature concerning Six Sigma from 1990 through 2003. This chapter presents a classification scheme for the articles, trends, topics covered, contributions, and tabulates identified success factors for Six Sigma. A definition of Six Sigma is given based on a synthesis of the literature.

•

Chapter 4 examines case based instruction in classes on SPC and DOE at Ohio State University. The approach is illustrated with an exercise based on an actual case study of increasing yields for manufacturing electronic components.

•

Chapter 5 describes methods for mining the Six Sigma project databases appearing at many companies and the properties of these new data sources. The results of a study based on 39 quality improvement projects conducted at a U.S. based mid-west manufacturing firm are used to investigate how this new database might be used to help operational management in the area of quality management practices.

•

Chapter 6 summarizes the findings, limitations, and conclusions of the study and discusses potential areas for future research.

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CHAPTER 2 SIX SIGMA OVERVIEW AND HISTORY

2.1 Overview of Six Sigma One definition of “Six Sigma” is a target for quality characteristics of units produced by the engineered system being improved (Shina, 2002; Tadikamalla, 1994). It is a rating that signifies “best in class”, with only 3.4 defects per million units or operations. A part or item is classified as defective if the desired measurement, denoted by X, is outside the upper or lower specification limits (USL or LSL). In addition to specifying the USL and LSL, a target value is specified, which typically is the midpoint between the USL and LSL. The symbol sigma (σ) is a letter in the Greek alphabet used by modern people to describe variability. In Six Sigma, the common measurement index is defects per million opportunities and can include anything from a component, piece of material, line of code, an administrative form, time frame or distance. A sigma quality level offers an indicator of how often defects are likely to occur, where a higher sigma quality level indicates a process that is less likely to create defects. Consequently, as sigma level of quality increases, product reliability improves, the need for testing and

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inspection diminishes, work in progress declines, cycle time goes down, costs go down, and customer satisfaction goes up. Six sigma is a condition of the generalized formula for process capability, which is defined as the ability of a process to turn out a good product. It is a relationship of product specifications to manufacturing variability, measured in terms of Cp or Cpk, or expressed as a numerical index. Six sigma is equivalent to Cp=2 or Cpk=1.5.The definition of the capability of the process or Cp is:

Cp =

specification width(or design tolerance) process capability(or totalprocess var iation)

(1.1)

USL − LSL 6σ (total process range from − 3σ to + 3σ )

(1.2)

Specifically,

Cp =

This formula can be expressed conceptually as, Cp =

product specifications manufacturing var iability

(1.3)

The equation for Cpk is: ⎡USL − X X − LSL ⎤ Cpk = min ⎢ , ⎥ 3σ ⎦ ⎣ 3σ

(1.4)

Six sigma is achieved when the product specifications are at ± 6σ of the manufacturing process corresponding to Cp=2 or Cpk=1.5. Design engineers normally set the product specifications, whereas manufacturing engineers are responsible for 6

production variability. The object of increasing the process capability to six sigma is twofold: either increase the product specifications by widening them, or reducing the manufacturing variability. Either effort can have a positive effect on reaching six sigma. An alternative and more common definition for “Six Sigma” methods, implied by Pande and Holpp (2001) and Watson (2002a), is a series of ordered activities with associated component methods (Allen, 2003). Six Sigma is a disciplined and quantitative approach involving setting up a system and process for the improvement of defined metrics in manufacturing, service, or financial processes. The approach drives the overall process of selecting the right projects based on an organization’s business goals and selecting and training the right people to obtain the results. Improvement projects follow a disciplined process defined by a system of five macro phases. These component methods derive from statistics, marketing, and optimization and are sequenced as Define, Measure, Analyze, Improve, and Control (DMAIC). In design projects the specifics of the DMAIC steps are often modified to DMADV;

Define customer requirements and goals for the product. Measure and match performance to customer requirements. Analyze and assess product design. Design and implement new product. Verify results and maintain performance.

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The phases of DMAIC are described by Rasis, Gitlow and Popovich (2003a and 2003b) as follows: Define Phase: Define the project’s objectives by identifying customer

requirements often called “CTQs” “critical to quality”, develop a team charter and define process map. •

Identify the process or product for improvement, identify customers and translate the customer’s needs into CTQs.

•

The team charter involves selection of team members and defining of roles, developing the problem and goal statements, determining project scope, setting project milestones and preparing a business case to gain management support.

•

Do a high level process map connecting the customer to the process.

Measure Phase: Measure the existing systems. Establish valid and reliable

metrics to help monitor progress towards the project goals. Customer expectations are defined to determine “out of specification” conditions. •

Identify and describe the potential critical processes/products. List and describe all of the potential critical processes obtained from brainstorming sessions, historical data, yield reports, failure analysis reports, analysis of line fallout and model the potential problems.

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•

Perform measurement system analysis. Determine precision, accuracy, repeatability and reproducibility of each instrument of gauge used in order to ensure that they are capable.

Analyze Phase: Analyze the system to identify ways to eliminate the gap

between the current performance of the system or process and the desired goal. In this phase, project teams explore underlying reasons for defects. They use statistical analysis to examine potential variables affecting the outcome and seek to identify the most significant root causes. Then, they develop a prioritized list of factors influencing the desired outcome. •

Isolate and verify the critical processes. Narrow the potential list of problems to the vital few. Identify the input/output relationship which directly affects specific problems. Verify potential causes of process variability and product problems.

•

Perform process and measurement system capability studies. Identify and define the limitations of the processes. Ensure that the processes are capable of achieving their maximum potential. Identify and remove all variation due to special causes. Determine what the realistic specifications are. Determine confidence intervals. A process is to be considered capable when it is in control, predictable, and stable.

Improve Phase: In this phase, project teams seek the optimal solution and

develop and test a plan of action for implementing and confirming the solution. 9

The process is modified and the outcome is measured to determine whether the revised method produces results within customer expectations. •

Conduct design of experiment. Select design of experiment factors and levels, Plan design of experiment execution. Perform design of experiment to find out the most significant factor.

•

Implement variability reduction designs/assessments. Implement permanent corrective action for preventing special cause variations. Demonstrate process stability and predictability.

Control Phase: Control the new system. Ongoing measures are implemented

to keep the problem form recurring. Institutionalize the improved system by modifying policies, procedures, operating instructions and other management systems. •

Specify process control methods. Establish on-going controls for the process based on prevention of special cause variation using statistical process control techniques.

•

Document the improvement processes. Record all the processes/steps in improvement phase using the decision tree and reaction plan.

The methods are generally taught in the context of system improvement projects and expertise is often characterized by an analogy to karate “belts”: “black belt”, “green belt”, etc. For thousands of participants at the lowest “green belt” level of accreditation, one of the main benefits of “Six Sigma” training is that it simplifies 10

(through restriction) the sequence and choice of available techniques to apply to a particular case. Therefore, the value of the six sigma movement derives partly from standardization of problem solving methods and partly in how it guides people to suggest which techniques to apply in which order to an improvement project. Contributing to the widespread deployment of Six Sigma is an abundance of anecdotal evidence attributing quality, productivity, and costs benefits to this particular quality improvement initiative. Scientific evidence to lead credence to the anecdotal evidence has been rather limited and exists primarily as small-sample case studies. Moreover, while the empirical results from these case studies have generally been atheoretical in nature, their conduct had not been governed by rigorous, a priori theory development. Bisgaard and Freiesleben (2000) showed how defect elimination and prevention associated with a Six Sigma program can improve financial results. Their view was to do or not to do a project. Hild, Sanders, and Cooper (2000) discussed the different structures of Six Sigma based on processes type, continuous or discrete. Sanders and Hild (2000a and 2000b) outlined the importance of considering organizational issues in the structuring of successful Six Sigma projects. Snee (2001a) similarly stated that one of the keys was to understand the environment in order to tailor Six Sigma projects; type of company (manufacturing or service), type of function (operations, transactional, administrative, or new product development) and type of industry (assembly, processing, chemical, etc.). Pyzdek (2001b) pointed out

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the importance of selecting the right individual to act as project leader even before they are trained. Pande, Neuman, and Cavanagh (2000) contributed probably the most complete and explicit version of the Six Sigma methods. Yet, even their version of the methodology leaves considerable latitude to the implementers to tailor approaches to applications and to their own tastes. This lack of standardization of the methodologies explains, at least in part, why the American Society for Quality did not have a certification process until 2001.

2.2 History of Six Sigma According to Folaron (2003) Six Sigma can arguably trace its roots as far back as 1798 and Eli Whitney. One of his greatest contributions to modern manufacturing was the introduction of his revolutionary uniformity system in the mass production of muskets. He proved it was possible to produce interchangeable parts that were similar enough in fit and function to allow for random selection of parts in the assembly. Throughout the next century, quality involved objective methods of measuring and assuring dimensional consistency. With the advent of the moving assembly line by Ford in the early 1900’s it was critical to predetermine the consistency of incoming parts to prevent a slow down or stoppage of the assembly line. In addition with the increased production rates, it became cost prohibitive to measure each part. This necessitated the development of 12

methods to monitor the part producing process for consistency and the use of sampling (Folaron, 2003). In 1924, Walter A. Shewhart from Bell Telephone Laboratories, proposed the concept of using statistical charts to control the variables of products manufactured at Western Electric. This was the beginning of statistical quality control (Small, 1956). The role of the quality inspector changed with the statistically based control charts form one of identifying and sorting defective product to one of monitoring the stability of the process and identifying when it had changed. Improved product quality resulted by early detection of the change and appropriate corrective action. Dr. Shewhart kept on with his efforts and applied the fundamentals of statistical quality control to industry. This lead to the modern attention to the use of statistical tools for the manufacture of products and process originated prior to and during World War II, when the United States of America geared up to a massive buildup of machinery and arms to successfully conclude the war. The need to manage the myriad of complex weapon systems and their varied and distributed defense contractors led to the evolution of the system of Statistical Quality Control (SQC), a set of tools that culminated in the military standards for subcontracting, such as MIL-Std 105 (Shina, 2002). The basis of the SQC process was the use of 3 sigma limits, which yields a rate of 2700 defective parts per million (PPM). Prior to that period, large U.S. companies established a quality strategy of vertical integration (Shina, 2002). In order to maintain and manage quality, companies had to control all of the resources used in the product. U.S. companies slowly realized 13

that quality improvements depended on the realization of two major elements. First, they have to be quantifiable and measurable, and second all elements that make the company successful must be implemented. These are superior pricing, delivery, performance, reliability, and customer satisfaction. The Western Electric manufacturing company is noteworthy during this time because it was the breeding ground for many quality leaders, not only Shewhart but Joseph Juran, Edwards Deming and Kaoru Ishikawa all worked there at some time (Dimock, 1977). After World War II, numerous manufacturing experts where involved with the rebuilding of the Japanese business infrastructure. Two prominent individuals were Deming and Juran. Deming promoted the use of the plan-do-check-act (PDCA) cycle of continuous improvement. Later Juran introduced the concepts of project by project quality improvement. Any discussion on quality today will most likely cite at least one from the group of Deming, Juran, Crosby, Feigenbaum, and Ishikawa, if not all. They certainly represent the preponderance of information about quality. In fact, the concepts of TQM are mainly based on their works on quality. Their collective philosophies can be summarized as follows: •

Management leadership and employee participation in the new philophy (Deming, 1986). Make quality the concern of everyone in the company (Crosby, 1980; Juran, 1989; Feigenbaum, 1991).

•

Emphasis on meeting the requirements of both the internal (Crosby, 1980; Feigenbaum, 1991) and external customers (Ishikawa, 1985). 14

•

Eliminate non-conformance, Appraise conformance to standards. Have zero defect standard of performance (Crosby, 1980). Reduce cost of appraisal, prevention and failure (Feigenbaum, 1991).

•

Use statistical and quantitative control methods. Implement problem solving using Quality Control Circles, Plan-Do-Study-Act cycle, and Quality Assurance (Deming, 1986; Ishikawa, 1985).

•

Search continually to improve process and product (Demin, 1986). Quality is a continuous program (Crosby, 1980: Feigenbaum, 1991).

Adding to this group, Bill Smith, Motorola Vice President and Senior Quality Assurance Manager, is widely regarded as the father of Six Sigma, Shina (2002), although several have played key roles in promoting this phrase including Harry (1994) and Pande, Neuman, and Cavanagh (2000). According to Shina (2002) before, January 15, 1987, Six Sigma was solely a statistical term. Since then, the Six Sigma crusade, which began at Motorola, has spread to other companies which are continually striving for excellence. While it is progressing, it has extended and evolved from a problem-solving technique to a quality strategy and ultimately into a sophisticated quality philosophy. However, this unique philosophy only became well known after GE’s Jack Welch made it a central focus of his business strategy in 1995. Today, Six Sigma is considered one of the fastest growing business management system in industry (Cook, 1990; Gill, 1990; Rayner, 1990; Behara et al.,1995; and Maguire, 1999b). Since its initial development and deployment at Motorola, Six Sigma has influenced virtually every sector of the 15

economy, from manufacturing to service and from the largest to the smallest organization. Today, Six Sigma processes are being executed in a vast array of organizations and in a wide variety of functions (Breyfogle, 1999). The evolution of what is known as Six Sigma began in the late 1970s, when a Japanese firm took over a Motorola factory that manufactured television sets in the United States and the Japanese promptly set about making drastic changes to the way the factory operated (Folaron, 2003). Under Japanese management, the factory was soon producing TV sets with 1/20th the number of defects they had produced under Motorola management. Finally, Motorola recognized it quality was awful. Since then Motorola management decided to take quality seriously (Main, 1994; Pyzdek 2000). When Bob Galvin became Motorola’s CEO in 1981, he challenged his company to achieve a tenfold improvement in performance over a five-year period. During 1985, Bill Smith wrote an internal quality research report which caught the attention of Bob Galvin, Smith discovered the correlation between how well a product did in its field life and how much rework had been required during the manufacturing process. He also found that products that were built with fewer nonconformities were the ones that performed the best after delivery to the customer (Harry, 1998; Maguire, 1999b). Although Motorola executives agreed with Smith’s supposition, the challenge then became how to create practical ways to eliminate the defects. Smith developed a four-stage problem-solving approach: Measure, Analyze, Improve, Control (MAIC). Later, the MAIC discipline became the roadmap for DMAIC and achieving Six Sigma quality. 16

On January 15, 1987, Galvin launched a long term quality program, called “The Six Sigma Quality Program”. The program was a corporate program which established Six Sigma as the required capability level standard. This new standard was to be used in everything, that is, in products, processes, services, and administration. After implementing Six Sigma, in 1988, Motorola was among the first recipients of the Malcom Baldrige National Quality Award. At that time, enamored by Motorola’s success, several other companies, such as Texas Instruments, began a similar pursuit, But, it wasn’t until late 1993 that Six Sigma really began to transform business. That’s the year Allied Signal (Honeywell) and its CEO, Larry Bossidy, decided to adopt Six Sigma. By adequately selecting the right Six Sigma projects and promptly providing the right support for them, Bossidy suggested that high level executives should also understand Six Sigma tools. At Allied Signal, an entire system of leadership and support systems began to form around the statistical problem solving tools of Six Sigma. Not long after Allied Signal began its pursuit of Six Sigma quality, Jack Welch, then Chairman and Chief Executive of General Electric, influenced by Bossidy, began to get interested in Six Sigma. Some argue that many of the tools used with Six Sigma are not new (Tadikamalla, 1994: Hahn et. Al, 1999; Watson, 2000). However, while Six Sigma uses conventional methods, its application is anything but conventional. Instead it stresses the impotence of searching for a new way of thinking and doing (Maguire, 17

1999b). In fact, Six Sigma defines a clear roadmap to achieve Total Quality (Balkeslee, 1999; Breyfogle, 1999; Pyzdek, 2000; Harry, 1998; Young, 2001). Six Sigma’s approach and deployment makes it distinguishable from other quality initiatives. The Six Sigma approach involves the use of statistical tools within a structured methodology for gaining the knowledge needed to achieve better, faster, and less expensive products and services than the competition. The repeated, disciplined application of the master strategy on project after project, where the projects are selected based on key business objectives, is what drives dollars to the bottom line, resulting in impressive profits. Moreover, fueled by the bottom line improvement, top management will continuously be committed to this approach, the work culture will be constantly nurtured, then customers will definitely be satisfied and Total Quality will ultimately be achieved.

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CHAPTER 3 LITERATURE REVIEW

3.1 Introduction Although Six Sigma originated in industry, it has inspired a considerable amount of academic literature.

This chapter reviews this literature

covering a fourteen-year timeframe (1990 through 2003) describing the trends, sources, and findings. The chapter also seeks to synthesize the literature, with an emphasis on establishing its relationship to quality management theory and topics for future research. In doing so, there is an attempt to answer the fundamental questions: (i) What is Six Sigma? (ii) What are its impacts on operational performance? and (iii) What roles can academics usefully play in relation to Six Sigma?

3.2 Literature Review Methods and List of Articles The list of articles was derived from a Science Citation Index (SCI) Expanded search spanning the time period from 1990 through 2003. Five descriptors were used: Six Sigma, quality systems, quality improvement, quality management, and quality

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meta-model. The test of each article was reviewed in order to eliminate those that were clearly not related to “Six Sigma” improvement strategies. For example, articles were removed that focused on detailed synthesis of chemicals and used the term Six Sigma in an unrelated context.

Also, a small number of articles were included from

magazines and conference proceedings that were subjectively assessed to be academic in character. The list of journals, proceedings, and magazines that provided at least one relevant article is shown in Table 1. Two hundred and one (201) articles were identified and covered in the review. The terms used to categorize these articles are defined in section 3.3. Overall, it is not claimed that the list of articles is exhaustive, only that the associated database serves as a reasonably comprehensive list for understanding Six Sigma related research. The focus of this review was in three areas. First, what is the definition of Six Sigma? A solid definitional foundation must exist before rigorous analysis can be undertaken. Second, what is the impact of Six Sigma on a firm’s performance? Six Sigma reportedly has saved millions of dollars for such companies as GE, but can its benefits be quantified in the literature? Third, what has been reported on how to implement Six Sigma in a real business setting? Is there guidance for the practitioner on the how and why to successfully implement a Six Sigma program?

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Accreditation and Quality Assurance AIAA-2002-1471 Annual Quality Congress Transactions Annual Reliability and Maintainability ----Symposium Proceedings Archives of Pathology & Laboratory Medicine Assembly Automation Aviation Week and Space Technology Building Research and Information Business Management Business Month Cancer Journal Chemical Engineering Communications Chemical Engineering Progress Chemical Week Clinical Chemistry Computers & Industrial Engineering Computers In Industry Control Engineering Electronic Business Fortune Genetic Engineering News Hospitals & Health Networks Hydrocarbon Processing IEEE Engineering Management Review IEEE Software IEEE Transactions on Neural Networks IEEE Transactions on Semiconductor ----Manufacturing IIE Solutions Industrial Management & Data Systems International Journal of Production Research International Journal of Quality & Reliability ----Management International Journal of Quality Science Journal of American Geriatrics Society Journal of Applied Statistics Journal of Engineering Design

Journal of Evaluation in Clinical Practice Journal of Healthcare Management Journal of Management Engineering Journal of Manufacturing Science and ----Engineering Transactions of the ----ASME Journal of Mechanical Design Journal of Operations Management Journal of Quality and Participation Journal of Quality Technology Journal of The IES Lecture Notes In Computer Science Manufacturing Engineering Milbank Quarterly Proceedings of the 2001 Winter Simulation ----Conference Proceedings of the 2002 Winter Simulation ----Conference Proceedings of the ASME Design ----Engineering Technical Conference Professional Engineering Quality and Reliability Engineering ----International Quality Digest Quality Engineering Quality Management in Health Care Quality Progress R&D Magazine Radiology Research-Technology Management Six Sigma Forum Magazine Technometrics The American Statistician The Physics Teacher Therapeutic Apheresis Total Quality Management Total Quality Management & Business ---- Excellence Training & Development

Table 1 List of journals or proceedings with at least one article in the study.

