Improvement of Failure Mode and Effects Analysis June, 2012
Student: 404340/Maria Bech Andersen Department: Business Administration Study: M.Sc. Business Intelligence
Supervisor: Rick Edgeman No. of characters (incl. space, excl. pictures): 116,633
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Table of content List of figures .......................................................................................................................3 List of tables ........................................................................................................................4 1.
2.
3.
Introduction .................................................................................................................5 1.1.
Motivation ..................................................................................................................... 5
1.2.
Topic .............................................................................................................................. 5
1.3.
Problem ......................................................................................................................... 6
1.4.
Problem Statement ....................................................................................................... 6
1.5.
Definitions/Abbreviations ............................................................................................. 6
1.6.
Limitations and assumptions ........................................................................................ 7
1.7.
Method and Paradigm .................................................................................................. 7
1.8.
Structure of the thesis ................................................................................................... 8
The traditional FMEA....................................................................................................9 2.1.
Failure Mode and Effects Analysis ................................................................................ 9
2.2.
Critique of FMEA and RPN........................................................................................... 13
Alternative FMEA approaches..................................................................................... 20 3.1.
Method A – Maximization & Minimization ................................................................. 20
3.1.1.
Theory ................................................................................................................. 20
3.1.2.
Example – method A ........................................................................................... 23
3.1.3.
Evaluation and comparison to traditional FMEA ................................................ 24
3.2.
Method B – Aggregated impact and if-then rules....................................................... 28
3.2.1.
Theory ................................................................................................................. 28
3.2.2.
Example ............................................................................................................... 32
3.2.3.
Evaluation and comparison to traditional FMEA ................................................ 36
3.3.
Method C – Geometric mean ...................................................................................... 38
3.3.1.
Theory ................................................................................................................. 38
3.3.2.
Example ............................................................................................................... 43
3.3.3.
Evaluation and comparison to traditional FMEA ................................................ 46
3.4.
Method D – Reliability of LEAN systems ..................................................................... 48
3.4.1.
Theory ................................................................................................................. 48
3.4.2.
Example ............................................................................................................... 49
3.4.3.
Evaluation and comparison to traditional FMEA ................................................ 49
Page 1 of 85
Master Thesis 29-06-2012 3.5.
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Method E – Experts average and ANOVA ................................................................... 51
3.5.1.
Theory ................................................................................................................. 51
3.5.2.
Evaluation and comparison to traditional FMEA ................................................ 54
4.
Comparison of alternative FMEA methods .................................................................. 56
5.
The combined FMEA................................................................................................... 60
6.
Conclusion ................................................................................................................. 62
7.
Perspective ................................................................................................................ 69
8.
Literature ................................................................................................................... 71
9.
Appendices ................................................................................................................ 74 9.1.
Appendix: Definition of the Severity scale .................................................................. 74
9.2.
Appendix: RPN values.................................................................................................. 76
9.3.
Appendix: Data for Occurrence scales ........................................................................ 78
9.4.
Appendix: Membership function RCN – Method B..................................................... 79
9.5.
Appendix: Action Categories – Method B ................................................................... 80
9.6.
Appendix: Excel functions for Severity – Method C .................................................... 81
9.7.
Appendix: Excel functions for Occurrence and Detections – Method C ..................... 82
9.8.
Appendix: Calculation of limits – Method C ................................................................ 83
9.9.
Appendix: Histograms – Method E2 ........................................................................... 84
9.10.