21

3.3 The Classification Scheme Articles were classified using the eleven descriptors in Table 2. Authors represented either academic institutions or industrial companies or constituted a team with representatives from both.

Many articles contain definitions of the phases

Define, Measure, Analyze, Improve, and Control (DMAIC) but most did not. Two schemes were used to evaluate the primary topic(s) of each article. Oakland (1989) divided quality issues roughly into systems, practices, people, or other focused, without providing precise definitions of these terms. Zain, Dale and Kehoe (2001) followed Oakland in using this division to classify articles (version 1). Sousa and Voss (2002) developed a modified scheme based on philosophies, practices, tools and techniques, and other (version 2). Sousa and Voss (2002) defined “philosophy” as “an approach to management,” and practices as “an observable facet of a philosophy and it is through them that managers work to realize organizational improvements.” Those authors also described “tools and techniques” as “core elements” with examples being process control and Pareto analysis. The Science Citation Index (SCI) provides a number called “journal impact factor” that is a ratio between the citations to articles in a journal to the average number of citations to journals in that field. The impact factor can be viewed as a rough evaluation of the academic quality of the journal. Many articles made explicit reference to either the manufacturing or service sector issues, while others offered general contributions. A common feature of articles was mentioning 3.4 defects per million opportunities in relation to the definition of Six Sigma. 22

The articles were each affiliated with one of the following sponsoring societies or areas of study: the American Institute of Chemical Engineers (AICHE), the American Society of Mechanical Engineers (ASME), the applied statistics area including publications sponsored by the American Society of Quality (ASQ) and the American Statistical Association (ASA), the Institute of Industrial Engineers (IIE), the operations research or management science (OR/MS) area including publications sponsored by the Institute for Operations Research and Management Science (INFORMS) and other related journals, or the medical area in general including the American Medical Association (AMA). Following Zain, Dale, and Kehoe (2001), articles were classified as focused on case studies, survey results, literature review, comparative analysis, or theoretical with application. A sizable fraction of the articles investigated the factors contributing to the success of Six Sigma implementations. For those articles, the specific success factors mentioned were tabulated. The terminology used to describe the success factors was standardized to correspond to the dimensions of quality management practice in Sousa and Voss (2002) whenever possible. Finally, articles that recommended the usage of one or more practices without clarifying conditions in which this practice has provable properties were classified as “speculative” in nature. This classification differentiated these articles from others without specific recommendations for practices or having rigorous statistical or optimization justifications.

23

Descriptor Authorship Define DMAIC Topics Version 1

Source Brady and Allen Brady and Allen Oakland (1989)

Topics Version 2

Sousa et al. (2002)

Industrial Sector

Zain et al. (2001)

Journal Impact Factor Mention of 3.4 ppm Research Approach

Science Citation Index Brady and Allen Zain et al. (2001)

Society or Area

Brady and Allen

Success factors Speculative in Nature

Brady and Allen Brady and Allen

Levels Industrial (I), Academic (A), or Both (I A) Yes (Y) or No (N) Systems (Sy), Tools and Techniques (To), and People (Pe) Philosophy (Ph), Practices (Pr), Tools and Techniques (To), and Other Manufacturing (M), Service (Se), or General (G) 0.13 to 4.76 Yes (Y) or No (N) Case Study (Ca), Comparative (Co), Survey (Su), Literature Review (R), or Theoretical with Application (TA) AIChe, ASME, ASQ, IIE, INFORMS, or Medical All combinations of 13 possible factors Yes (Y) or No (N)

Table 2 Descriptors used to classify articles.

3.4 Literature Trends In this section, a characterization of the database of articles using statistics derived from the classifiers described in the last section is presented. Goals include the identification of trends including those that relate to the authorship of articles and the subjects addressed. There is also an investigation of the interaction of authorship with research focus and a tabulation of the associated sponsoring societies or areas of study. Finally, results relating to success factors including a tabulation of the success factors cited most often in the literature are discussed. Figure 1 plots the number of articles verses the year. Based on the number of papers there is little doubt that the subject is actively reported. The plot suggests two 24

findings. First, the number of articles by industrial authors peaked in 2000. It is hypothesize that this declining trend was influenced by condemnations of Six Sigma in the popular press such as Clifford (2001) in Fortune Magazine. Second, at the same time, interest among academics continued to grow in 2003. Over the entire search period, 69.2% of the authors had industry affiliations and 30.8% had academic affiliations. These proportions have been changing to the point where 53% of the authors reviewed in 2003 were associated with a university or college. This trend in authorship from industry dominated to academic dominated is not surprising considering the industrial origins of Six Sigma. It would be anticipated that the growing interest in Six Sigma from the academic arena would add rigor and theoretical understanding to the subject.

25

45 40 Academia

35

Industry

Number of Articles

30 25 20 15 10 5

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

0

Year

Figure 1 The yearly number of Six Sigma related articles and their authorship.

Another trend is the diversification of research topics from primarily manufacturing focused to more general in nature as indicated by Figure 2. This trend is characterized with increased emphasis on generic issues and on service related business sectors. Particularly, there is increased emphasis on generic statistical tools such as design of experiments (DOE), probabilistic design, and statistical process control (SPC) in the context of Six Sigma, e.g., Mason and Yong (2000), Coleman et. al. (2001), McCarthy and Stauffer (2001), Koch (2002) and Goh (2002). Figure 3 charts the percentages of articles associated with different areas. The fact that the 26

earliest medical related publication in the database is Buck (1998) supports the finding that the medical area is playing an important role in increasing the topic diversity. Six Sigma has been advocated as universally applicable to organizations, a one-size-fitsall. Rigorous academic studies are needed to question the universal validity of Six Sigma across such dimensions as industry sector, company size, country/culture, product/process/service, and frequency of product change or introduction.

% of Manufacturing Articles

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1990

1992

1994

1996

1998

2000

2002

Figure 2 The percentage of articles focused on manufacturing tropics. Figure 3 also indicates that the applied statistics journals such as the Journal of Quality Technology, Quality Engineering, Quality Management Journal, Quality Progress, and Technometrics dominate scholarly publications on Six Sigma. Note that Technometrics is sponsored jointly by ASQ and the American Statistical Association (ASA). This dominance is perhaps surprising considering the

27

multidisciplinary nature of Six Sigma as noted by Hahn, Doganaksoy, and Hoerl (2000) and others.

IEEE OR+MS Medical ASME AICHE Applied Statistics 0%

10%

20%

30%

40%

50%

Figure 3 Percentages of articles sponsored by difference societies or areas.

3.5 Literature Research Topics and Methods Next, the topics and research approaches of the articles in the database are examined. We begin by focusing on the topics covered and the dependence of the number of articles and scholarly impact on the authorship. Then, the methods used in relation to scholarly impact are investigated. Table 3 contains a cross tabulation of the topic and authorship variables. It supports three findings. First, the majority of articles focused on either philosophy or 28

systems topics. The percentages on these topics were 54.7% and 66.2% respectively. In general, papers in these categories provided a general description of Six Sigma and advocated its use, e.g., Rayner (1990), Harry (1998), Snee (2001) and Does et. al. (2002). It was found that 32% of the total articles are in this category are introductory in nature. Overall, only 6% of the articles were written at the practices level which Sousa and Voss (2002) argued are most useful for stimulating actual organizational improvements. Academic authors wrote about practices with higher frequency (10%). Second, Table 3 also shows that academics were more likely to choose topics amenable to theoretical study such as tools and techniques and practitioners were more likely to present philosophical or systems level contributions. For example, only 17% of articles by exclusively industrial authors concerned tools and techniques compared with 36% of the articles by exclusively academics. The literature has focused primarily in the two areas of philosophy or tools and techniques. These areas of study are not helpful for development of usable models to aid decision makers in the implementation of Six Sigma. More research in needed into the linkage between the practices involved in Six Sigma.

29

Topics Version 1 from Oakland (1989) Systems Tools and Techniques People and Systems People and Tools and Techniques Systems and Tools and Techniques Topics Version 2 from Sousa and Voss (2002) Philosophy Tools and Techniques Philosophy and Tools and Techniques Philosophy and Practices Practices Practices and Tools and Techniques Totals

Academic 23 20 3

Industrial 83 28 18

Mixed 4 5 2

Totals 110 53 23

4

5

0

9

0

5

1

6

Academic 26 18

Industrial 101 25

Mixed 6 5

Totals 133 48

1 3 1

6 3 2

1 0 0

8 6 3

1 50

2 139

0 12

3 201

Table 3 Tabulations of articles by focus and authorship.

Figure 4 is a Pareto chart of the number of articles associated with the different research methods. The papers containing case studies constituted a sizable fraction of papers on all topics. For example, 40% of the papers classified as philosophy focused contained case studies with no new tools and techniques and 50% of the papers exclusively on tools and techniques contained a case study with no new tools and techniques. Of the articles with case studies the majority contained only a single case. These articles for the most part have been descriptive in nature lacking rigor. Those articles classified as theoretical with application where written primarily by academics. It was noted that they offered more solid foundation but mostly dealt with 30

tools and techniques and where not helpful in developing a model on how and why six Sigma works.

# of Articles 0

10

20

30

40

50

60

70

80

Research Approach

Case Study Theoretical with Application Survey Comparitive Literature Review Other

Figure 4 Pareto chart of articles by research approach .

As described in Section 3.3, journal impact factors were developed by the Science Citation Index (SCI) to provide a rough measure of journal quality or impact. Figure 5 is a box and whisker plot of the journal impact factors associated with the articles in the database. It shows that, not surprisingly, academic authors tended to publish in journals with higher scholarly impact. Again, these dealt mostly at the technique level and not the level of practices, which is most helpful to those decision makers looking for guidance. Figure 6 is a box and whisker plot of the journal impact

31

factors associated with articles associated with either manufacturing or service sectors of business or of generic interest. The plot shows that service related publications have the highest scholarly impact. This can be attributed to the relatively greater impact associated with the specific journals Clinical Chemistry, Radiology, and the Journal of the American Geriatrics Society. The associated articles covered topics classified as systems and tools and techniques.

5

Impact factor

4 3 2 1 0 Academic

Industry

Mixed

Figure 5 Journal impact factors associated with articles by different types of authors.

32

5

Impact factor

4 3 2 1 0 General

Manufacturing

Service

Figure 6 Journal impact factors of publications pertinent to business sectors.

A sizable fraction of the articles in the most prestigious statistics journals concerned the tools that Six Sigma black belts “should” know, e.g., the discussion of Hoerl (2001a) and Hoerl (2001b) and Montgomery, Lawson, and Molnau (2001). These articles were classified into people combined with tools and techniques in the Oakland (1989) scheme and philosophy and tools using the Sousa and Voss (2002) scheme. These articles caused both categories to be associated with the highest median journal impact factors. Figure 7 and Figure 8 provide box and whisker plots of the impact factors associated with the research topics. Surprisingly, the topic

33

associated with the least impact is “practices.” Sousa and Voss (2002) argued that this topic was the one most likely to stimulate organizational change. Two other important themes related to people topics. First, articles focusing on the cultural implications or management actions included Sanders and Hild(2000b) and Wiklund (2002). Second, leadership and training are also popular themes (e.g., see Hahn, 1999, and Hoerl, 2001). Many of these articles examined of success factors as we describe next. 5

Impact factor

4 3 2 1 0 Pe Sy

Pe To

Sy

Sy To

To

Figure 7 Journal impact factors associated with articles focusing on people (Pe), Tools and Techniques (To), Systems (Sy), or a combination of these.

34

5

Impact factor

4 3 2 1 0 Ph

Ph Pr

Ph To

Pr

Pr To

To

Figure 8 Journal impact factors associated with articles focusing on philosophy (Ph), practices (Pr), Tools and Techniques (To), or a combination of these.

3.6 Success Factors In the database, 26.9% of the articles made a claim to the “success factors” necessary for Six Sigma to succeed. Fourteen separate factors can be found among the literature, some being in conflict with each other, Figure 9. Half would be classified as infrastructure, half would be classified as core as defined by Sousa and Voss (2002). The most commonly cited factor is “Top Management Commitment”, which could be said of any organization initiative. These success factors are offered for the most part without rigorous proof. The second most common factor was training. This high lights that training is an integral part of Six Sigma. 35

Critical thinking Adaptable system Change management

Listed Success Factors

Goal based approach Right project leadership Customer focused Project selection Team involvement Bottom line focus Forming the right team Structured approach Data system Team Training Top Management Commitment 0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

Figure 9 Percentages of articles mentioning each of 14 success factors.

3.7 Six Sigma in the context of Management Theory Six Sigma was developed by industry practitioners at Motorola who were not primarily interested in academic contributions. It is not surprising, then, that the role of Six Sigma in the context of management theory is obscure and, as noted in Linderman et. al. (2002), only a small fraction of the Six Sigma literature has been devoted to theory.

In this section, the description of Six Sigma to bring its

contribution into clearer focus is synthesized. Then, modifications appropriate for the

36

evaluation of Six Sigma to the quality performance model of Garvin (1987) are suggested.

3.8 The Academic Contribution of Six Sigma This section begins by reviewing four facts established previously about Six Sigma. First, it can be debated whether or not the principle of establishing monetary justification for applying the Six Sigma method belongs in the definition.

Yet,

monetary justification of projects assuredly is associated with Six Sigma. Second, Six Sigma is relatively specific in nature in relation to the pantheon of quality management practices. This fact is established by the definition in Linderman et. al. (2002) of Six Sigma as a “method”. Also, 24% of articles defined the DMAIC phases and many of the most popular books on Six Sigma associate specific core statistical methods with phases (e.g., Breyfogle, 2003, Harry 1998a, and Pande et al., 2001). Third, the books and training materials associated with Six Sigma are relatively vocational in nature. For example, Hahn, Doganaksoy, and Standard (2001) wrote that the aim is not to train “statistical experts”. Fourth, the most important success factors associated with six sigma were believed to be (1) top management commitment and (2) multidisciplinary team training. We begin by connecting the emphasis on monetary justification with achieving top management commitment. As noted by Hahn and Hoerl (1998), money is the language spoken by management and key to getting projects funded (paraphrasing). 37

Next, we connect greater specificity and relatively vocational materials with training large numbers of practitioners from multiple disciplines.

Intuitively, greater

specificity about what “should” be used and when it “should” be used in the context of a project, combined with the omission of complicated theory, would seem appropriate for motivating adult learners to use the methods. Combining these observations, we conclude that widespread multidisciplinary usage of statistical techniques is the implied goal of Six Sigma and its main contribution to the business world. Academically, we see three related contributions. First, the bottom line and multi-phase nature of Six Sigma has likely increased the scope of research to embrace total projects and not just the portions associated with the application of a single statistical method. This explains the interest on modeling quality savings in Bisgaard and Feriesleben (2000) and why over one third of the articles contained case studies. Second, the relatively greater emphasis on specific core (SC) methods and specific infrastructure (SI) has spawned considerable academic discussion with greater specificity. For example, there is a substantial academic thread focused on what tools “should” be learned and used by Six Sigma trained participants or “black belts” (e.g., see Hoerl 2001a and the related discussion in the Journal of Quality Technology). While the discussion of training materials is not new to the quality literature, the emphasis on relatively specific references to the phases of projects is somewhat new. Third, Six Sigma has caused many people from multiple disciplines to become aware of and apply statistical methods. It is perhaps remarkable that 69% of authors 38

of academically relevant publications had industry affiliations. While, in general, Six Sigma practitioners have learned only standard methods, they constitute a large potential market for research and, perhaps, new methods. Distinguishing features of this market include that participants: (1) are relatively practical and focused on business results, (2) need techniques for predicting the bottom line impacts of projects before they embark upon them, and (3) apply statistical methods without, in general, being experts in statistics. In Section 3.10, we discuss the implications of these findings on the roles that academics can most usefully play in relation to Six Sigma. Next, where the specific infrastructure and core elements of Six Sigma fit into the quality performance model is discussed.

3.9 Defining Six Sigma Linderman et. al. (2003) emphasized the need for a common definition of Six Sigma and proposed: “Six Sigma is an organized and systematic method for strategic process improvement and new product and service development that relies on statistical methods and the scientific method to make dramatic reductions in customer defined defect rates.” Those authors further acknowledged that “the name Six Sigma suggests a goal” of less than 3.4 defects per million opportunities (DPMO) for every process. However,

39

Linderman et. al. (2003) did not include this principle in the definition because, “Six Sigma advocates establishing goals based on customer requirements.” One concern with the Linderman et. al. (2003) definition of Six Sigma as a “method” is that the definition leaves out philosophy and principles. For example, Dean and Bowen (1994) defined quality management to include techniques and a set of principles and practices. We suggest that emphasis on monetary gains in Harry (1998a), Hahn et. al. (1999), Bisgaard and Freiesleben (2000), and other seminal literature warrants the following addition: “The Six Sigma method only fully commences

a

project

after

establishing

adequate

monetary

justification.”

Montgomery (2001) argues that it is this focus on the bottom line that keeps management interested while its predecessors like Total Quality Management (TQM) are “dead”. Virtually all popular books and training materials describe statistical methods much more vocationally than standard statistical texts (Breyfogle, 2003, Harry, 1998a, and Pande et al., 2001). Specifically, these books and training materials omit much of the associated theory and include, in some cases, simplified versions of standard statistical methods. Further, Hahn, Doganaksoy, and Standard (2001) wrote that the related education goals are not to train “statistics experts” but only to give the “knowledge essential to…obtaining business results.” We therefore propose to add the following principle to the definition of Six Sigma: “Practitioners applying Six Sigma can and should benefit from applying statistical methods without the aid of statistical experts.” 40

Another concern with the Linderman et. al. (2003) definition is that it may be unnecessarily vague. It can be argued from a review of the literature this vagueness in the definition of Six Sigma is partly in an attempt to avoid controversy as most authors have historically been practitioners advocating its use. We submit that there is sufficient consensus within the Six Sigma literature to offer the following additional details about the Six Sigma method in its definition: The Six Sigma method for completed projects usually but not always includes as its phases either Define, Measure, Analyze, Improve, and Control (DMAIC) for process improvement or Define, Measure, Analyze, Design, and Verify (DMADV) for new product and service development, Design for Six Sigma (DFSS). Widely read books such as Harry (1998a) and Pande et al. (2001) clearly imply that this refinement is part of the definition of Six Sigma. Again, Linderman et. al. (2003) points out that this definition may only be useful for improvement efforts on complex challenging projects. For simple tasks; the so called “low hanging fruit” this ridged approach may not create substantial benefits. The use of an “organized and systematic method for strategic process improvement … that relies on statistical methods … to make dramatic reductions in customer defined defect rates” would still apply. Harry (1998a), Pande et al. (2001), and others also imply that multiple techniques are often used in applying Six Sigma. Therefore, the definition of Six

41

Sigma as “a method” complicates reference to the techniques used in its application. We propose to refer to these techniques as “sub-methods” to clarify their relative scope to that of Six Sigma. The existence of “sub-methods” helps to connote the idea that Six Sigma is broader than its definition as a method might imply. Also, Six Sigma then becomes more like a “practice” than a “core method” as defined by Sousa and Voss (2002). Sousa and Voss (2002) also defined “infrastructure practices” as those that create “an environment supportive of the use of core practices”. With these definitions in mind, it becomes apparent that both of the principles above are associated with what might be called specific “Six Sigma infrastructure” (SSI) practices. It is also unmistakable from reading the most popular books on six sigma (Breyfogle, 2003, Harry, 1998a, and Pande et al., 2001), and others that there is a strong attempt to associate sub-methods with specific phases of the application of Six Sigma.

For example, the application of gauge R&R would generally not be

considered appropriate in the Define phase. However, to our knowledge no specific associations have currently received sufficient consensus to become part of the definition of Six Sigma. Also, any specific set of associations could justifiably be viewed as undesirable restrictions by some portion of Six Sigma users.

3.10 The Quality Performance Model Much research has focused on the relationship of quality management practices with the various aspects of firm performance (Voss and Sousa, 2002). 42

Garvin (1984) introduced a quality performance model to set up an empirical examination of the separate effects of management practices on internal process quality and product quality performance (QP) and their effects on operational performance (OP) and business performance (BP). In reviewing the literature on Six Sigma, it is helpful to place Six Sigma into this diagram. In our definition of Six Sigma in Section 2.1, we identified principles and methods associated with “Six Sigma infrastructure” (SSI) and “Six Sigma core” (SSC) quality management practices. It was argued that the method of Six Sigma is itself a quality practice while sharing some characteristics with a core method. Figure 10 shows the placement of these specific core practices and infrastructure in the Garvin (1984) model.

Internal Process Quality

Operational Performance

Quality Management Practice Six Sigma Practice Six Sigma Infrastructure

Business Performance

Six Sigma Product Quality Performance

Figure 10 Extended quality performance model of Garvin.

43

3.11 Review of Empirical Evaluations of Six Sigma In this section, the literature relating to the performance evaluation of Six Sigma is briefly reviewed. Only a small fraction of articles in the database pertain to an empirical model or evaluation with scope greater than estimating the savings associated with a single case study. Table 4 below lists five of these articles with reference to Six Sigma core (SSC) and Six Sigma infrastructure (SSI) practices. The other acronyms used are referenced in the extended quality performance model in Figure 10. The fourth article by Gautreau et al. (1997) does not make specific reference to Six Sigma but was included because it addresses issues related to the inclusion of specific methods in the context of quality projects. This seems relevant given Six Sigma’s emphasis on specific core methods and business outcomes. Table 4 contains a description of the roles each article plays for empirical validation in relation to Six Sigma. Goh et al. (2003) examined stock performance associated with announcements of Six Sigma programs and dates of quality awards. They found hints of short-lived abnormal returns but no significant evidence of short or long term returns. Another data driven meta-analysis that we found was Lee (2002), which was based on survey data. The associated surveys indicated positive self assessments of the value of the company’ own Six Sigma efforts. Also, to our knowledge, the impacts of specific core sub-method selection on bottom line impacts has not been studied empirically, with Gautreau, Yacout, and Hall (1997) providing one of few relevant theory based modeling approaches.

44

Study

Bisgaard and Feriesleben (2000)

Quality performance model SSI→BP

Gautreau, Yacout, C→QP→BP and Hall (1997)

Goh et al. (2003)

SSI/SSC→BP (stocks)

Lee (2002)

SSI/SSC→BP

Linderman, SSC→QP/OP Schroeder, Zaheer →BP and Choo (2003)

Study method

Main findings

Economic brake-even analysis model

Fraction nonconforming and unnecessary activities can significantly influence cost and reduce profit Partially Decision based model Observed of process improvement Markov activities, e.g., do nothing Decision or inspect and separate can Process each be optimal depending on assumptions Hypothesis The majority of firms testing show positive returns after announcing Six Sigma programs but no statistical significance was established Survey of 106 Top management firms commitment, project selection, team leader, training and the specific tools used effect business results Goal-theoretic Types of goals effect model quality and operational performance that effect business results

Table 4 Literature pertinent to evaluation of Six Sigma’s effects on firm performance. (BP – Business Performance, C – Core, SSC – Six Sigma Core, SSI – Six Sigma Infrastructure, OP – Operational Performance, QP – Quality Performance)

45

Considering the emphasis on modeling profits to justify each project, it is not surprising at some attempts to provide meta-modeling tools, e.g, see Bisgaard and Feriesleben (2000).

Yet, Bisgaard and Feriesleben (2000) explore prediction of

product value under simple, generic assumptions. As they themselves suggest, more research on related topics will likely be needed for broad applicability.

3.12 Synthesis and Future Research In this chapter, a definition of Six Sigma and characterized the associated body of academic literature is proposed. Also Six Sigma’s contributions to scholarly research and its relationship to quality management theory was clarified. Reflecting on the findings, we next return to the questions: (i) What is Six Sigma? (ii) What are its impacts on operational performance? and (iii) What roles can academics usefully play in relation to Six Sigma? Six Sigma is defined as a method usually involving either Define, Measure, Analyze, Improve, and Control (DMAIC) or Define, Measure, Analyze, Design, and Verify (DMADV) as phases. This definition of Six Sigma as a method builds on the one proposed by Linderman et. al. (2003). The inclusion of DMAIC and DMADV in the definition is supported by the fact that 75% of introductory articles on Six Sigma reference these structures. Two principles are included in this definition. The first emphasizes attention to the bottom line in initiating projects. This was supported by

46

comments of seminal writers relating to how Six Sigma differs from Total Quality Management (TQM), e.g., Harry (2001a) and Montgomery (2001). Also, bottom line focus was mentioned by 24% of relevant articles as a critical success factor. The second principle emphasized the training of non-statisticians with minimal theory. This inclusion is based on remarks by Hahn, Doganaksoy, and Standard (2001) and others about the goals of Six Sigma training. In addition, relatively frequent mention of multidisciplinary training as a critical Six Sigma success factor (roughly 24% of relevant articles) is found. Finally, popular books on Six Sigma such as Breyfogle, (2003), Harry (1998a), and Pande et al. (2001) noticeably de-emphasized theory. To a great extent, the financial impact of Six Sigma on operational performance is well established. This follows because a defining principle of Six Sigma is that such justifications are needed for each Six Sigma project. For example, Dupont reported an expected profit from Six Sigma practices of over $1 billion between 1999 and 2003 (Noble, 2001). Also, Goh et al. (2003) found hints of short lived abnormal stock performance associated with the decisions to start Six Sigma programs. Yet, those authors found no statistical significance in relation to these claims nor evidence of long term effects. Those authors also included specific caveats about the ability to connect Six Sigma programming effects at divisions with overall parent company performance. Considering that failure to find significant effects does not constitute proof, the conclusion is that more work is needed for a thorough evaluation of the bottom line impacts of Six Sigma.

47

In Section 3.8, we identified three main types of contributions of Six Sigma to academia embodied in the literature: (1) increased emphasis on complete case studies compared with single sub-method applications, (2) new, relatively specific core and infrastructure practices, and (3) the development of a large new market of industrial non-experts who might be interested in practically oriented research and new methods. Many authors have proposed areas for further research building on these contributions. Also, Cooper and Noonan (2003), Linderman et. al. (2003), and Snee (1999) suggest that, in general, too much research has been focused on descriptions of practice rather than on theory development that is of use to managers and scholars. We provide only a sampling of selected suggestions, which we divide into three groups.

First, Sousa and Voss (2002) highlighted the need for empirical

justifications of assertions of all types in the quality management literature. In the context of Six Sigma, statements abound that are unsupported by objective evidence. Examples include self reported profits, the effects of success factors, and advocacy for Six Sigma in general. For example, as noted above, the impacts on stock performance investigated by Goh et al. (2003) are not fully resolved. This suggests a need for additional data collection and analysis to answer the important question of long term impacts of decisions to adopt Six Sigma programs. Second, while over 50% of the articles in the database either explicitly or implicitly recommend Six Sigma programs, empirical study of the appropriateness of implementing Six Sigma in specific business contexts has, apparently, not been investigated. Related, largely unanswered questions include: How can data about any 48

specific company’s management, training programs, or environment be useful in decision-making about the adoption of Six Sigma programs? Third, Snee (1999 and 2000a) calls for research to help practitioners identify a robust set of improvement tools to be used in conjunction with the DMAIC process. The focus in these recommendations is not so much on new techniques as on refined techniques associated with specific phases. However, as it was suggested in Section 3.8, new techniques might be relevant to Six Sigma practitioners who are often not experts in statistics. Fourth, additional modeling techniques to predict and evaluate the bottom-line impacts of projects are needed. This follows because of the central importance of profit related justifications in Six Sigma for initiating decisions on projects. Also, Bisgaard and Feriesleben (2000) admit that the assumptions associated with their models have limited scope and may ignore indirect savings. New models that are also easy-to-use could be developed with broader applicability and improved prediction accuracy. It might also be useful to extend profit models to investigate the selection of specific core methods or sub-methods in specific situations. These efforts could be combined with empirical investigations to permit the development of prescriptive models to aid practitioners from different disciplines select the most advantageous techniques. This could build on research related to the most appropriate methods for training black belts, e.g., in Hoerl (2001a), by associating the methods more specifically to phases in a project and to situations. 49

In conclusion, it is proposed that Six Sigma is both a method and two principles. These principles relate both to building and maintaining management support and to fostering usage of methods among practitioners who are not experts in statistics. Trends in the literature include an increasing academic participation and a broader focus than solely on manufacturing. Only partial consensus about the factors making Six Sigma effective is found. Opportunities for new research on Six Sigma including creating more realistic project payback models, clarifying which techniques are most applicable in which situations, and developing new statistical methods with clear advantages for business.

3.13 Literature Review Summary As the nature of research on Six Sigma is difficult to confine to specific disciplines, the relevant material is scattered across various journals. The search resulted in the identification of 201 articles published between 1990 and 2003. Although this review cannot claim to be exhaustive, it does provide reasonable insights into the state-of-the-art. It is felt that the results presented in this chapter have several important implications. Although the industry has an increased interest in Six Sigma implementation and many companies have gained the profits and advantages from this disciplined approach, the literature is limited and the research of the impacts of Six Sigma implantation and factors contributed to Six Sigma success remain unclear. Many

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articles on the impact analysis of operations performance do not mention the detailed improvements in the operating areas such as scrap rate, rework rate and so on, but focus on the overall bottom line impact [Breyfogle (2001), Noble (2001) and Lucas (2002)]. Therefore, it is necessary to do a deeper and more detailed study in this area. In addition, only a few articles were found that dealt with factors in the area of success factor analysis to Six Sigma implantation. Even the existent studies are not well integrated and the research is mostly anecdotal. Current concepts in the field of Six Sigma are largely based upon case studies, anecdotal evidence and the prescriptions of leading “gurus.” Consequently there is little consensus on which factors are critical to the success of the approach. Most of the articles reported that top management leadership is the main factor to Six Sigma success [Blakeslee (1999) and Scalise (2001)]. However, many other factors affecting Six Sigma’s success are important and need to be better documented. Even so, there is substantial evidence that Six Sigma and other quality management systems have a positive effect on the value of a company. Goh (2003), Hendricks (2000) and Adams (1997) all found improvement of companies financial performance with the implementation of quality initiatives. Several of the leading authors have produced broad frameworks for implementing and sustaining competitive advantages through quality management. Although some authors have called for theoretic research (see Cooper and Noonan 2003, Linderman et. al. 2003 and Snee 1999), too much research is focused on descriptions of practice rather than on theory development that is of use to 51

managers and scholars. The attempt to build a theory of how and why Six Sigma works is aimed at building a prescriptive model. From this, managers would be able to identify which activities from which programs are more or less likely to be useful in their situations, as well as which of their goals would be most affected. With the future success of corporations riding on the outcome, there has been little theory to explain the differences between successful and unsuccessful efforts.

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CHAPTER 4 CASE STUDY BASED TRAINING

This chapter discusses one of the major themes of Six Sigma: training of practitioners. From the literature, Six Sigma differs from most quality management systems by its emphases on training what people need to know to implement improvement programs effectively. A subset of this topic is the training of nonstatisticians in the use of statistical tools. A major concept then becomes how to effectively train participants in the necessary tools and techniques of Six Sigma. In this chapter, we describe one case study and associated exercises used in senior and introductory graduate level engineering courses on SPC and DOE at The Ohio State University. The role of the case study exercises in the context of material covered in the lectures is described. Section 4.2 provides an overview of the case study structure. In Sections 4.3 a case study and associated in-class exercises is presented. Finally, a description of the student feedback to the case based teaching approach is reviewed.

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4.1 Introduction One constant tread in the literature dealing with Six Sigma is the training and the limited chose that non-statisticians have to make. For thousands of participants at the lowest “green belt” level of accreditation, one of the main benefits of “Six Sigma” training is that it simplifies (through restriction) the sequence and choice of available techniques to apply to a particular case. Therefore, the value of the Six Sigma movement derives partly from standardization of problem solving methods and partly in how it guides people to suggest which techniques to apply in which order to an improvement project. Drawing a box as a way of teaching judgment is based on one of the most successful methods that is used to teach skills: breaking a task into small bits and presenting it to the student with practical, logical steps that he or she can understand and apply. By simplifying the decision-making model and helping our students to define and operate within a well-defined “box” of their limitations, we have a practical way of teaching good judgment. The first step is to simplify the decision-making model. The purpose of decision making is to reach the right decision at the right time. We can make the whole decision-making process practical by applying it to various actual situations. Now, rather than trying to teach an ambiguous “good judgment” concept, we are giving our students a practical route to good decisions.

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Drawing a box for our students involves expanding on the familiar concept of personal knowledge and capabilities. The first step in the model is the ability of a student to operate within his or her own capability. The second step involves looking at a given situation, evaluating current skills, and setting boundaries for that specific situation. In essence, you’re drawing a box of operating parameters for your student in that situation. The third and final step is to insist that he or she always operate within that box. By drawing the box before the situation a good decision was made before a crisis forced the student’s hand. Everyone’s box will be different, since we all have different levels of experience and ability. As proficiency is gained, the size of the box will change. Teaching decision making is a daunting- some would say impossible task, but one that is imperative. By giving students the tools and ability to draw their own box, we are providing the foundation for good decision making. Six Sigma has caused many people from multiple disciplines to become aware of and apply statistical methods. It is perhaps remarkable that 69% of authors of academically relevant publications had industry affiliations. While, in general, Six Sigma practitioners have learned only standard methods, they constitute a large potential market for research and, perhaps, new methods. Distinguishing features of this market include that participants: (1) are relatively practical and focused on business results, (2) need techniques for predicting the bottom line impacts of projects

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before they embark upon them, and (3) apply statistical methods without, in general, being experts in statistics. There is increasing recognition in the statistics, engineering, and education literatures that exercises based on case studies can play an important role in reinforcing understanding as well as motivating students to learn and apply statistical process control (SPC) and design of experiments (DOE) techniques, e.g., see Alloway (1993), Barton and Nowack (1998), Cobb (1992), Nolan and Speed (1999), Petruccelli, Nandram, and Chen (1995). There is also abundant evidence, e.g., Czitrom (1999), that most practicing engineers continue to display a lack of motivation to apply the technology they have learned and in general see their class experiences as largely irrelevant to their professional life. Engineering students generally gain deeper understanding of the theory once they are exposed to the realistic engineering contexts in which the related methods are applied. The growing literature on the benefits of case-based learning approaches in engineering, Howell (1996), McKeachie (1993,) and Wankat (1993) gives us insight into restructuring traditional class outlines into a more productive approach. For these reasons it is important to devote a substantial fraction of class time (roughly 20%) to in-class case study based exercises that emphasize the other forms of knowledge and reinforce the lecture materials. These exercises also seem to aid in establishing linkages with the students’ lives outside of the university. A major challenge in using case studies in classes has been that the examples in standard textbooks generally seem highly contrived to the students and divorced 56

from real life contexts. As described by Bisgaard (1998) and in our own experience, it is important that the case study examples used in the course are impressive to the students in their relevance to their own possible careers. Therefore, we have found that it is helpful to use exercises based closely on case studies from local companies in which the application of the techniques taught in the course played a key role in achieving a measurable success. Perhaps the most important purpose of these exercises is that the students can visualize themselves in the role of facilitating real world successes. The case study based exercises were introduced into the two combined senior and first year graduate level courses at The Ohio State University. The classes meet twice a week for 10 weeks, each period is for one hour and twenty minutes. Many of the students have had two quarters in statistics. Topics addressed in the SPC courses can be divided into four categories: (1) a survey of quality techniques and a review of probability and inference relating to continuous random variables, (2) control charts for continuous random variables, (3) review of probability relating to discrete random variables and attribute control charts, and (4) acceptance sampling and assorted topics including ISO9000 and “six sigma” methodology. The topics in the DOE class are: (1) t-testing and ANOVA, (2) screening experiments, (3) response surface experiments, and (4) robust optimization. In both classes, each category corresponds to approximately five class periods and one homework assignment. The case study exercises are timed on the days after each of four assignment due dates, so that the students are responsible for knowing the material involved. 57

The case studies are true but for proprietary concerns some are modified in order to maintain the confidentiality of the companies involved. Each case study is selected from area industries to provide relevant experience and important evidence of the practicality of the statistical techniques described in the lecture and textbook.

4.2 Case Study Exercises Each case study has five components: 1) an introduction, 2) a problem statement, 3) the background information relating to prior attempts to solve the problem, 4) questions for the students, and 5) the team implementation of course techniques and results from the actual study. The exercise begins by handing out written materials summarizing components 1-4. In the introduction, we use 5 minutes of lecture time to provide a brief description of the industry in question and some of the standards, issues and terminology used so the students have some familiarity with the subject. The introduction also serves the important role of establishing that the students might realistically find themselves in similar situations in their future careers. In the problem statement, we use 5 minutes of lecture time to describe the goal, e.g., 5% defective products from a particular process, and the associated business objective, e.g., avoid a $2.5 million capital expenditure to meet increased product demand. In our oral description of the problems, we encourage creative analyses and emphasize that there is no one solution. An additional 10 minutes are used to describe supplemental background information which includes the relevant data that was available to the 58

company at the time of the team intervention involving class methods and sufficient information such that the students can be expected to provide their own analyses and recommendations. Our goal is to present the problem such that the students should be able to easily identify themselves as playing the role of consultant and advocate of SPC and DOE techniques in a real-world context. Next, we supply abbreviated lists of potential investigations and leading questions. These questions involve both critiquing the results of earlier investigations and developing recommendations for future study. The students are divided into groups of 4-6 and given a 30-minute exercise period to answer the questions. Students can ask technical questions and when relevant we sketch results on the blackboard including, e.g., formulas for sample size estimation and additional details requested by the students. From group input, we use 15 minutes class time to construct composite answers to questions in class and write these answers on the blackboard. During this process, we also provide limited feedback to increase the sophistication of the proposed approaches while preserving the students intent. After the answers from the class are on the board, we use the remaining class time to describe the actual company’s actions and results.