Appendix: Kruskal-Wallis – Method E2 ................................................................... 85
Page 2 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
List of figures Figure 1 – Structure of the thesis………………………………………………………..8 Figure 2 – The RPN distribution……………………………………………………….14 Figure 3A – Occurrence comparison…………………………………………………..16 Figure 3B – Chrysler‟s Occurrence…………………………………………………….16 Figure 3C – Wang et al.‟s Occurrence…………………………………………………16 Figure 3D – Stamatis‟ Occurrence……………………………………………………..16 Figure 4A – Traditional RPN vs. Inputs at Occurrence = 10…………………………..19 Figure 4B – Fuzzy RPN with FPR vs. inputs at Occurrence = 10……………………..19 Figure 4C – Fuzzy RPN with WFPR vs. inputs at Occurrence = 10…………………..19 Figure 5 – Membership Functions for (O), (CI), (TI), (SI), (AI)………………………29 Figure 6 – Membership Functions for (D)……………………………………………..30 Figure 7 – Fuzzy if-then-rules………………………………………………………….34 Figure 8 – Membership functions for fuzzy Occurrence rating………………………..39 Figure 9 – Membership functions for fuzzy Severity rating…………………………...40 Figure 10 – Membership functions for fuzzy Detection rating………………………...41 Figure 11 – Membership functions for fuzzy weights………………………………….42
Page 3 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
List of tables Table 1 – Definitions of Severity Scale (rank 1-4)……………………………………..12 Table 2 – Risk levels based on RPN……………………………………………………13 Table 3 – Statistics for the RPN………………………………………………………..14 Table 4 – Average RPN………………………………………………………………...15 Table 5 – Overview of levels – Method A……………………………………………..21 Table 6 – Calculations – Method A…………………………………………………….23 Table 7 – Failure mode indices – Method A2………………………………………….26 Table 8 – Membership functions for (O), (CI), (TI), (SI), (AI) – Method B…………..29 Table 9 – Comparison Scale for sub dimensions – Method B…………………………31 Table 10 – Membership function for RCN – Method B………………………………..31 Table 11 – Data – Method B…………………………………………………………...32 Table 12 – Defuzzification of Impact sub dimensions – Method B……………………33 Table 13 – Relations between Impact sub dimensions – Method B……………………33 Table 14 – Aggregated Impact – Method B……………………………………………33 Table 15 – Evaluation of failure modes – Method B…………………………………..35 Table 16 – Results of traditional FMEA – Method B………………………………….36 Table 17 – Fuzzy Rating of Occurrence – Method C………………………………….39 Table 18 – Fuzzy rating of Severity – Method C………………………………………40 Table 19 – Fuzzy Rating of Detection – Method C……………………………………41 Table 20 – Fuzzy weights – Method C………………………………………………...41 Table 21 – Team members‟ evaluation – Method C…………………………………...43 Table 22 – Severity Calculations – Method C…………………………………………44 Table 23 – Occurrence Calculations – Method C……………………………………...45 Table 24 – Detection Calculations – Method C………………………………………..45 Table 25 – Calculations for centroids – Method C…………………………………….46 Table 26 – Prioritization of failure modes – Method C………………………………..46 Table 27 – Results – Method D………………………………………………………..49 Table 28 – Statistics for the RAV – Method D………………………………………..50 Table 29 – RPN – Method E1………………………………………………………....52 Table 30 – Skewness and Kurtosis…………………………………………………….53 Table 31 – Test of homogeneity……………………………………………………….53 Table 32 – ANOVA……………………………………………………………………53 Table 33 – Bonferroni‟s test……………………………………………………………54 Table 34 – Kruskal-Wallis test…………………………………………………………55 Table 35 – Average of Occurrence ranks………………………………………………59 Page 4 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
1. Introduction 1.1.Motivation For eight months I have been working full time with different kinds of risk assessments in a large global company delivering energy solutions around the world. One of the most used methodologies was the Failure Mode and Effects Analysis (FMEA). Working with FMEA in practice has been really exciting and challenging but also frustrating from time to time. There are many ways to perform a FMEA and even more ways to interpret the result. Often people tend to do as usual without questioning if it is the most efficient way. Stamatis (2003, p. xxiii) describes the problem perfectly: “If you always do what you always did, you will always get what you always got”. Personally the FMEA keeps appearing in my head, I need to know the answer: Does the optimal FMEA exist and if not, how much can the traditional FMEA be improved?
1.2.Topic The first formal FMEA design was developed in the 1963 by NASA (Gilchrist, 1993). Besides the aerospace industry the methodology quickly expanded to the automotive industry and the nuclear industry. Today FMEA is widely used, especially in connection with Six Sigma. One of the most famous Six Sigma methodologies is DMAIC, which is used for making incremental improvement of existing processes. The DMAIC methodology consists of the five phases; Define, Measure, Analyze, Improvement and Control (Kubiak and Benbow, 2009). In Six Sigma the use of FMEA differs depending on the phase of the DMAIC model. Even though the overall approach is the same in all phases, the focus of the FMEA will change. In the Measure phase FMEA is mainly used for prioritizing the elements of the project in order to find the right focus. Furthermore FMEA can be used to find potential failure modes regarding the process itself. In the Analyze phase FMEA creates an overview of the root causes. The FMEA is not used for the actual identification of root causes but it is used for connecting and prioritizing the root causes and the potential failure modes. There are three main goals of the Improvement phase (Ginn et al., 2004); first of all actions should be planned and tested in order to eliminate or reduce root causes of a problem. Secondly a “before” and “after” analysis should be made based on data in order to show how much of the concerned gap has been closed. And finally the output should be measured to show the actual implementation against Page 5 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
the intended plan. The Improvement Phase contains several tools, among those one of the most important is FMEA. In the Improvement phase FMEA is often used before implementing the improvements in order to identify potential failure modes that the improvements could arise. Unlike the cases above FMEA is based on real data in the Control phase. Here FMEA is often used as a tool for continuous improvement.