4.3 Sample Case Study “Improving the Yields of Printed Circuit Boards” This case study exercise is used in both the SPC and the DOE classes and illustrates how with a small number of quality technology tools highly valuable

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information can be learned. This case study involves the use of Pareto diagrams, p charting, hypothesis testing, and fractional factorial designs. The study also illustrates potential dangers from one-factor-at-a-time experimental approaches.

4.4 The Problem Statement In early 1998, an electronics manufacturing company introduced to the field a new advanced product that quickly captured 83% of the market in North America. During initial production period, yields (the % of product requiring no touchup or repair) had stabilized in the 70% range. In early 1999 the product was selected as a major equipment expansion in Asia. In order to meet the increased production demand, the company needed to purchase additional test and repair equipment at the cost of $2.5 million or the first test yield had to increase to above 90%. The latter was the preferred situation due to the substantial savings in capital and production labor cost thus, the problem was how to increase the yield in a cost-effective manner.

4.5 Background Information A team of highly regarded engineers was assembled from various design and manufacturing areas throughout the company. Their task was to recommend ways to improve the production yield based on their prior knowledge and experience. Table 5 gives the weekly first test yield results for the 16 weeks prior to the team’s activities with production volume of 1500 units per week.

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Week 1 2 3 4

Yield 71% 58% 69% 77%

Week 5 6 7 8

Yield 87% 68% 71% 59%

Week 9 10 11 12

Yield 66% 70% 76% 82%

Week 13 14 15 16

Yield 63% 68% 76% 67%

Table 5 The yields achieved for 16 weeks prior to the initial teams activities.

Based on their technical knowledge and experience, the assembled improvement team reviewed the design and production process. They created a list of 15 potential process and design changes for improvement based on their engineering judgment and anecdotal evidence. With this list in hand, they proceeded to run various single factor experiments to prove the validity of their plan. Due to perceived time and cost constraints, only one run of each factor was completed using a sample of 30 units. Results were compared with the yield from the previous 13 weeks of production. Each unit could only succeed or fail to meet specifications. Factors that showed a yield decrease below the 13 week average were discarded along with the experimental results. Table 6 shows the results of the experiments with yield improvements predicted by the team. Based on their analysis of the circuit, the above experimental results and past experience the improvement team predicted that a yield improvement of 18% would result from their proposed changes. All of their recommendations were implemented at the end of week 17. Table 7 gives the weekly first test yields results for the six weeks of production after the revision.

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FACTOR Replace vendor of oscillator Add capacitor to transistor Add RF absorption material New power feed layout Increase size of ground plane Lower residue flux Change bonding heat sink Solder reflow in air vs. N2 Temperature of solder tips

YIELD IMPROVEMENT 8.5% 8.5% 5.5% 5.5% 2.5% 2.5% 2.5% 2.5% 2.5%

Table 6 The initial team's predicted yield improvements by adjusting each factor.

Week 17 18 19 20

Yield 62% 49% 41% 42%

Week 21 22 23

Yield 40% 41% 45%

Table 7 The performance after the implementation of the initial team's recommendations.

Reviewing the data we see that the yield actually dropped 29%. On week 22 it was apparent that the proposed process changes were not achieving the desired outcome. Two additional engineers, with exposure to quality improvement tools through continued education at local universities and company-sponsored seminars, were added to this project.

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4.6 In-class Exercise for PCB Study In our SPC classes, we then give the students the following questions based on the premise that the company is hiring them as a quality and manufacturing consultant. (1) Critique the methods used by the engineers for predicting improvements, e.g., is there any evidence that they increased the yield? Roughly how many samples would they need for the standard deviation of the estimated yield to approximately equal 5%, i.e., they could begin to resolve differences of approximately 5%? (2) What additional procedures would you recommend to measure the process capability? Include in your answer what specific types of data or information would you request or collect. (3) What addition procedures would you recommend to aid in improving the process? In DOE classes, we ask the students: (1) What size of experiment should they start with? (2) How should they determine which runs to perform? A representative from each team presents their group’s answers in class, which are written on the board. The entire class then comments on the reviews and coherent consulting answers to the questions are created. In the real study, Pareto Charts were used to direct the investigation, p-charts were used to measure the common cause variation, and formal approaches were used to improve the process. Therefore, a wide variety of class techniques are relevant, presenting life-like ambiguities for the students. If we do not finish and/or if we feel it is appropriate we include unanswered questions as part of the homework assignments. After the class discussion we relate in detail what actually occurred in real life.

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4.7 The Team Actions and Results The second team’s first step was to construct a yield attribute control chart (a yield chart or 1- defective chart “1-p”) with the knowledge of the process change date (Figure 1). The engineers were able to tell that most of the fluctuations in yield observed before the team implemented their changes were, as Deming calls it, common cause variation or random noise. The engineers’ first decision was to revert back to the original, documented process in place during week 16 since the evidence that had supported these changes was probably due to random noise within the process. Table 8 gives the weekly test yields for the five weeks after this occurrence. This had the effect of restoring the process to its previous in control state with yields around 75%. The increase in yield shown on the control chart (Figure 11) during this time frame was discounted as random noise or the “Hawthorn” effect since no known improvement was implemented. By Hawthorn effect, we mean an effect caused by our attention to and study of the process. Next the procedure of Pareto charting was applied to help visualize the problem, Table 9.

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100% 90%

UCL

Y ie ld

80% 70% CL 60% 50% LCL 40% 30% 0

10

20

30

40

Subgroup

Figure 11 Control chart for the entire study period.

Week Yield

24 62%

25 78%

26 77%

27 75%

28 77%

Table 8 The yields for the 5 weeks subsequent to the initial intervention.

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ACP –30 kHz ACP +30 kHz ACP –60 kHz ACP +60 kHz ACP –90 kHz VDET 1950 mHz VDET 1990 mHz ACP +90 kHz Power supply Gain Output return Bias voltage Max current Other

6.7% 5.0% 2.9% 2.8% 2.7% 2.4% 2.0% 1.4% 1.2% 1.0% .8% .5% .2% .4%

Table 9 The data for a Pareto chart of the data from week 1 to week 16.

It can clearly be seen from a Pareto graphs that 21.5% of the 30% of total defects was attributed to one parameter called “ACP”. The engineers concentrated their efforts on this dominant defect code. The team of experts was reassembled with the addition of representation from the production workers to identify what variables might cause this defect. Four factors identified were: (1) transistor performance distribution (high end of spec or low end of spec), (2) transistor mounting (socket or solder), (3) input circuit tuning (centered or low end of spec), and (4) transistor heat sink type (current or new configuration). This last factor was added at the request of a representative from production. This factor was not considered important by most of the engineering team. The two lead engineers decided to include this factor as the 66

marginal cost of adding it was small. An eight run fractional factorial experiment was conducted as shown in Table 10. Each run corresponded to 350 units.

STD 7 4 6 2 3 5 8 1

Run 5 6 7 9 10 11 13 14

Yield 92.7 71.2 95.4 69.0 72.3 91.3 91.5 79.8

Table 10 The data from the fractional factorial design in four factors.

Using ANOVA and main effects plots, the heat sink type emerged as the main effect. The two engineers went forward based on the DOE results and recommended that the process change to the new heat sink. This was implemented during week 29. Table 11 gives the weekly yield results for the period of time after the recommended change was implemented. Using the yield charting procedure, the engineers were able to confirm that the newly designed process produced a stable first pass yield in excess of 90% thus avoiding the equipment purchase and saving the company $2.5 million. The main points that we emphasize in our wrap-up of the exercise are the following. First, the technology of fractional factorial experiments permitted the fourth factor to be added without additional runs being needed. The importance of this factor was controversial because it had been suggested the operators. If fractional

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factorial had not been used, then the additional costs would likely have precluded its inclusion and the important subsequent discovery. Second, the case also illustrates the important benefit of a “balance experimental design”, i.e., half of a total number of experiments are at each level of each factor providing the maximum power to identify small effects. Week

Yield

Week

Yield

Week

Yield

29

87%

34

94%

39

91%

30

96%

35

90%

40

93%

31

94%

36

90%

41

89%

32

96%

37

86%

42

96%

33

91%

38

92%

Table 11 The confirmation runs establishing the process shift/improvement.

4.8 Student Feedback Students seem to identify with the case study "stories" much better than the traditional lectures. Before implementation of the case study exercises, end-of quarter evaluations by students for the two classes had been below the average end-of-quarter class evaluations in the department. After the implementation of the case study approach and with minimal other changes, the evaluations climbed well above average. We attribute this dramatic turn-around mainly to the introduction of the case

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based method. Further, we conjecture that presenting applications of course methods in which literally millions of dollars are saved effectively motivates students concerned about job security and advancement in the highly competitive industrial marketplace. It is our belief that these results should generalize to other statistics, operations research, and engineering design theory related courses. This follows because all of these courses are fundamentally concerned with the students' usually voluntary application of formal techniques to solve engineering problems. Since this requires discipline and motivation, we feel that both practicing the application of techniques in relatively real-world contexts and disseminating success stories are critical to maximizing benefits from applying the techniques.

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CHAPTER 5 THE CHALLENGE OF SIX SIGMA PROJECT MESO-ANALYSIS

5.1 Introduction One outcome of the wide spread acceptance of Six Sigma and with its systematic program is the fact that many databases describing the performance of improvement projects and the methods used have been generated. Even with its apparent highly visible success, one area of investigation is the use of this new source of data, the industry Six Sigma database, for additional insight into the management of corporate business improvements. How might this database be used to help operational management in the area of quality management practices? Three levels of decision-making can be defined: Micro – dealing with individual statistical methods. Meso – supervisor level decision-making about method selection and timing. Macro – related to overall quality programs and stock performance.

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Martin (1982) pointed out that the availability of certain type of data might disproportionately influence the problems that are investigated as well as the conclusions drawn. Reviewing the literature with historical data sources reveals a large portion concerning macro level decision-making, the question to implement a Six Sigma methodology at a company, Bisgaard and Freiesleben (2000), Chan and Spedding (2001), Gautreau, Yacout and Hall (1997), Yacout and Gautreau (2000), and Yu and Popplewell (1994). This is mostly based on single case studies and anecdotal information. A second large grouping of articles deals at a micro level, concerning component tools and techniques for green belts and black belts. These are the terms used for the individuals working on project implementation. Little work is published that relates to the meso level of managing and decision-making of Six Sigma, the midmanagement operational decisions regarding Six Sigma and improvements to the system, Linderman et. al. (2002). The uses of these databases are likely being ignored at most companies for at least two reasons. First, there is little assistance form academics in how to make sense of them. Second, the people with the most statistical expertise are involved in the individual projects and not in cross project evaluation. Most managers are not statisticians and need help in making sense of the data now available to them. According to Juran and Gryna (1980) the activities in companies that assure quality can be grouped in three processes: quality planning, quality control and quality improvement. Quality improvement consists of the systematic and proactive pursuit of improvement opportunities in production processes to increase the quality levels. 71

Typically, quality improvement activities are conducted in projects. This proactive and project wise nature distinguishes improvement form quality control, which is an online process that is reactive in nature. In Harry (1994) all things are a process. A central belief of Six Sigma is that the product is a function of the design and the manufacturing process which must produce it. This is symbolized as Y=f(X), where Y is characterized as dependent, output, effect, symptom and its role as “to be monitored”. The X is described as independent, input, cause, problem, and its role as “to be controlled”. The view is that the emphasis should shift from monitoring Y to controlling the relevant Xs. With Juran and Harry in mind, Six Sigma can be viewed as a process and subject to the same controls and improvement objectives of other processes. Against this background, the purpose of this study was to look at this growing database in a way that could help management better-run improvement projects.

5.2 Potential Use of Database The use of this growing database of project related quality improvement activities could be useful in the empirical study of some important research questions. Potential research topics include: the health of a given company’s quality system, modeling Six Sigma, or the optimality of selection and ordering component methods associated with Six Sigma. Researchers focus on what they have data and tools for. Now, new data sources and the associated ability to ask and answer new types of questions are more readily available. For example, “Is my quality system 72

out-of-control?” “Which method would lead to greatest expected profits in my case?” “Under what circumstances does it make business sense to terminate a project?” If these kinds of questions can be systematically explored in the Six Sigma discourse then important lessons can be learned regarding investment decisions. Moreover, there will be an increase in critical writings and inquiry on this subject, which will add depth and meaning to Six Sigma in organizations. To help in this study empirical data on multiple quality/cost improvement projects at a medium size U.S. manufacturing company was collected over a 30-month period starting in January 2002. A total of 39 projects were included in the study.

5.3 Database Example The company used for study is a U.S. based mid-western manufacturing company, which manufactures components for the aerospace, industrial and defense industries. It has approximately 1000 employees, annual sales of $170 million, with six factories located in five states. The data is all derived from one of its six manufacturing sites. This one site has 250 employees with sales of $40 million. Quality improvement and cost reduction are important competitive strategies for this company. The ability to predict project savings and how best to manage project activities would be advantages to future competitive posture and the long-term strength of the company.

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5.4 General Procedure Over the course of this study data was collected on 20 variables. Two additional dependent variables are tabulated in the data, which are functions of some of the other variables. The two variables are Profit, which is Actual Savings minus cost and Formal Methods (FM) which is any combination of Charter, Process Mapping, Cause & Effect, Gage R&R, DOE or SPC. Table 12 lists and describes the variables tracked during this study. Data was collected on each project by direct observation and interviews with team members to determine the use of a variable such as DOE or Team Forming. No attempt was made to measure the degree of use or the successfulness of the use of any variable. We only were interested if the variable activity took place during the project. A count was maintained if an activity was used multiple times such as multiple DOE runs i.e. a screening DOE and an optimization DOE would be recorded as 2 under the variable heading. Expected Savings and Actual Savings are based on an 18 month period after implementation. The products and processes change fairly rapidly in this industry and it is standard company policy to only look at 18 month to evaluate projects. These calculations were based on the current monthly production forecast. Costs were tracked with existing company accounting procedures. All projects where assigned a work order for the charging of direct and non-direct time spent on a specific improvement activity. Direct and non-direct labor where charged at the

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average loaded rate. All direct materials and out side fees (example, laboratory analysis) where charged to the same work order to capture total cost. The raw data derived form this study in tabulated in Appendix B.

5.5 Data Collection The empirical analysis for this exploratory study is based on the data collected at one manufacturing site over a 30 month time frame. Not all programs followed DMAIC nor was it the intent. Our intent was to observe unbiased projects in a real world setting to start to develop a model of improvement activities. Observation and interviews determined the use or non use of a tool. No measure of the degree of use was attempted. We only indicated whether or not a tool was used and how often. The number of times a tool was used during a project was recorded and listed in the data summary, Appendix B. These projects did not include all activity but where judged to be project unbiased by the author. As a manager at the facility where the study was conducted one author could influence the activities. The studied projects where selected because they were judged to be unbiased by the author.

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Field Expected savings

Expected time

M/I management or self initiated Assigned or participative # people EC Economic analysis CH Charter PM Process Mapping

CE Cause & Effect GR Gage R&R DOE SPC

Description An estimate of the projects saving over an 18 month period based on the current business forecast. An estimate made at the start of a project as to the time needed to complete the project s-short less than 3 months m-medium between 3 and 9 months l- long over 9 months Whether the project was initiated by management or initiated by team members Whether the project was assigned to a team by management or the members actively chose to participate Number of team members A formal economic analysis was preformed with the aid of accounting to identify cost and cost brake allocations Formally define project scope, define goals and obtain management support Identify the major process steps, process inputs, outputs, end and intermediate customers and requirements; compare the process you think exists to the process that is actually in place Fishbone diagram to identify, explore and display possible causes related to a problem Gage repeatability and reproducibility study A multifactor Screening or optimization design of experiment Any statistical process control charting and analysis

Table 12 Continued on next page.

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Table 12 Definition of variables (Continued from last page) DC Documentation EA Engineering analysis OF one factor experiment Time Profit Actual Savings Cost Formal Methods

Formally documenting the new process and or setting and/or implementing a defined control plan Deriving conclusions based solely on calculations or expert opinion A one factor at a time experiment Actual time the project took to completion A current estimate of the net profit over the next 18 months after implementation based on the actual project cost and actual savings A current estimate of the savings over the next 18 months after implementation based on the new operating process and current business forecast The actual cost as tracked by the accounting system based on hours charged to the project, material and tooling, equipment A composite factor, if multiple formal methods were used in a project this was positive Table 12 Definition of variables

As stated in section 3.11 one of the main principles of Six Sigma Harry (2001a) and Montgomery (2001) is the emphasis placed on the attention to the bottom line results in initiating projects. In the literature reviewed, bottom line focus was mentioned by 24% of relevant articles as a critical success factor. Profit, which is a combination of cost and actual savings, than becomes the dependent variable. The remaining eighteen variables are the independent variables. Of these variables, Process Mapping, Cause & Effect, Gage R&R, DOE, and SPC are related to Formal Methods.

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These 39 improvement projects generated a total of $4,385,099 in net savings (profit). The projected savings form these projects ranged rorm $1600 to $2,200,000 with actual net savings of -$220,000 to $3,874,500 over the first 18 moths after implentation. Cost to implement the projects ranged from $1,000 to $325,500. Fifteen of the thirty nine projects resulted in negative net savings as reported. Table 13 presents descriptive statistics for project duration, number of team members and profits.

Factor Time Profit Team members

Median 8 months $3,025 1

Low 1 month -$220,000 1

High 30 months $3,874,500 9

Average 10 months $112,438 3

Table 13 Summary statistics for the 39 projects, duration team memberrs and profits

We looked at directed assignments vs. self-initiated, as one factor identified in the literature was team participation. Of the projects, 72% were initiated by management directive. Management assigned the team members in 48.7% of the tasks. The other teams were self-initiated by the team members. Additional characteristics of the study samples are given in Table 14.

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Item

Economic Analysis Formal Charter Team Forming Exercise Process Mapping Cause & Effect Gage R&R Design of Experiment Statistical Process Control Formal Documentation Engineering Analysis One Factor Experiment

Number in Study 15 28 12 21 11 7 11 7 28 29 10

Percent of the Study Sample 38.5% 71.8% 30.8% 53.8% 28.2% 17.9% 28.2% 17.9% 71.8% 74.4% 25.6%

Table 14 Characteristics of the Study Variables

Three potential uses of this database were investigated using analyses by regression, Markov Decision Process, and SPC. Each analyses tool was used to look at a different problem that this database might be useful in researching.

5.6 Statistical Process Control A control chart is one of the primary techniques of Statistical Process Control (SPC). The control chart is a very useful process monitoring technique; when unusual sources of variability are present, sample averages will plot outside the control limits. Control charts can be used to monitor the health of a process improvement 79

methodology (Six Sigma) or changes to a process such as did training have a positive effect on process improvement activities. The first step in deriving a process control chart is to check the assumption of normality. Figure 12 in a normal probability plot of the project data. It can be seen

z-score

from an examination that the data is comprised of two populations and two outliers.

-2000000

2.5 2 1.5 1 0.5 0 -0.5 0 -1 -1.5 -2 -2.5

2000000

4000000

Profit ($)

Figure 12 Normal Probability Chart for Six Sigma Projects.

With the data base in the example the logical subgroup size is n=1. With only one measurement per subgroup (a project) a subgroup range can not be calculated. The data is comprised of a small number of non-normal observations. The exponentially 80

weighted moving-average (EWMA) control chart is typically used with individual observations (Montgomery 1997). The exponentially weighted moving average is defined as: Z i = λx i + (1 − λ ) Z i −1

(5.1)

where 0 < λ ≤ 1 is a constant and the starting value is the process target so that Z0 = μ0

(5.2)

The average of preliminary data can also be used such that Z0 = x

(5.3)

The EWMA control chart is constructed by plotting Zi versus the sample number i with the following control limits and center line: UCL = μ 0 + Lσ

[1 − (1 − λ ) ] (2 − λ ) λ

2i

CL = μ 0 LCL = μ 0 − Lσ

(5.4) (5.5)

[1 − (1 − λ ) ] (2 − λ ) λ

2i

(5.6)

According to Montgomery (1997) values of λ in the interval 0.05 ≤ λ ≤ 0.25 work well, with λ=0.05, λ=0.10, and λ=0.25 being popular. L values between 2.6 and 3.0 also work reasonably well. Hunter (1989) has suggested values of λ=0.40 and L=3.054 to match as closely as possible the performance of a standard Shewhart control chart with Western Electric rules. One of the important variables that might be of interest in monitoring the health of a quality improvement methodology like Six Sigma is savings per project.

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From the database under investigation and the above equations a control chart in can be generated. We start with plotting the first 25 points to obtain the control limits as shown in Figure 13. One out of limit point was discarded after the derivation of this chart. This one project was a DFSS (Design for Six Sigma) vs. a DMAIC project and as such was unique. This chart was constructed with based on Hunter (1989) with λ=0.40 and L=3.054.

2000000 1500000 Profit ($)

1000000 UCL zi LCL

500000 0 -500000

1

3

5

7

9 11 13 15 17 19 21 23 25

-1000000 -1500000 Project

Figure 13 EWMA Control Chart for first 25 Six Sigma Projects.

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EWMA Chart for Profit

150000

100000

Profit $

50000

0 1

3

5

7

9

11

13

15

17

19

21

23

25

27

29

31

33

35

37

-50000

-100000 Six Sigma Project

Figure 14 EWMA Control Chart for Six Sigma Projects.

The projects are listed in rough chronological order therefore Figure 14 can be considered a time series graph. One major outlier was removed from the plot. Traditionally since their introduction by Walter Shewart, control charts have been used to characterize the behavior of a time series. If a time series displays unpredictable behavior, then the underlying process which gives rise to the time series is said to be out-of-control. Likewise a process will be said to be in control when,

83

through the use of past experience, we can predict, at least within limits, how the process will behave in the future, Shewhart (1931). This distinction between predictability and unpredictability is important because prediction is the essence of doing business. Predictability is a great asset for any process because it makes the manager’s job that much easier. The fact that a time series remains within the computed limits, and that there is no obvious trend, not any long sequences of points above or below the central line, suggests that a process may display a reasonable degree of statistical control. In this case, the process has an average profit per team of $112,438 and values have varied form a low of -$220,000 to a high of $3,874,500 Of special interest are the last seven projects that took place after Six Sigma training provided by Honeywell and Raytheon. This would tend to indicate “proof” that training helps in project improvement. This is limited data but future study with this same technique could be used to verify if training contributed to a fundamental change in the process.

5.7 Regression The popularity of ordinary linear regression models is attributable to its low computational costs, its intuitive plausibility in a wide variety of circumstances, and its support by a broad and sophisticated body of statistical inference. Given the data, the tool of regression can be employed on at least three separate conceptual levels. 84

First, it can be applied mechanically, or descriptively, merely as a means of curve fitting. Second, it provides a vehicle for hypothesis testing. Third, and most generally, it provides an environment in which statistical theory; discipline-specific theory and data may be brought together to increase our understanding of complex physical and social phenomena. Simply put regression can be used to derive a model that will help predict average performance for a new combination of inputs and/or to understand which input changes cause changes in average outputs. The familiar multiple regression equation is represented by equation 5.7 below: yest(βest,x) = f1(x)΄βest

(5.7)

Where f1(x) is a vector of functions only of the system inputs, x. In most regression analysis the coefficients of the independent variables are the major point of interest. The slope of the regression line measures the relationship of each independent variable to the dependent variable of interest; the regression coefficients are these slopes. The most interesting parameter in a linear model is usually the slope. In this equation the slope of Y on X1 has a constant value across the range of X2. For complex systems researcher may notice that regressions based on different subsets of the data produce very different results, raising questions of model stability. This may result in confusing or conflicting recommendations. This may be caused by interaction between the independent variables and the response. Terms involving products e.g. f1,7(x) = x1x7, are called interaction terms, a relationship represented by equation 5.8 below: yest = β1X1 + β2X2 +β3X1X2 + β0 85

(5.8)

The effect of this first order interaction is to shift the regression line based on the level of the independent variables producing a family of results. The X1X2 interaction signifies that the regression of Y on X1 depends upon the specific value of X2 at which the slope of Y on X1 is measured. There is a different line for the regression of Y on X1 at each and every value of X2. The regressions of Y on X1 at specific values of X2 form a family of regression lines. An analogy to chemistry, this has the effect of a buffer. That is while X1 is positively related to Y the strength of this relationship depends on the level of X2. Much of the literature on Six Sigma converges on the importance of management commitment, employee involvement, teamwork, training and customer expectation among others in Six Sigma implementation. A number of research papers have been published suggesting key Six Sigma elements and ways to improve the management of the total quality of the product, process, corporate and customer supplier chain. However, most of the available literature considers different factors as an independent entity affecting the Six Sigma environment. But the extent to which one factor is present may affect the other factor. The estimate of the net effect of these interacting factors is responsible for the success of the Six Sigma philosophy. Quantification of Six Sigma factors and their interdependencies will lead to estimating the net effect of the Six Sigma environment. The authors are not aware of any publication in this direction.

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5.8 Regression Data Analysis The data was analyzed using a commercial software regression modeling program. The software is a polynomial regression program based on Microsoft® EXCEL spreadsheets and has the capability of simple regression models, multiple regression models or custom modeling. The software regression model features permit the user to select models automatically or manually. They facilitate fitting high order terms (i.e. second or third order terms). The motivation for this study was to evaluate the use of an emerging database due to the expanded use of Six Sigma methodologies in management decision-making. We utilized regression techniques which are readily available to management in the business environment for the analyses. The data was analyzed using a commercial polynomial software regression modeling program. One of the models that was derived from the data was an interaction model between the use of Formal Methods and Engineering Analysis. This model illustrates the possible use of these techniques and appears helpful in validating the importance of estimating expected savings and then deciding how formal to be. The model can be represented by equation 5.9:

Profit = 79931 + 0.848*Exp Savings - 76708.7*FT + 1258.21*EA + 2.2*Exp Savings*FT - 4.04*Exp Savings*EA

Where: Exp Savings is the amount of expected savings in dollars,

87

(5.9)

FT is the number of Formal Methods used, EA is the use of engineering analysis

And Profit is the response.

Figure 15 is the main effects plot produced by the software for this model. It can be seen that as the expected savings increases the model would suggest a greater reliance on the use of formal methods. Likewise, based on this limited database, as the expect savings decrease; a greater reliance on engineering analysis should be used. The results of the regression model are presented in Table 15, with the summary statistics given in Table 16. A 3-D plot of the results is included in Figure 16. Last, normal scores vs. residuals are found in Figure 17.

Pseudo Main Effects Plot - Model Predictions 12000000 10000000 6000000 4000000 2000000

-8000000 -10000000

Factors

Figure 15 Main Effects Plot of Regression Model.

88

Time:1 Time:15.5 Time:30

EA:0 EA:2 EA:4 OF:0 OF:0.5 OF:1

DC:0 DC:1 DC:2 FT:0 FT:3.5 FT:7

SPC:0 SPC:1 SPC:2

DOE:0 DOE:2 DOE:4

GR:0 GR:1 GR:2

CE:0 CE:1.5 CE:3

PM:0 PM:1 PM:2

CH:0 CH:0.5 CH:1 TF:0 TF:0.5 TF:1

EC:0 EC:0.5 EC:1

#people:1 #people:5 #people:9

-6000000

k3:A k3:P

-4000000

k1:L k1:M k1:S k2:M k2:I

0 -2000000

Exp Savings:1600 Exp Savings:1.1008e+ Savings:2.2e+006

Predicted Response

8000000

Summary statistics from the model are presented in Table 15. The model produced an R2 value (observed vs. predicted) of 0.934 and an SSE (Sum of Squared Errors) of 0.883. Summary Statistics Criterion R^2 R^2 adj R^2 predict R^1 PRESS s (est. err.) SSE(LSE)/SSE(LAD)

Value 0.934 0.924 0 0.743 4.54E+15 171190.53 0.833

Table 15 Summary statistics for model.

Coefficient Estimates

const Exp Savings FT EA Exp Savings*FT Exp Savings*EA

Coefficients 79930 0.85 -76708 1258 2.20 -4.04

Standard Error 62285 0.80 19028 56503 0.17 0.22

pvalue 0.208 0.297 0.000 0.982 0.000 0.000

t Stat 1.28 1.06 -4.03 0.02 13.09 -18.37

Lower 95% -46790 -0.78 -115422 -113699 1.86 -4.48

Table 16 Coefficient estimates

89

Upper 95% 206652 2.47 -37994 116216 2.54 -3.59

VIF 101.65 2.04 2.22 222.24 123.45

Profit

20000000 15000000 10000000

15000000-20000000

5000000

10000000-15000000

0

5000000-10000000

-5000000

0-5000000

-10000000

-5000000-0 6.2

-15000000

3.1 1955733.3

1467200.0

Exp Savings

978666.7

490133.3

-20000000 1600.0

Profit

-10000000--5000000 FT

0.0

Figure 16 3-D plot of the results.

90

-15000000--10000000 -20000000--15000000

Normal Scores vs. Residuals 2.5 2

Normal Scores

1.5 1 0.5 0 -800000 -600000 -400000 -200000-0.5 0

200000 400000

-1 -1.5 -2 -2.5 Residuals

Figure 17 Normal sores vs. residuals. This model is intuitive and appears to provide a good fit. With higher expected savings it seems logical to apply more formal methods and obtain higher profit as the model predicts. With any regression questions should be asked as to the goodness of fit and evaluated against a checklist such as Table 17. Issue

Evaluation Method

Checks

Inputs supports model

Variance Inflation Factors (VIFs)

9

Outputs fit the model

Outliers

9

Outputs fit the model

Residual Plots

9

Table 17 Regression Checklist.

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An examination of the variance inflation factors (VIF) associated with this model would indicate that they are unacceptable and this model should not be used for predictions. Variance inflation factor measures the impact of collinearity among the inputs in a regression model on the precision of estimation. It expresses the degree to which collinearity among the predictors degrades the precision of an estimate. In a regression model we expect a high variance explained (r-square). The higher the variance explained is, the better the model is. However, if collinearity exists, probably the variance, standard error, parameter estimates are all inflated. The high variance might not be a result of good independent predictors, but a mis-specified model that carries mutually dependent and thus redundant predictors. Scaling the inputs does not always cause improvements in the VIFs, as in this example problem. Some model forms may not be suitable to fit the given data. Another simple model involving training and management direction was investigated. This model is represented by equation 5.10.

Profit = 13510+38856*M_I+19566*Training

(5.10)

Where: M-I is whether the project was initiated by management or by team members, Training is before of after Formal Six Sigma Training

And Profit is the response.

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The main effects plot for this model is shown in Figure 18, with the results of the regression model presented in Table 19, and the summary statistics given in Table 18.

Predicted Response

60000

40000

20000

0 k1:M

k1:I

Training:-1

Training:0

Figure 18 Main Effects Plot of Simple Regression Model.

93

Training:1

Summary Statistics Criterion R^2 R^2 adj R^2 predict R^1 PRESS s (est. err.) SSE(LSE)/SSE(LAD)

Value 0.194 0.148 0.0251 0.102 1.33E+11 56133.32 0.827

Table 18 Summary statistics for Simple model.

Coefficient Estimates Coefficients const M/I_I Training

13509.53 38856.45 19566.38

Standard Error 12750.01 21245.49 11002.61

t Stat

p-value

1.06 1.83 1.78

0.297 0.076 0.084

Lower 95%

Upper 95%

12374.36 -4274.20 -2770.10

39393.43 81987.09 41902.86

VIF

1.06 1.06

Table 19 Coefficients for Simple model.

5.9 Regression Results This model was based on the results of 39 separate projects at one company while most of the current literature is based on only a single case study. Specifically, our results indicate the importance of estimating expected savings with an economic study prior to the project start. With this information management can more

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effectively decide how formal to be in the approach to the proposed project. From our data the brake even point is $12,500. If a project is projected to save less than $12,500, formal Six Sigma methods are not advised. Instead relying on quick engineering input would tend to generate more profit sooner. On projects over $12,500, the model states formal quality improvement tools should be employed. As anticipated savings increase it is more advisable to spend increasing time with statistical tool to increase the probability of increased profits. The ability to estimate potential effects of changes on the profitability of projects is valuable information for policymakers in the decision-making process. This study demonstrated that utilizing existing data analysis tools to this new management data source provides useful knowledge that could be applied to help guide in project management. In this study we compared results of various sized projects and the use of formal tools. In our case study we found determining the estimate of the economical value to be important to guide the degree of use of formal tools. Based on the results of this study, when predicted impact is small a rapid implementation based on engineering input is best. As projects expand more statistical data improves outcome. This study had a crossover point of $12,500. The simple model also tends to show a strong benefit to training. This model has good VIF values and supports the findings from the SPC findings. Of interest is the correlation on management initiation of projects. There is still ambiguity in the results. For example it is not know if people worked harder on projects they initiated or if due to better familiarity they picked better projects. 95

However, replication of these results for other projects at other companies and industries is warranted to determine the generalizability of these findings. Natural extensions of this study would be to expand the scope of the analysis to include other variables such as multiple manufacturing sites and other statistical methods.

5.10 Markov Decision Processes Recently, there has been considerable interest in modeling the utility of data and analysis method, including Six Sigma related methods. For example, Bisgaard and Freiesleben (2000) used simple financial models to investigate the return on investment for any process improvement method for a particular context. Yu and Popplewell (1994) proposed a neural network meta-model as an online decisionsupport model for Six Sigma quality improvement efforts, taking into consideration yield and cost. Chan and Spedding (2001) expanded on this work. Eid, Moghrabi and Eldin used simulation to compare quality/cost decision scenarios. Goh (2002) discussed some strategic perspectives of Six Sigma based on organizational security. A hole in this growing literature is the optimality of selection and ordering component methods associated with Six Sigma improvement projects. A proposed method to investigate optimal selection is the use of Markov Decision Processes (MDP, Puterman, 1994) and Partially Observed Markov Decision Processes (POMDP, Lovejoy, 1991, and White, 1991). MDPs are used to model systems in which the evolution is controlled by available actions which can be chosen by the system in each state. The use of MDP 96

models has encompassed a wide range of applications. They have been widely applied to inventory control problems which represent one of the earliest areas of application. MDP models have been used to study equipment maintenance and replacement problems, (Rust, 1987) and (Golabi, 1993) as well as computer, manufacturing and communications systems. MDP models have become popular in behavioral ecology used in a wide range of contests to gain insight into factors influencing animal behavior. Examples include models of social and hunting behavior of lions (Clark, 1987: Mangel and Clark, 1988), site selection and number of eggs laid by apple maggots and medflys (Mangel, 1987), daily vertical migration of sockeye salmon and plankton (Levy and Clark, 1988: Mangel and Clark, 1988), changed in mobility of spiders in different habitats (Gallespie and Caraco, 1987), and singing versus garaging tradeoffs in birds (Huston and McNamara, 1986) as well as Games of Chance (Dubins and Savage, 1965). Kelly and Kennedy (1993) used MPD models in their study of mate desertion in Copper’s hawks. Details about Markov decision processes can be found in Puterman (1994). The Markov decision processes describe a model for sequential decision making under uncertainty which takes into account both the outcomes of current decisions and future decision making opportunities. At each decision epoch, the system state provides the decision maker with all necessary information for choosing an action from the set of available actions in that state. As a result of choosing an action in a state, two things happen; the decision maker receives a reward (or cost), and the system evolves to a possibly different state at the next decision epoch. Both the rewards and transition 97

probabilities depend on the state and the choice of action. As this process evolves through time, the decision maker receives a sequence of rewards. At each decision epoch, the decision maker chooses an action in the state occupied by the system at that time. A policy provides the decision maker with a prescription for choosing this action in any possible future state. A decision rule specifies the action to be chosen at a particular time. It may depend on the present state alone or together with all previous states and actions. A policy is a sequence of decision rules. Implementing a policy generates a sequence of rewards. The sequential decision problem is to choose prior to the first decision epoch a policy to maximize a function of the reward sequence. The key ingredients of this sequential decision model are the following: 1.

A set of decision epochs.

2.

A set of system states.

3.

A set of available actions.

4.

A set of state and action dependent immediate rewards or costs.

5.

A set of state and action dependent transition probabilities.

When confronted with a decision, there are a number of different alternatives (actions) available. Choosing the best action requires a consideration of more than just the immediate effects of the action. The immediate effects are often easier to calculate than the long-term effects. Sometimes actions with poor immediate effects can have better long-term ramifications. To maximize the total expected value function, the 98

right tradeoffs between the immediate rewards and the future gains are needed to yield the best possible solution. When making a decision, we need to consider how actions will affect the system. The state is the way the system currently exists and an action will have the effect of changing the state. The actions are the set of possible alternatives that can be chosen. The problem is to know which of these actions to take when in a particular state of the system. When deciding between different actions, we need to consider how they will affect the current state. The transitions specify how each of the actions changes the state. Since an action could have different effects, depending upon the state, we need to specify the action’s effect for each state. The most powerful aspect of the Markov decision process is that the effects of an action can be probabilistic. We could specify the effects of doing action ‘a1’ in state ‘s1’ if there is no question about how ‘a1’ changes the system. However, many decision processes have actions that are not this simple. Sometimes an action usually results in state ‘s2’ but occasionally it might result in state ‘s3’. MDPs allow specifying a set of resulting states and the probability that each state results. As an agent moves through its environment, it bases its actions on information received from a number of sources including sensory input and memories of previous inputs. This information tells the learner something about the state of the world. An agent in some state at time t executes an action and receives a reward from the environment. This is called a decision process. If the next state is dependent only

99

on the current state and action the decision process is said to obey the Markov property. This is called a Markov decision process (MDP) (Bellman 1957b). If the set of states and actions are finite, then the problem is called a finite MDP. We can also distinguish between finite and indefinite horizon problems, where the task has a natural endpoint, and infinite horizon problems, where the task continues forever. Formally an MDP consists of: o A set of state S, and actions A, o A transition distribution P ( s t +1 s t , a t ), s t , s t +1 ∈ S , a t ∈ A , and o A reward distribution P (r t s t , a t ), s t ∈ ℜ, a t ∈ A.