1.3.Problem Even though FMEA is a very popular methodology it has drawbacks that can lead to wrong decisions. When dealing with failure modes a wrong decision can have huge costs both for replacement of the damaged component, compensation to the involved people in case of human injuries but especially also for injuring the company‟s reputation. The method to prioritize risks is a highly discussed subject. But a lot of different approaches solving one problem at a time do not help the companies. They need one “best practice” or at least a “best practice given the business situation”. The method needs to be simple and easy to use and understand. That said the method also need to be reliable otherwise there is no reason for using it.
1.4.Problem Statement 1. 2. 3. 4.
What is the traditional FMEA approach? Which different kinds of overall FMEA exist? What are the advantages and drawbacks of using the traditional FMEA? What optimizing alternatives exist to the traditional FMEA?
5. In a comparison how well are the alternative FMEA methods doing? 6. What would be a preferable FMEA approach?
1.5.Definitions/Abbreviations FMEA S O D AI CI TI SI RPN RPC RCN RAV FRPN
Failure Mode and Effects Analysis Severity Occurrence Detection Aggregated Impact Cost Impact Time Impact Scope/Quality Impact Risk Priority Number Risk Priority Code Risk Criticality Number Risk Assessment Value Fuzzy Risk Priority Number Page 6 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
1.6. Limitations and assumptions Only the use of Failure Mode and Effects Analysis (FMEA) in connection with the Improvement phase in the DMAIC model will be discussed in this thesis. In this connection it is assumed that only qualitative data is available for the user of the FMEA. The thesis is delimited from the FMEA methods interaction with other Six Sigma tools such as brainstorming, tree diagram, cause-and-effects diagram and production board. The main focus of the thesis will be; how to rank the risks against each other in order to make a prioritization of actions. Consequently a big part of the focus will be how to use the Risk Priority Number in a more balanced way than a simple multiplication of Severity, Occurrence and Detection. Another main topic will be the definition of the dimensions used for the prioritization of the risks. It should be mentioned that this Master Thesis does not contain any information from the company mentioned in chapter 1.1. All data in the thesis will only be of an illustrative purpose in order to highlight advantages and drawbacks of the different approaches.
1.7. Method and Paradigm The paradigm that will be used during the thesis is constructivism with the aim of understanding and reconstruction of other people‟s constructions (Guba & Lincoln, 1994). Following the Hermeneutical point of view there will not be only „one reality‟. The answer for the ontological question is that the reality cannot be understood 100 %, it depends on the individual mind. The answer to the epistemological questions is that the result of the analysis depends on the interaction between the researcher and the research hence subjectivism will be an important part. And finally the answer to the methodological question is that the researcher will find information based on a broad variation of individual constructs. The thesis will follow the Actor based way of thinking. Firstly a pre-understanding of FMEA will happen, then an understanding of the alternative FMEA methods by analysis of advantages and drawbacks will be achieved and finally a post understanding will be made during a comparison of the alternative FMEAs and a construction of a combined FMEA.
Page 7 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
1.8.Structure of the thesis The thesis consists of seven chapters. Chapter 1 is an introduction and includes the motivation for writing the thesis, the problem and the problem statement, definitions and limitations. Chapter 2 includes a description of the traditional FMEA approach and an analysis of the advantages and drawbacks. In chapter 3 some of the most interesting alternative FMEA approaches will be investigated with the purpose of overcoming the drawbacks of the traditional FMEA. Chapter 4 contains a comparison of the alternative FMEAs. Based on chapter 1-4 a new FMEA approach will be constructed in chapter 5. Chapter 6 contains the conclusion and chapter 7 contains the perspective.
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
• Introduction • Motivation / Topic • Problem / Problem statement • Definitions / Limitations
Figure 1: Structure of the thesis
• The Traditional FMEA • Desciption of the traditional FMEA approach • Analysis: advantages and drawbacks
• Alternative FMEA approaches • Desciption of alternative FMEA approaches • Examples to explain the methods • Analysis: advantages and drawbacks in relation to the traditional FMEA
• Comparision of alternative FMEA approaches • Analysis: advantages and drawbacks in relation to the other alternative FMEAs • Any preffered FMEA approach to use?