In the above, t indexes the time step, which ranges over a discrete set of points in time. The transition probability is denoted by Pij (a), Pr( s t +1 = j s t = i, a t = a). The

expected immediate reward received by executing action a in state i by ri (a ) :

{

ri (a) = E r t s t = i, a t = a

}

(5.11)

The solution to an MDP is called a policy and it simply specifies the best action to take for each of the states. The goal of solving an MDP is to find a policy that maximizes the total expected reward received over the course of the task. A policy tells the learning agent what action to take for each possible state. It is a (possibly stochastic) mapping π : S → A from states to actions. The policy can be nonstationary, in which case a different mapping from states to actions can be used at each 100

point in time. Alternatively, it can be stationary, in which case the same mapping is used at every point in time. The expected return for a policy π is defined as the total reward that is expected when following policy π : ⎧n ⎫ Eπ {R t } = Eπ {r t + γ r t +1 + ... + γ n r t + n } = Eπ ⎨∑ γ k r t + k ⎬ ⎩ k =0 ⎭

(5.12)

where t is current time. Notice that the expectation is taken with respect to the policy π . By assuming that the problem is Markov, we know that an optimal policy need only be a function of the current state: no other information is required to act optimally (Howard 1960). The class of MDPs is a restricted but important class of problems. By assuming that a problem is Markov, we can ignore the history of the process, and thereby prevent an exponential increase in the size of the domain of the policy. The Markov assumption underlies a large proportion of control theory, machine learning and signal processing. Dynamic programming is a technique for finding solutions to optimization problems. It is similar to divide and conquer techniques, where a problem is broken down into sub-problems that can be solved. To be amenable to dynamic programming, the optimization problem has to exhibit optimal substructure: An optimal solution must contain within it optimal solutions to sub-problems.

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In the case of MDPs, we must find a policy that produces the greatest expected return. With knowledge of transition probabilities Pij (a) and expected immediate rewards ri (a), and given a stochastic policy π , we can calculate the expected discounted return from the current state s:

⎧n ⎫ V π ( s ) = Eπ ⎨∑ γ k r t + k s t = s ⎬ ⎩ k =0 ⎭

(5.13)

Here t denotes the current time. The function V π is called the value function for policy π . The value function gives the expected return that can be achieved by starting from any state, and then following policy π . Markov Decision Process approaches involve modeling a sequence of selections in which (1) the outcomes are random with probabilities that depend upon the current state (st) at time t, and action taken, a, and (2) the rewards, rt, depend on the current decision and results form a sequence of future decisions. With a finite number of decision periods, e.g., days in a project, the optimal policy can be derived using a recursive approach called dynamic stochastic programming. To apply MDP to support decision-making, one needs to know the current system state, st. Depending upon how the states are defined; a team in a process improvement project might not have complete knowledge of the current state of their project. Partially Observed Markov Decision Processes (POMDP) permit the user the flexibility to supply only probabilities that the system is in specific states. Intuitively,

102

the fact that project improvers have only partial knowledge of the system state might provide important justification for a “one-size-fits-all” approach such as Six Sigma type methods. Yet, while MDP models permit the derivation of globally optimal decision policies, POMDP methods do not generally lead to guarantees that the derived policies are optimal. Lovejoy (1991) and White (1991) both survey solution methods for these problems including work in Smallwood and Sondik (1973) and White and Scherer (1989). Yacout and Gautreau (2000) used POMDP models to compare three quality assurance policies: do nothing, inspect, or improve. In Gautreau, Yacout, and Hall (1997), they had already used POMDP directly as a tool for quality improvement. In our study we only considered unconstrained, discrete time, finite horizon MDPs.

5.11 Markov Decision Process Analysis Suppose that a manufacturer is currently losing $500K/year running a certain process but knows a competitor is making $150K/year from running a similar process. Instead of shutting the process down, the manufacturer decides to invest in an improvement project with a three month time limit. Assume that the resident quality expert, a “green belt” six sigma practitioner, has already declared that the process state (st) must be one of those listed in the left-hand column of Table 20. Also, assume that the possible actions (a) are listed in the top first row of the table.

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These actions include applying statistical process control (SPC) p charting, a relatively inexpensive ($) design of experiments (DOE) application (e.g., a standard screening method using fractional factorials), and a relatively expensive ($) DOE method (e.g., a response surface method application). The quality expert estimates the annualized cost of applying each action for processes in the various states, including the cost of measurement equipment, record keeping, and training. If either a control plan is applied or the production action is taken, then the system improvement ends (all future states are #6).

State (st) 1. Settings lose money and capability unknown 2. Settings lose money and capability known 3. Measured but input-output func. not known 4. Input-outputs func. known but not fully opt. 5. Improved settings found but not validated 6. System improvement ends

Meet

SPC p Charting

$ DOE

action

(a)

$$ DOE

Optimize

Control Plan

Produce

-20

-50

-70

-70

-10

-150

-500

-20

-30

-40

-70

-10

-10

-200

-20

-30

-40

-70

-10

-50

-100

-20

-30

-40

-70

-10

-30

80

-20

-30

-40

-70

-10

250

150

-20

-30

-40

-70

-10

0

50

Table 20 Costs and rewards (in $K), rt(st,a), of applying actions (a) in different states (st).Coefficient estimates

104

Assume further that the quality expert has documented that each of the m = 6 actions will cause systems in each of the q = 6 states to transition to each state (st+1 = 1,…,6). Table 21 shows the probabilities for an example action, which is applying an expensive design of experiments method (a = $$ DOE) such as response surface methods.

From State (st+1= j)

1 2 3 4 5 6

1 0.9 0.0 0.0 0.0 0.0 0.0

2 0.1 0.2 0.00001 0.0 0.0 0.0

To State 3 0.0 0.8 0.1 0.0 0.0 0.0

(st= i) 4 0.0 0.0 0.79999 0.5 0.01 0.0

5 0.0 0.0 0.1 0.5 0.99 0.0

6 0.0 0.0 0.0 0.0 0.0 1.0

Table 21 Assumed transition probabilities for applying DOE, pt(st+1= j|st= i,a = $$ DOE).

With this information, an algorithm is generated to find the actions that globally maximize the expected reward at every decision period for every possible state. This calculation is based on the following recursion for t = 5,4,…,1 and i = 1,…,q:

ERt*(st = i) = max {rt(st,a) + Σj=1,…,q pt(st = j|st = i,a) ERt+1*(st+1= j)} (5.14) a

where ERt=6*(s6 = i) = r6(s6 = i,a = Produce) for i = 1,…,q. The results are shown in Table 22. The quality expert inputs the time period and the state and the table indicates which method is recommended. A second table also gives the expected

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reward or return on investment shown in Table 23. Note that if the current state cannot be observed and one has only the probability of being in a certain state, solution to global optimality is, in general, computationally difficult (e.g., see Lovejoy, 1991a).

StateWeeks 1-2 1 Meet 2 SPC 3 $ DOE 4 Optimize 5 Control Plan 6 Produce

Weeks 3-4 Meet SPC $ DOE Optimize Control Plan Produce

Weeks 5-6 Meet SPC $$ DOE Optimize Control Plan Produce

Weeks 7-8 Meet SPC $ DOE Optimize Control Plan Produce

Weeks 9-10 Meet Produce $$ DOE Produce Control Plan Produce

Weeks 11-12 Produce Produce Produce Produce Produce Produce x

Table 22 Optimal decision policy for five decision periods.

StateWeeks 1-2 1 65.0 2 175.0 3 307.8 4 429.4 5 500.0 6 500.0

Weeks 3-4 -27.6 96.8 251.3 379.1 450.0 250.0

Weeks 5-6 -101.5 -5.3 183.4 327.2 400.0 200.0

Weeks 7-8 -179.6 -75.7 67.7 264.5 350 150.0

Weeks 9-10 -272.2 -150.0 -1.0 130.0 300.0 100.0

Weeks 11-12 -500.0 -200.0 -100.0 80.0 150.0 50.0 x

Table 23 The expected reward, ERt*(st = i), in $K as a function of period and state. The above illustrates the application of Markov decision process (MPD) to assist in selecting which methods to use in which order in an improvement project. The results are subjective in the sense that the transition probabilities associated with each action, pt(st = j| st = i,a), e.g., the numbers in Table 18 were subjectively estimated. Therefore, the resulting decision policy may be viewed as a rationalization for the choice of methods with explicit assumptions. Another possible benefit of using 106

the above method for planning improvement projects is the possibility that the probabilities can capture knowledge of experts and make this knowledge available to novices or “green belts”. A more detailed model might be useful as it relates to the data used in the regression model and based on the component methods definition of Six Sigma. Component methods can be associated with a phase of Six Sigma as shown in Table 24.

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Phase DEFINE- (Finding the Ys in the model)

MEASURE – (Finding the Ys in the model)

ANALYZE (find the factors or x’s in the model)

Deliverables • Establish process responsibilities • Define system (inputs, outputs, customers) • Identify customer requirements • Gap between customer requirements and process capability

• • • •

IMPROVE - (Define Y=(x,z) and move toward Max Y) CONTROL – Maintain improvements to the system

Cause and effect matrix Prioritized list of all x’s Few vital x’s Statistical analysis for significance

•

Target setting for x’s

•

Control plan

Component methods Surveys Focus Groups Interviews Process MAP Pareto Analysis

Process mapping Pareto analysis Process capability Gage R&R Measurement system analysis Cause and effect analysis Process mapping Benchmarking Histograms Cater diagrams Run charts Multivariate charts Box and whisker Pareto chart Regression Process mapping Simulation DOE Risk assessment SPC Process capability Checklists Documentation

Table 24 Component Method of Six Sigma.

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A Six Sigma type method is an arrangement of component methods such that there is at least one selection of the associated activities that is consistent with a DMAIC ordering of activities. Also, in Six Sigma type methods multiple components methods can be used in the contest of the same activity and no method needs to be performed associated with any of the activities. The Figure 19 below shows an example of Six Sigma type method that the team might tentatively lay out in the design phase of a project.

109

Define: Hold formal meeting

Measure: Perform gage R&R Create SPC charts Perform benchmarking

Analyze: Plan and perform DOE Fit regression model Apply FMEA

Improve: Apply formal optimization

Control: Develop control plan Continue SPC charting

Figure 19 Flow Chart of DMAIC Six Sigma Project.

110

The optimality of any particular Six Sigma type method in question or Six Sigma type method for a particular application can be investigated using Markov decision processes. Possible states could be defined as: “Right” initial team Found “right” project Charter is established Initial baseline established Confirmed gauge capability “Right” initial factors Confirmed important factors “Accurate” Yr(x) models Developed “recommendations” Establish new baseline Updated SOPs Project completed We have the limited data form the previously covered study of 39 improvement projects and the actions as defined in Table 21. The rewards or costs of these actions are easy to estimate based on the data. The transition probabilities are not as easy to estimate based on this limited data. One method for this estimate is a Bayesian approach based on Dirichlet prior distributions. Bayesian probabilities are sometimes called subjective probabilities. It is important to understand exactly what is meant by subjective in this contest. Decision analyses are often unique. The situation in which one is making the decision may occur only once. It cannot be replicated, so there is no possibility for measuring probabilities by repeated sampling. People in the same state might take different action dependent on skill level, taste or problem particulars. Nevertheless, Bayesian analysis may be used to compute the probabilities needed to make decision. Because these

111

probabilities cannot be measured by repeated sampling, they are called subjective and they represent a degree of belief in a particular outcome. Bayesian analysis is a kind of meta-analysis in which observed data in combined with a prior belief to end up with a posterior belief. In short, it’s a way to update a belief with new data. A positive aspect of the Bayesian approach is that it encapsulates the manner in which research findings are assimilated. Meta-analysis is literally an analysis of analyses, a synthesis of all research on a particular effect. If there is no basis in observed data for estimating the prior probability distribution, then the analyst may simply assume a particular prior distribution. Most commonly, a noninformative prior distribution is assumed. A classic approach to multinomial estimation is via the use of the Dirichlet distribution. The Dirichlet distribution entertains several properties that become very useful in statistical inference. According to Friedman and Signer (1999), estimates derived using Dirichlet priors are consistent, the estimate converges with probability one to the true distribution; conjugate, the posterior distribution is also a Dirichlet distribution; and can be computed efficiently, all queries of interest have a closed-form solution. In Bayesian parameter estimation, the prior incorporates prior knowledge or beliefs about the parameters. As data is gathered, these beliefs do not play a significant role anymore. More specifically, if the prior is well-behaved, does not assign 0 probability to feasible parameter values, the approach will converge in the limit to the real values. A Dirichlet prior with parameters β1, … βk is defined as: P(θ) = α ∏ θiβi-1

(5.15) 112

Then the posterior will have the same form, with parameter βi + Ni: P(θ|D) = P(θ) P(D|θ) = α ∏ θiβi-1+Ni

(5.16)

The property that the posterior distribution follows the same parametric form as the prior is called conjugacy. The Dirichlet prior is a conjugate family for the multinomial likelihood. Conjugate families are useful because they can be represented in closed form, incremental updates to the parameters can be done as data is gathered, and often there is a closed-form solution for the prediction problem. With this background a MDP model for Six Sigma based on the previous collected data and action definitions could take the form of Figure 20.

113

0 0 0 0 0 0 1 0 1 .5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 .5 0 0 1 1 0 0 1 1 .2 0 1 1 .4 0 1 1 .6 0 1 1 .8 0 1 1 1 0 1 1 1 .3 1 1 1 .5 1 1 1 .8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

U pd ated S O P s

E s ta blis h n ew ba s e line

D ev elo pe d "r ec om m e nd atio ns "

"A c c u ra te " Yr ( x ) m o de ls

C on fir m e d inp or ta nt fac to rs

"R ig ht" in itial fac to rs

C on fir m e d ga ug e c a pa bility

Initia l ba s e line es ta blis h ed

F o un d "r igh t" p ro jec t 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

C ha r ter is es ta blis h ed

"R ig ht" in itial tea m 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 0 0 TF TF EC 0 0 0 EC EC EC TF 0 0 0 TF TF TF TF SP 0 0 0 SP SP SP SP SP 0 0 0 SP SP SP SP GR 0 0 0 GR GR GR GR CE 0 0 0 CE CE CE CE CE 0 0 0 CE CE CE CE SD 0 0 0 SD SD SD SD SD 0 0 0 SD SD SD SD SD 0 0 0 SD SD SD SD SD 0 0 0 SD SD SD SD SD 0 0 0 SD SD SD SD RD 0 0 0 RD RD RD RD RD 0 0 0 RD RD RD RD RD 0 0 0 RD RD RD RD RD 0 0 0 RD RD RD RD OP 0 0 0 OP OP OP OP SP 1 0 0 SP SP SP SP SP 1 0 0 SP SP SP SP CP 1 .5 0 CP CP CP CP TE 1 1 .5 CP CP CP TE 1 1 1 TE TE TE

Figure 20 Morkov Decision Process for Six Sigma. The actual actions taken might be along the diagonal as indicated. The amount of data obtained to date has not allowed for the construction of an adequate model and continues to be an area of research interest for future work.

114

5.12 Sample MDP Example The data associated with the 30 improvement projects can be used in the derivation of state/action rewards and the state/action transition probabilities. In this simplified case six states are defined which map to the standard DMAIC as follows in Table 25. State 1 2 3 4 5 6

Description No Charter No Base line Define input-output No Recommendation Not Controlled Production

Map to DMAIC Define Measure Analysis Improve Control

Table 25 State Description Mapped to DMAIC for Sample MDP.

Ten actions were possible with average cost calculated form the collected data. These action-rewards are presented in Table 26 with the tabulation of the number of state transitions by action for the projects displayed in table 27.

Action Charter Team Forming Process Mapping Cause & Effect GR&R

Cost of action $1440 $1440 $2080 $1580 $1700

Action

DOE SPC Documentation One Factor Experiment Engineering Analysis

Cost of action $16000 $750 $1500 $4000 $4000

Table 26 Actions and Rewards for Sample MDP.

115

Action Charter Charter Charter Charter Charter Charter

State to State 1 2 3 4 5 6

1 12 -

2 8 -

3 6 -

4 2 -

5 -

6 -

Team Forming Team Forming Team Forming Team Forming Team Forming Team Forming

1 2 3 4 5 6

1 -

11 -

-

-

-

-

Process Mapping Process Mapping Process Mapping Process Mapping Process Mapping Process Mapping

1 2 3 4 5 6

-

3 -

3 5 -

3 2 -

5 -

-

Cause & Effect Cause & Effect Cause & Effect Cause & Effect Cause & Effect Cause & Effect

1 2 3 4 5 6

-

-

5 -

6 -

1 -

-

GR&R GR&R GR&R GR&R GR&R GR&R

1 2 3 4 5 6

-

1 -

1 5 -

-

-

-

Tabulation of State Transitions for Sample MDP (continued on next page)

116

Tabulation of State Transitions (continued from previous page) Action DOE DOE DOE DOE DOE DOE

State to State 1 2 3 4 5 6

1 -

2 -

3 -

4 -

5 9 -

6 2 -

SPC SPC SPC SPC SPC SPC

1 2 3 4 5 6

Documentation Documentation Documentation Documentation Documentation Documentation

1 2 3 4 5 6

-

-

3 -

1 -

3 -

26 -

One Factor Experiment One Factor Experiment One Factor Experiment One Factor Experiment One Factor Experiment One Factor Experiment

1 2 3 4 5 6

-

-

-

4 -

6 -

-

Engineering Analysis Engineering Analysis Engineering Analysis Engineering Analysis Engineering Analysis Engineering Analysis

1 2 3 4 5 6

-

-

-

1 15 2 -

1 10 -

3 4 -

Table 27 Tabulation of State Transitions for Sample MDP.

117

An examination of Table 27 illustrates the limited data available from the improvement projects and the need for Bayesian estimation. Table 28 gives an example of the tabulated actual data and Alpha priors which when added together results in a usable transition matrix for the action Engineering Analysis. Continuing with the remaining actions, (estimating Alpha priors and adding to the tabulated data) results in a matrix that can be used to solve for a MDP policy. One possible Bayesian distribution based on the data from the 39 projects and Alpha priors as described above is presented in Table 29.

Tabulation No Charter No Base line Define input-output No Recommendation Not Controlled Production

State to State 1 2 3 4 5 6

1 -

2 -

3 -

4 1 15 2 -

5 1 10 -

6 3 4 -

Alpha Priors No Charter No Base line Define input-output No Recommendation Not Controlled Production

1 2 3 4 5 6

67 7 2 2 2 0

3 80 3 2 5 0

5 6 50 4 20 0

9 4 19 10 30 0

5 2 6 50 40 0

7 1 4 16 3 10

Table 28 Bayesian Estimate of State Transitions for Sample MDP.

118

Action Charter Charter Charter Charter Charter Charter

State to State 1 2 3 4 5 6

1 .01 .3 .2 .02 .02 0

2 .61 .5 .3 .2 .02 0

3 .189 .1 .4 .3 .2 0

4 .071 .05 .05 .4 .3 0

5 .07 .03 .03 .05 .41 0

6 .05 .02 .02 .03 .05 1

Team Forming Team Forming Team Forming Team Forming Team Forming Team Forming

1 2 3 4 5 6

.3 .3 .2 .02 .02 0

.4 .5 .3 .2 .03 0

.1 .1 .4 .3 .2 0

.08 .05 .05 .4 .3 0

.07 .03 .03 .05 .4 0

.05 .02 .02 .03 .05 1

Process Mapping Process Mapping Process Mapping Process Mapping Process Mapping Process Mapping

1 2 3 4 5 6

.6 .07 .1 .05 .05 0

.2 .16 .1 .1 .05 0

.2 .3 .5 .1 .1 0

.1 .13 .2 .5 .1 0

0 .3 .05 .2 .5 0

0 .04 .05 .05 .2 1

Cause & Effect Cause & Effect Cause & Effect Cause & Effect Cause & Effect Cause & Effect

1 2 3 4 5 6

.5 .1 .05 .05 .05 0

.2 .5 .07 .1 .05 0

.1 .2 .35 .1 .1 0

.1 .1 .4 .5 .1 0

.05 .05 .08 .2 .5 0

.05 .05 .05 .05 .2 1

GR&R GR&R GR&R GR&R GR&R GR&R

1 2 3 4 5 6

.07 .03 .1 .05 .1 0

.1 .12 .1 .1 .05 0

.61 .75 .5 .1 .05 0

.1 .05 .2 .5 .1 0

.07 .03 .05 .2 .5 0

.05 .02 .05 .05 .2 1

State Transitions for Sample MDP (continued on next page)

119

State Transitions (continued from previous page) Action DOE DOE DOE DOE DOE DOE

State to State 1 2 3 4 5 6

1 .4 .02 .02 .02 .02 0

2 .3 .4 .05 .02 .05 0

3 .17 .3 .1 .04 .2 0

4 .05 .2 .75 .05 .3 0

5 .05 .05 .05 .73 .4 0

6 .03 .03 .03 .14 .03 1

SPC SPC SPC SPC SPC SPC

1 2 3 4 5 6

.64 .01 .01 .01 .01 0

.01 .07 .07 .02 .01 0

.07 .8 .8 .07 .04 0

.2 .07 .07 .8 .07 0

.07 .04 .04 .07 .07 0

.01 .01 .01 .04 .8 1

Documentation Documentation Documentation Documentation Documentation Documentation

1 2 3 4 5 6

.8 .07 .02 .01 .01 0

.07 .8 .07 .02 .01 0

.06 .06 .8 .06 .03 0

.04 .04 .06 .8 .05 0

.02 .02 .04 .07 .1 0

.01 .01 .01 .04 .8 1

One Factor Experiment One Factor Experiment One Factor Experiment One Factor Experiment One Factor Experiment One Factor Experiment

1 2 3 4 5 6

.8 .07 .02 .01 .02 0

.07 .8 .07 .01 .05 0

.06 .06 .8 .03 .2 0

.04 .04 .06 .35 .3 0

.02 .02 .04 .55 .4 0

.01 .01 .01 .05 .03 1

Engineering Analysis Engineering Analysis Engineering Analysis Engineering Analysis Engineering Analysis Engineering Analysis

1 2 3 4 5 6

.67 .07 .02 .02 .02 0

.03 .8 .03 .02 .05 0

.05 .06 .5 .04 .2 0

.1 .04 .34 .12 .3 0

.05 .02 .07 .6 .4 0

.1 .01 .04 .2 .03 1

Table 29 State Transitions for Sample MDP.

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The above Bayesian probabilities and the rewards given in Table 26 where used in the development of an optimal MDP policy for the six listed states. It was also assumed that the production state had two different rewards. This was based on real data gathered from the improvement project. The average reward for a project that terminated early was $4,700. The average reward for a project that entered production at epoch 9 was $180,875. The optimal policy calculated with these assumptions is presented in Table 30.

State No Charter No Base Input-output Recomm Controls Ready

Period 1 GR&R P. Map DOE Eng. Anal. Docs. Production

Period 2 GR&R P. Map DOE Eng. Anal. Docs. Production

Period 3 GR&R P. Map DOE Eng. Anal. Docs. Production

Period 4 GR&R P. Map DOE Eng. Anal. Docs. Production

No Charter No Base Input-output Recomm Controls Ready

Period 6 Eng. Anal. P. Map DOE Eng. Anal. Docs. Production

Period 7 Eng. Anal. P. Map C & E Mat. Eng. Anal. Docs. Production

Period 8 Eng. Anal. C & E Mat. C & E Mat. Eng. Anal. SPC Production

Period 9 Production Production Production Production Production Production

Period 5 GR&R P. Map DOE Eng. Anal. Docs. Production

Table 30 Optimal Policy for Sample MDP.

This optimal policy has the structure on the standard DMAIC but does not follow the five phases explicitly. This could arise for numerous reasons. The Alphas selected may not be reasonable. The validity of the selection would become more apparent with added real data which would allow an update to the Bayesian estimates. 121

DMAIC may not be optimal in all cases. Again more data is needed to investigate this possibility. Both Linderman et. al. (2003) and Harry and Crawford (2005) have indicated that DMAIC may not be optimal for small project, the “low hanging fruit” and that DMAIC should be focused on complex challenging problems. For simple tasks such a system may decrease performance. The 39 improvement projects included in this study included a wide array of programs with estimated savings ranging from a low of $1,600 to a high of $2.2 million. It is possible that the data should be split into simple and complex projects. This is an area for future work, relating the size of a project to its optimal structure.

5.13 Conclusions Much of the literature related to six sigma focuses on knowledge that participants at various levels “should know” (Hoerl 2001). Other literature has addressed organization design to accommodate a “Six Sigma Culture” (Sanders and Hild 2000, and Hoerl 2001). Goh (2002) has discussed some strategic perspectives of Six Sigma based on organization needs. The literature on supporting method selection section in the context of Six Sigma has focused on decisions at a high level such as whether to perform projects at all including Bisgaard and Freiesleben (2000), Chan and Spedding (2001), Gautreau, Yacout and Hall (1997), Yacout and Gautreau (2000), and Yu and Popplewell (1994). In this study some methods for the evaluation of the expanding Six Sigma database are investigated. These approaches help to express Six

122

Sigma in more quantitative terms, which has more often been expressed in qualitative terms. Clearly the list of methods considered here for meso-analysis is incomplete and each has some advantages and limitations as shown in Table 31.

123

Tool Regression

Strength Simple and many diagnostics available

Limitation Necessary sample size can become large as n = 4 × [1 + m pre + m act + (m pre × m act )]

MPDs

Can address sequencing effects of method applications and interactions between them.

There is strong pressure to define only a small number of states for simplicity.

They permit the theoretical development of a prescriptive, data driven expert system that could advise novices about the methods relevant to their situations.

Because of this pressure assumptions about the system performance depending only on the state are critical.

SPC

Can provide simple way to evaluate whether changes in business practices are adversely or positively affecting quality programs

Further, the data must be coded into transitions between these states. Finally, because of the need to estimate many transition probabilities, Bayesian priors are generally needed for the transition probabilities. Generally, databases are limited. There is intuitive pressure to chart individual observations because every project is important in some sense. There may be a need for the development of new short run charts such as EWMA charts.

Table 31 Comparison of strengths and limitations for meso-analysis methods used.

124

To our knowledge no research has focused on the use of this database in this way. Practical implementation of these methodologies in a systematic manner will help industry to identify, analyze and evaluate factors and their interdependency, which would help to understand and unveil the complexity of Six Sigma. This could open the door to research that more clearly clarifies and capitalizes on the primary value of the Six Sigma movement which lies in providing a relatively detailed approach to problem solving (e.g., see Watson, 2000). In addition to providing algorithms that can be used to generate software for green belts, the research may lead to substantially more valuable methods than those of the Six Sigma type.

125

CHAPTER 6 CONCLUSIONS AND FUTURE RESEARCH

A summary and conclusion of this study is presented in this chapter. The first section provides an overview of the research while the second section summarizes the major research findings. The third section addresses the limitations of the study and potential areas for future research. Finally, the contributions of this study are presented in the fourth section.

6.1 Overview The main objective of this dissertation was to review the published literature on Six Sigma and identify opportunities for additional contributions for the academy. The major problems addressed in this dissertation are: 1. With reference to past academic contributions, what is Six Sigma? Also, what are the on-going research trends? 2. What are the implications of Six Sigma philosophy and methods for university education?

126

3. What methods should be used to mine the new databases about project financial results? Also, what insights can be gained form studying data at a real company?

This dissertation addressed these aspects of the university-industry relationship with Six Sigma as follows: For the first question a literature review covering a fourteen year timeframe was undertaken to describe the trends, sources and findings in the publications on Six Sigma. Secondly, case base training was examined as a method to improve Six Sigma education and increase usage on the job among university student learners. Third, Six Sigma’s acceptance and implementation by a large number of companies has resulted in the accumulation of a substantial database on quality improvement projects. The study explored methods to utilize this new data source to benefit industry management in their decision making process concerning quality policies.

6.2 Summary of Findings The literature search resulted in the identification of 201 articles published between 1990 and 2003. Although this review cannot claim to be exhaustive, it does provide reasonable insights into the state-of-the-art. As the nature of research on Six Sigma is difficult to confine to specific disciplines, the relevant material is scattered across various journals. It is felt that the results have several important implications. 127

To a great extent, the financial impact of Six Sigma on operational performance is well established. That follows because a defining principle of Six Sigma is that such justifications are needed for each Six Sigma project. The impacts on overall company performance as revealed in stock performance are not fully resolved. Some authors found hints of short-lived abnormal stock performance associated with the decisions to start Six Sigma programs. Yet, those authors found no statistical significance in relation to these claims nor evidence of long-term effects. This suggests a need for additional data collection and analysis to answer the important question of long-term impacts of decisions to adopt Six Sigma programs. It is proposed from the study that Six Sigma can be defined as a component based method involving Define, Measure, Analyze, Improve and Control (DMAIC) or (DMADV) and two principles. These principles relate both to building and maintaining management support and to fostering usage of methods among practitioners who are not experts in statistics. The first principle emphasizes attention to the bottom line in initiating projects. The second principle emphasized the training of non-statisticians with minimal theory. Trends in the literature include an increasing academic participation and a broader focus than solely on manufacturing. Three main types of contributions of Six Sigma to academia were identified embodied in the literature: (1) increased emphasis on complete case studies compared with single sub-method applications, (2) new, relatively specific core and infrastructure practices, and (3) the development of a large new market of industrial non-experts who might be interested in practically oriented research and new methods. 128

While over 50% of the articles in the database either explicitly or implicitly recommend Six Sigma programs, empirical study of the appropriateness of implementing Six Sigma in specific business contexts has, apparently, not been investigated. Related, largely unanswered questions include: How can data about any specific company’s management, training programs, or environment be useful in decision-making about the adoption of Six Sigma programs? Focusing on the second principle covered in the definition of Six Sigma which emphasizes training, an examination of case-based instruction methods was undertaken. Case-based instruction was introduced into senior and introductory graduate level engineering courses on statistical process control (SPC) and design of experiments (DOE). Students seem to identify with the case study "stories" much better than the traditional lectures. Before implementation of the case study exercises, end-of quarter evaluations by students for the two classes had been below the average end-of-quarter class evaluations in the department. After the implementation of the case study approach and with minimal other changes, the evaluations climbed well above average. This dramatic turn-around can mainly be attributed to the introduction of the case based method. Further, presenting applications of course methods in which literally millions of dollars are saved appears to effectively motivate students concerned about job security and advancement in the highly competitive industrial marketplace. One outcome of the wide spread acceptance of Six Sigma and with its systematic program is the growing database that now exist within industry and specific 129

companies on individual project improvement activities. The purpose of this study was to look at the database in a way that could help management better run improvement projects. Three possible analysis methods investigated for this task were regression, SPC, and Markov Decision Processes (MDP). The study was based on 39 quality/cost improvement projects at a medium size U.S. manufacturing company with data collected over a 30 month period. It was found that by viewing the quality improvement process in the same light as other processes and applying such techniques to the accumulating database could provide better insight for operational managers dealing with defective implementation decisions.

6.3 Limitations and Future Research One of the defining principles of Six Sigma is the financial justification for each project. Yet, the literature review found no published work showing statistical significance in relation to the decisions to start Six Sigma programs and stock performance. Considering that failure to find a significant effect does not constitute proof, more work is needed for a thorough evaluation of the bottom line impacts of Six Sigma. In the contest of Six Sigma, statements abound that are unsupported by objective evidence. Examples include self reported profits, the effects of success factors, and advocacy for Six Sigma in general. For example, as noted above, the impacts on stock performance investigated by Goh et al. (2003) are not fully resolved. 130

This suggests a need for additional data collection and analysis to answer the important question of long term impacts of decisions to adopt Six Sigma programs. Snee (1999 and 2000a) calls for research to help practitioners identify a robust set of improvement tools to be used in conjunction with the DMAIC process. The focus in these recommendations is not so much on new techniques as on refined techniques associated with specific phases.

However, new techniques might be

relevant to Six Sigma practitioners who are often not experts in statistics. Additional modeling techniques to predict and evaluate the bottom-line impacts of projects are needed. This follows because of the central importance of profit related justifications in Six Sigma for initiating decisions on projects. Our research did indicate a correlation with training and the bottom-line impact of projects. New models that are also easy-to-use could be developed with broader applicability and improved prediction accuracy. It might also be useful to extend profit models to investigate the selection of specific core methods or sub-methods in specific situations. These efforts could be combined with empirical investigations to permit the development of prescriptive models to aid practitioners from different disciplines select the most advantageous techniques. This could build on research related to the most appropriate methods for training black belts, e.g., in Hoerl (2001a), by associating the methods more specifically to phases in a project and to situations. Although the industry has an increased interest in Six Sigma implementation and many companies have gained the profits and advantages from this disciplined 131

approach, the research of the impacts of Six Sigma implantation and factors contributed to Six Sigma success remain unclear. Even the existent studies are not well integrated and the research is mostly anecdotal. Current concepts in the field of Six Sigma are largely based upon case studies, anecdotal evidence and the prescriptions of leading “gurus.” Consequently there is little consensus on which factors are critical to the success of the approach. Most of the articles reported that top management leadership is the main factor to Six Sigma success [Blakeslee (1999) and Scalise (2001)]. However, many other factors affecting Six Sigma’s success are important and need to be better documented. As part of this work the database was examined at one manufacturing company. This comprised 39 improvement projects conducted over a 30 month time frame. This is limited data, collected at one site and no definitive conclusions should be drawn. The data does provide a start into the use and modeling of Six Sigma, utilizing the growing database describing the performance of improvement projects and the methods used that is being generated as a result of it implementation. The attempt to build a theory of how and why Six Sigma works is aimed at building a prescriptive model. From this, managers would be able to identify which activities from which programs are more or less likely to be useful in their situations, as well as which of their goals would be most affected. An example is the correlation between training and increased profit seen in this study. With the future success of corporations riding on the outcome, there is a need for more theory to explain the differences between successful and unsuccessful efforts. 132

APPENDIX A:

THE ARTICLE DATABASE

The descriptors used in the table below are defined in Section 3. The complete

Speculative in Nature? Success Factors Management committed Right team Training Change Management Data system Team involvement Project selection Bottom line Project leadership Goals based Structured approach Customer focused Adaptable system

Research Approach

Industrial Sector Impact factor

Topics Version 2 Sousa and Voss (2002)

Topics Version 1 Oakland (1989)

Authorship Define DMAIC Define 3.4

Year

references to the articles are described below in the reference section.

Author(s) Pe 2001 A 0 0 To Pe Ackermann 1993 I 0 0 To Ackermann et.al. 1993 I 0 1 To Ali et.al. 1999 I 0 0 To Antony et.al. 2002 I 0 1 Sy Arvidsson 2003 A 0 0 Sy Pe Bailey 2001 I 0 0 Sy Bartos 1999 I 0 0 Sy Basu 2001 I 0 1 Sy Abraham et.al.

Behara et.al.

1995 I A 0 1 Sy

Ph To G 1.5 Co N N - - - - - - - - - - - - Ph To To To Ph Ph

G M M M M

Ph Ph Ph

M 1.5 C N M 0.3 TA Y M 0.2 Co N N M A C N

Ph

0.7 C 0.7 C 1.5 C 0.3 C 0.3 Su

133

N N N Y N

N N N N N

-

-

-

-

-

-

-

-

-

-

-

-

-

N - - - - - - - - - - - - Y - Y - - - - - - - - - - N - - - - - - - - - - - - N - - - - - - - - - - - - -

Breyfogle et.al. 2002 I Breyfogle et.al. 2001 I (a) Breyfogle et.al. (b) 2001 I Broderick et.al. 2002 A

1 1 Sy Pe 0 0 Sy

Ph

N Se A C Se 2.9 C R M 0.8 Co N M A TA Se 0.2 C N Se A C G 0.2 TA Se 0.2 C M 0.7 TA N Se A TA

Ph

G 1.5 TA Y N - - - - - - - - - - - - -

0 0 To 0 0 Sy

To Ph

N - - - - - - - - - - - - N - - - - - - - - - - - - -

Buck et.al.

2001 I

1 0 Sy

Ph

Buck

1998 I

1 1 Sy

Ph

Buck Buggie Card

2001 I 2000 I 2000 I

Ph Ph To

Caulcutt Chan et.al. Chassin Chowdhury

1 1 Sy 0 0 Sy 0 0 To Sy 2001 I 1 1 To 2001 A 0 1 To 1998 A 0 1 Sy 2000 I 1 0 Sy

G 0.2 C Y Se 4.8 C N N Se A C N C Su Se 1.9 R N N Se A C N M 0.1 TA Y M 0.8 Co N

Ph Pr To Ph Ph

M M Se G

Y N N Y

-

-

Y

-

Y -

-

-

-

-

-

-

-

-

Clifford Coleman et.al. Connolly Conner Cooper

2001 I 0 2001 I A 0 2003 I 0 2003 I 0 1992 I 0

Ph To Ph Ph Ph

M M M M M

Y N N N N

Y -

-

-

-

-

-

-

-

-

-

-

-

-

Cooper

2003 I

0 0

Ph

Se 0.2 Su

N Y - - - - - Y - - - - - - -

Crom

2000 I

0 0

Ph

Y Y Y - - - - - - - - - - - -

Dasgupta Davies Davig et.al. De Mast De Mast et.al.

2003 A 2001 A 2003 A 2003 A 2000 A

1 0 0 0 1

G 0.2 Co N Se A C Se 0.8 R M 0.2 Su G 0.2 Co G 0.2 Co

Benedetto Berlowitz Binder

2003 I 1 0 Sy 2003 A 0 1 To 1997 I 1 1 Sy

Ph To Ph

Bisgaard et.al. Blakeslee

2000 A 0 0 Sy 1999 I 0 0 Sy

Ph Ph

Blanton Bossert Breyfogle Breyfogle et.al.

2002 A 2003 I 2002 I 2003 I

Sy Sy Sy Sy

Ph Ph Ph Ph

0 0 0 0

0 0 0 0

1 0 0 0 1

1 0 0 0 0

Sy To Sy Sy Sy Pe Sy Pe Sy Pe Sy Sy Sy Sy Sy

Ph Ph Ph Ph Ph

N Y Y - Y Y - - - - - - - - N Y - - - - Y - - - - - - - N N - - - - - - - - - - - - Y N - - - - - - - - - - - - Y Y Y - Y - Y Y - Y - - - - Y Y N Y

-

-

-

-

-

-

-

-

-

-

-

-

-

Y N - - - - - - - - - - - - -

0.3 C N 0.4 C Y 1.9 R N 0.3 TA Y N A C CoN 0.3 TA Y 0.7 C N 0.3 C N 0.1 C N

134

N N N N

Y N N Y N

Y Y - - - - - - - - - - - N - - - - - - - - - - - - N - - - - - - - - - - - - N - - - - - - - - - - - - N - - - - - - - - - - - - -

Y N Y N N

Y Y -

-

-

-

-

-

-

-

-

-

-

-

-

Dedhia

1995 I

0 0 Sy Pe DeFeo 2000 I 0 1 Sy Deshpande 1998 A 0 0 To Deshpande et.al. 1999 I A 1 1 Sy Does et.al. 2002 A 1 0 Sy Doganaksoy et.al. 2000 I A 0 0 To Dornheim 2001 I 0 0 To

N - - - - - - - - - - - - N - - - - - - - - - - - - N - - - - - - - - - - - - -

Ferrin et.al. Finn Fontenot et.al.

2002 I 1 1 To 1999 I 1 0 Sy 1994 I A 0 1 To

Fuller

2000 I

Gano Gautreau et.al.

2001 A 0 0 To 1997 A 0 0 To

Gill Gnibus

1990 I 2000 I

Goh (a) Goh (b) Goh

2002 A 1 1 Sy Pe 2002 A 1 0 Sy 2001 A 0 0 To

Goh et.al. (a)

2003 A 1 0 Sy

Ph

Goh et.al. (b) Gordon

2003 A 1 1 To 2002 I 0 0 Sy

To Ph

Grandzol et.al. Greek Gross

1998 A 0 0 To 2000 I 0 1 Sy 2001 I 0 0 Sy Pe 1998 I 0 0 Sy Pe 1999 I 1 1 Sy Pe 2002 I 0 0 Sy

Pr Ph Ph

G 0.2 R M 0.3 TA N M A R N G A TA G 0.2 Co N M A Su M 0.3 Su G 0.2 TA

Ph

M 0.2 TA N N - - - - - - - - - - - - -

Ph

M 1.2 TA N Y - - - - - - Y - - - - - -

Ph

G 1.2 TA Y N - - - - - - - - - - - - -

Hahn

Sy To To To Sy To

N - - - - - - - - - - - - N - - - - - - - - - - - - N - - - - - - - - - - - - -

2000 I 2000 A 2002 I 1997 A 2001 I 1997 A

Hahn et.al.

0 1 0 0 0 0

Y Y - Y - - - - - - - - - -

Douglas Du et.al. Duguesaoy et.al. Eid et.al. Farntz Feng et.al.

Hahn et.al.

0 0 0 0 1 0

N Se A TA Y N Ph G A Su N To M 0.2 C Y Ph G 0.4 C N N Ph Se A Co N To M 0.2 C Y To M 0.3 TA Y N Ph G A C Su N Pr To M 0.5 Co Y To G 0.4 C N To M 0.4 TA Y Ph M 0.3 C N To M 0.4 C N N To M A Su N Ph M 0.3 TA Y To M 0.2 Su N N Ph M A TA Y N To G A C N To M 0.4 TA Y N Ph M A Su N To G 0.2 C Y N Ph G A Co N Ph

0 0 Sy

0 1 Sy 0 0 To

Ph To

135

N N N N N N

-

-

-

-

-

-

-

-

-

-

-

-

-

N - - - - - - - - - - - - N - - - - - - - - - - - - N - - - - - - - - - - - - Y - - - - - - - - - - Y - N - - - - - - - - - - - - N - - - - - - - - - - - - N - - - - - - - - - - - - N - - - - - - - - - - - - N - - - - - - - - - - - - -

N Y - - Y - - - Y - - - - - Y Y Y - - - - - - - - - - - N N - - - - - - - - - - - - Y N - - - - - - - - - - - - Y N - - - - - - - - - - - - N N - - - - - - - - - - - - N Y Y - - - - - - - - - - - Y Y Y - - - - - - - - - - - -

Hahn et.al. Hahn et.al.

2000 I 2001 I

1 1 Sy 0 0 To

Ph To

Hammer

2002 I

Ph

Harrold Harrold et.al.

1999 I 1999 I

Ph Ph

M 0.3 C N Y - - - - - Y - - - - - - M 0.3 TA Y N - - - - - - - - - - - - -

Harry

1998 I

Ph

M 0.2 C

N Y - - Y - - - - - - - - - -

Harry (a) Harry (b) Harry (c) Harry (d) Harry (e) Harry (f) Henretta et.al.

2000 I 2000 I 2000 I 2000 I 2000 I 2000 I 2003 I

1 0 Sy Pe 1 1 Sy 1 0 Sy Pe 1 1 Sy Sy 0 0 To 0 0 To 0 0 To 0 1 Sy 0 0 To 0 0 To 1 1 Sy

N G A TA Y Y Y - - - Y - Y - - - Y - G 0.2 TA Y Y - - Y - - - - - - - - - N M A TA N Y - - - - - - Y - - - - - -

Ph To To To Ph To To Ph

G G G G G G Se

N Y Y Y Y Y N

Hild et.al.

2000 I

Johnstone et.al. Kandebo Kane

0 0 Sy Pe 2001 I 0 0 To 1998 I 0 0 Sy Pe 2001 I 0 0 Sy Pe 2001 I 0 0 Sy 1999 I 0 0 Sy 2000 I 0 0 Sy 2001 I 0 0 Sy 1999 I 0 0 Sy 2000 I 0 0 Sy 1999 I 0 0 Sy Pe 2000 I 0 0 Sy Pe 2001 I A 1 1 Sy Pe 2002 I 0 1 Sy 2003 I 1 1 Sy 2002 I 0 1 Sy Sy 2003 I 0 1 To 1999 I 0 0 Sy 1998 I 0 1 Sy

Kazmer et.al. Kazmierczak

2002 A 0 1 To 2003 A 0 1 To

Hill Hoerl Hoerl (a) Hoerl (b) Horst Howell Howell Hunter Hunter Hunter et.al. Hutchins Ingle et.al. Johnson Johnson et.al. Johnstone et.al.

Ph

0.2 Su 0.2 TA 0.2 TA 0.2 TA 0.2 TA 0.2 TA 0.2 C N M A Co

Ph To M 1.5 C Ph G 0.2 C

Y N N N N N N

-

-

-

-

Y -

-

-

Y -

-

-

-

-

-

N N - - - - - - - - - - - - N N - - - - - - - - - - - - N Y - Y - - - - - - - - - - -

Ph

G 1.5 TA N Y - - - - - - - - Y - - - -

Ph Ph Ph Ph Ph Ph Ph

G Se M M Se G M

Ph Ph

G 0.2 TA Y N - - - - - - - - - - - - N M A Co N N - - - - - - - - - - - - -

Ph Ph Ph

G 0.3 TA Y N - - - - - - - - - - - - M 0.3 Su N N - - - - - - - - - - - - Se 2.9 C N N - - - - - - - - - - - - -

1.5 TA Y 0.3 C CoN 0.3 Su N 0.3 Su N 0.3 C N 0.3 TA Y 0.3 C N

Ph Pr Se 1.2 C Ph M 0.3 TA Ph M 0.2 C N To M A C To Se 1.6 R

136

N N N Y N N Y

Y Y

-

-

-

-

-

-

-

-

-

-

-

-

N Y Y - - - - - - - - - - - N N - - - - - - - - - - - - N N - - - - - - - - - - - - Y N - - - - - - - - - - - - N N - - - - - - - - - - - - -

Kendall et.al. Kenett et.al. Knowles et.al. Koch Koonce et al. Krouwer Kunes Landin et.al.

2000 I 0 2003 I A 0 2003 A 0 2002 I 0 2003 A 0 2002 I 0 2002 I 1 2001 A 0

0 0 0 1 0 1 0 0

Leffew et.al. 2001 I A 1 1 Linderman et.al. 2003 A 1 1 Lucas (a) Lucas (b) Mader Maguire (a) Magure (b)

2002 I 2002 I 2002 I 1999 I 1999 I

1 0 0 0 0

1 0 0 1 1

Mandal et.al. Mason et.al.

1998 A 0 0 2000 I 1 0

To To To To To To Sy Sy Sy To Sy Sy To Sy Sy To Sy Pe To To

McCarthy et.al. McFadde

To To To To To To Ph Ph

G M Se M M Se G G

0.2 TA 0.2 C 0.2 C 0.8 C 0.4 C 0.8 C 0.2 TA 0.3 Su

Y N N N Y N Y N

N N N N N N N Y

-

-

-

-

-

-

-

-

-

-

Y

-

-

Ph To M 0.4 C N N - - - - - - - - - - - - Ph G 1.5 TA Y Y - - - - - - - - - Y - - Pr To Ph Ph To Ph

G G M M M

Ph Pr G To G To Ph

M M

0.2 TA Y 0.2 TA Y 0.2 TA Y 0.2 TA N 0.2 C N N A Su R N 0.2 C N N A C N 0.2 TA Y

Y N N N Y

Y -

-

-

-

-

-

-

-

-

-

Y

-

-

Y Y Y Y - - - - - - - Y - Y - - - - - - - - - - - - -

2001 I 1 1 To 1993 A 1 1 Sy Pe Montgomery 2000 A 0 0 To Montgomery 2001 A 0 0 Sy Pe Montgomery 2002 A 0 0 To Montgomery et Pe al. 2001 I A 0 0 Sy Mukesh 2003 I 1 1 Sy Munro 2000 I 0 1 Sy Murugappan Sy 2003 I 0 0 To et.al. Nave 2002 I 1 0 Sy Neuscheler et.al. 2001 I 1 0 Sy Nevalainen et.al. 2000 I 0 0 Sy (a) Nevalainen et.al. 2000 I 1 1 Sy (b) Nielsen et.al. 1999 I 0 0 Sy Noble 2001 I 0 1 Sy Olexa 2003 I 0 0 To Pearson 2001 I 0 0 To

N - - - - - - - - - - - - N - - - - - - - - - - - - -

Ph

Se 1.3 TA Y N - - - - - - - - - - - - -

Ph Ph Ph Pr To

Se Se M M G

Plotkin et.al.

1999 I

0 1 Sy

Ph

Pyzdek (a)

2001 I

0 0 Sy

Ph

Ph Pr G 0.2 TA Y N - - - - - - - - - - - - Ph G 0.2 TA Y Y Y - - - - - - - - Y - - Ph Pr G 0.2 TA Y N - - - - - - - - - - - - Ph Ph Ph

G 1.5 TA Y N - - - - - - - - - - - - M 0.4 C N N - - - - - - - - - - - - M 0.2 Co N N - - - - - - - - - - - - -

Ph Pr Se 0.8 C N N - - - - - - - - - - - - Ph G 0.2 Co Y N - - - - - - - - - - - - Ph G 0.2 TA Y N - - - - - - - - - - - - -

1.3 Co 0.3 C 0.4 Su 0.3 C 0.2 TA N M A C N M A Co

137

N N N N Y

N N N Y N

-

-

-

-

Y -

-

-

Y -

-

-

-

-

-

N N - - - - - - - - - - - - N N - - - - - - - - - - - - -

Pe 0 0 To

Pyzdek (b)

2001 I

Ramberg

2000 A 0 1 Sy

Rasis et.al. (a)

2003 I A 1 1 Sy

Rasis et.al. (b)

2003 I A 1 0 Sy

Rayner Ribardo et.al.

1990 I 0 0 Sy 2003 I A 0 0 To

Riley et al. Rowlands et.al.

2002 A 1 0 Sy 2003 A 0 0 To

Sanders et.al. (a) 2000 I

0 0 Sy

Sanders et.al. (b) 2000 I

0 0 Sy

Sanders et.al. Sarewitz

2001 I 2000 I

0 0 Sy 0 0 Sy

Scalise

2001 I

0 0 Sy

Scalise Schmitt Schmitt Schmitt Sigal et al. Smith

2003 I 2000 I 2001 I 2002 I 2001 A 2003 I

0 0 0 0 1 0

Snee

1999 I

1 1

Snee (a)

2000 I

0 1

Snee (b) Snee (a)

2000 I 2001 I

0 0 0 0

Snee (b) Snee

2001 I 2003 I

0 0 1 0

Sy Sy Sy Sy Sy Sy Pe Sy Pe Sy Pe To To Pe To Sy

Stamatis Stein Studt Takikamalla Tang et.al. Treichler et.al. Trivedi Tylutki et.al.

2000 I 2001 I 2002 I 1994 A 1997 A 2002 I 2002 I 2002 A

0 0 1 0 0 0 0 0

Sy To Sy To To To Sy Sy

0 1 1 1 0 0

0 0 0 1 0 0 0 0

Ph To G 1.5 TA N Ph G A TA N Ph M A C N Ph M A C N Ph G A C To M 0.2 C N Ph Se A C To M 0.6 C N Ph G A TA N Ph Se A C N Ph G A TA Ph Se 1.3 TA N Ph M A Su N Ph Se A C Ph M 0.3 Su Ph M 0.3 Su Ph G 0.3 Su Ph Se 4.8 C Ph M 0.2 C Ph Ph

Y N - - - - - - - - - - - - Y Y - - - - - - - - Y - - - N N - - - - - - - - - - - - N N - - - - - - - - - - - - N N - - - - - - - - - - - - N N - - - - - - - - - - - - N N - - - - - - - - - - - - N N - - - - - - - - - - - - Y Y Y - Y - - - - Y - - - Y N N - - - - - - - - - - - - Y N - - - - - - - - - - - - Y N - - - - - - - - - - - - N N - - - - - - - - - - - - N N N N N N

N N N N N Y

Y

-

-

-

-

-

-

-

-

-

-

-

-

G 0.2 TA Y Y - - - - - Y - Y - - Y - N G A R Y N - - - - - - - - - - - - -

Ph To G 0.2 TA Y Y - - Y - - - - - - - - - To G 0.2 TA Y Y Y - - - - - Y - - - - - Ph To G 1.5 TA Y Ph G 0.2 TA Y N Ph M A C CoY To G 0.2 TA Y Ph G 0.7 TA Y To M 0.2 TA Y To M 0.2 Co Y Pr G 0.2 C N Ph M 0.4 C N Ph Se 0.2 C N

138

N - - - - - - - - - - - - N - - - - - - - - - - - - N N Y N N Y Y N

Y -

Y Y -

Y Y -

-

Y -

Y -

-

-

-

-

Y -

Y -

-

Vandenbrande

1998 I

0 0 To

To

Vaugham Velocci (a) Velocci (b) Velocci (c) Velocci Velocci Voelkel Walsh et.al.

1998 A 1998 I 1998 I 1998 I 2000 I 2002 I 2002 A 2000 I

0 0 0 0 0 0 0 0

1 1 0 0 1 0 0 0

To Ph Ph Ph Ph Ph To Ph

M 0.2 TA N G A C M 0.3 Co M 0.3 C M 0.3 C M 0.3 C M 0.3 Su G 0.2 C G 0.3 Su

Watson Watson (a) Watson (b) Waurayniak

2000 I 2002 I 2002 I 2002 I

0 0 1 0

0 0 0 0

Ph To Ph To

G Se Se M

Weinstein et.al. Westgard Wheeler

1998 A 0 0 2002 I 0 0 2002 I 0 0

Wiklund et.al. Wood

2002 A 0 0 Sy 2001 I 0 0 Sy Pe 2000 I 1 1 Sy 2003 A 0 0 Sy 1994 A 0 0 Sy

Wyper et.al. Yeung et.al. Yu et.al.

To Sy Sy Sy Sy Sy To Sy Pe Sy To Sy To Pe Sy To Sy

Y N - - - - - - - - - - - - N N N N N N N N

N N N N N Y Y N

-

Y -

Y -

-

Y -

-

-

Y -

-

-

-

Y -

Y -

0.2 Co N 0.2 C CoN 0.5 TA Y 0.3 Su N

N N N Y

-

-

-

-

Y

-

-

-

-

-

-

-

-

Ph G 0.2 Su Pr To Se 4.4 TA Ph M 0.4 Co N Ph Se A C Ph G 0.3 C N Ph Se A C Ph M 1.5 Su Ph M 0.4 R

139

N N - - - - - - - - - - - - N N - - - - - - - - - - - - N Y - - - - Y - - - - - - - N Y Y - Y - Y - - - - - Y - N Y Y Y - - - - - - - - - - N N - - - - - - - - - - - - N Y Y - - - - - - - - - - - N N - - - - - - - - - - - - -

APPENDIX B:

PROJECT DATABASE

Tabulated data from the 39 quality improvement and cost reduction projects used in the Meso-analysis study is presented on the next two pages.

140

Project 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Exp Savings $35000 $70000 $81315 $40000 $250000 $150000 $125000 $2200000 $50000 $39195 $34500 $21000 $25000 $20000 $10000 $20000 $28000 $20000 $20000 $4350 $13750 $8500 $1600 $12500 $4000 $13000 $15000 $6000 $11500 $4500 $11000 $5400 $150000 $8600 $90000 $30000 $45000 $240000 $50000

Exp Time L L M M L L L L M M L L M M M S M S S S S S S S S S L M M M S S S S M M S S S

M/I M M M M I M I M M M M M M M M M I M M M M M M M M M I I I I M M I I M M M I I

A/P A A A A P P P P P P A A A A A A P P P A A A A A A A P P P P P P P P A P A P P

#people 7 1 2 1 6 4 3 9 5 1 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 2 1 5 5 4 2 5 7 3 3 4

141

EC 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1

CH 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1

TF 1 0 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0

PM 2 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1

CE 1 0 0 0 2 0 0 3 1 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0

GR 0 0 0 0 2 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0

Project 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

DOE 0 1 0 0 2 0 1 4 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 1 0 2 0 1 0 1 0 0

SPC 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 1 0 0 1 0

DC 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 2 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1

FT 2 1 1 0 7 1 2 7 7 1 3 0 0 0 1 0 2 6 1 1 1 1 1 1 0 0 2 1 1 1 5 3 5 1 5 2 3 2 1

EA 0 1 1 1 0 1 1 4 2 1 2 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0

OF 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0

Time 13 18 25 20 16 9 7 30 5.5 14 18 18 18 20 8 9 4 1.5 3 3 3 3 3 3 18 8 19 2.5 8 4.5 3 1.5 6 1 3 10 13 12 1.5

142

Cost $48700 $7590 $35300 $2900 $325500 $76000 $17725 $220000 $31125 $12350 $22800 $2600 $2000 $7500 $30800 $2000 $12000 $5300 $1900 $1000 $1000 $1000 $3525 $3000 $1900 $1900 $12125 $1700 $12880 $3060 $4250 $2400 $38900 $1500 $12640 $18780 $38584 $15690 $1275

Act Savings $36000 $0 $31500 $0 $4E+06 $170000 $130500 $0 $97800 $19575 $13500 $0 $0 $21740 $17200 $0 $7000 $23220 $8050 $4025 $4025 $4025 $3125 $8400 $0 $0 $14985 $6500 $11700 $6300 $10900 $5375 $165440 $10750 $66100 $34056 $46300 $236280 $11927

Profit $-12700 $-7590 $-3800 $-2900 $3874500 $94000 $112775 $-220000 $66675 $7225 $-9300 $-2600 $-2000 $14240 $-13600 $-2000 $-5000 $17920 $6150 $3025 $3025 $3025 $-400 $5400 $-1900 $-1900 $2860 $4800 $-1180 $3240 $6650 $2975 $126540 $9250 $53460 $15276 $7716 $220590 $10652

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