• Construction of an improved FMEA • Include the best parts from existing FMEAs • Focus on userfriendliness
• Conclusion • Any FMEA approach better than the rest • How much can the traditional FMEA approach be improve
• Perspective • Quantitative FMEAs •Cost-based FMEAs
Source: Own contribution
Page 8 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
2. The traditional FMEA 2.1.Failure Mode and Effects Analysis In accordance to Stamatis (2003) there are four types of overall FMEAs; System-, Design-, Process- and Service-FMEA. The System-FMEA (also called ConceptFMEA) is used in the beginning of the concept and design stage to analyze systems and subsystems. The System-FMEA focuses on failure modes between the functions of the system caused by deficiencies in the system. The Design-FMEA shows attention to the failure modes caused by deficiencies in the design and is used to analyze products before going to production. The Process-FMEA is used for analysis of manufacturing and assembly processes. The focus of a Process-FMEA is failure modes caused by deficiencies in processes or assembly. The Process-FMEA is e.g. used in the measurement phase in the DMAIC model. In the Service-FMEA the service is analyzed before it reaches the customer. The focus of the Service-FMEA is on failure modes like tasks, errors and mistakes caused by deficiencies in processes or the system. That the FMEA is a well accepted approach is also reflected by its appearance in international standards. FMEA is described in four international standards; MIL-STD 1629A (DoD 1980), IEC 60812 (IEC 1985), BS EN 60812 (BSI 2006) and the SAEJ1739 (SAE 2002) (Braksmaa et al., 2011). According to Stamatis (2003) the FMEA has two overall goals; one short term and one long term. The short term goal is to reduce the failures as much as possible and the long term goal is to eliminate all failures. Having that said the costs of reduction/elimination should of course also be considered. At one point in time the cost of reducing a failure mode further will probably be higher than the benefit of doing so. Beside that the rest of the organization should also be considered when evaluating what is most important; to do a FMEA over again or maybe to do another risk assessment with a new focus. For some companies the only purpose of performing a FMEA is to please the customers (Teng and Ho, 1996). Performing a FMEA based on this reason is very dangerous because the benefits of performing the FMEA will be reduced and often the increased customer satisfaction will not compensate the cost of performing the FMEA. The purpose of the FMEA in general is to identify potential failure modes and rank those against each other based on the risk level they pose from the ranking of the failure Page 9 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
modes the mitigation actions can be prioritized. Most risk assessments only evaluate on two dimensions; the consequence of the risk and the likelihood that it will happen. The traditional FMEA classifies the failure modes based on three dimensions; evaluation of Severity (O) of the failure effect, frequency of Occurrence (O) and likelihood of Detecting (D) if the failure mode occurs (Gitlow and Levine, 2010). Stamatis (2003) describes the process of conducting a FMEA as an eight stage process. 1) The team is selected and brainstorming is performed in order to identify the main problems and to decide which kind of FMEA should be used. The team can beneficially consist of both customers, manufacturing-, test-, quality-, reliability-, product- and sales-engineers (Teng and Ho, 1996). 2) In case of a System-FMEA or Design-FMEA a functional block diagram should be made. In case of a Process-FMEA or a ServiceFMEA a flowchart should be made instead. The graphics should be made to make sure that everybody is aligned. 3) A prioritization of the elements in the project should be performed based on the importance of the elements. Furthermore a plan should be made for where the team should begin. 4) Data of the failures should be collected and a categorization should be made. 5) The actual analysis is made either as a qualitative or quantitative analysis depending of the phase of the products development. Several tools can be helpful such as; brainstorming, cause-and-effect analysis, Quality Function Deployment, Design of Experiments, Statistical Process Control, other FMEAs performed earlier and reliability analysis. 6) Results will be delivered in the shape of a quantification of Severity, Occurrence, Detection and RPN. 7) Finally it should be confirmed, evaluated and measured whether the new situation is better or worse than before. 8) Because the philosophy behind FMEA is continuous improvement it should be considered to do the FMEA all over again. Teng and Ho (1996) also highlight the importance of ensuring that the FMEA process does not stop just because the FMEA report is done. The FMEA is a continuous process and it should be linked to process control. According to Teng and Ho (1996) one of the goals of implementing the FMEA should be to create a process control plan in order to minimize the occurrence of failures. Besides the S, O and D ranks the traditional FMEA also includes a lot of other important information. The following list in based on a traditional FMEA by Stamatis (2003): Page 10 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
System/Design/Process/Service Function Potential Failure Mode Potential Effect(s) of Failures Potential Cause(s) of Failure Detection Method Severity (S) Occurrence (O) Detection (D)
Student no.: 404340 Maria Bech Andersen
Risk Priority Number (RPN) Recommended Action Responsibility & Completion Date Actions Taken (Completion Date) Severity (new evaluation) Occurrence (new evaluation) Detection (new evaluation) RPN (new evaluation)
A slightly modified version by Chrysler LLC et al. (2008) adds three extra columns; Requirements of the function being analyzed, Classification with the purpose of highlighting high-priority failure modes and Current Prevention Controls describing activities that have been done to prevent the causes of the failure. Whereas many other risk assessments use a 5-point scale, the traditional FMEA uses 10-points scales (1-10) for S, O and D which gives a finer ranking. The definitions of the scales vary from author to author but in general the scales are used for transferring a verbal evaluation of the failure mode into an ordinal number that can be used for ranking the failure modes against each other. It is important to be aware that the ordinal scale only allows ranking and does not contain any relation between the failure modes e.g. a Severity rank of 8 is not four times as severe as a rank of 2. In table 1 two sets of scale definitions for Severity in a Design-FMEA are shown. Comparing the two sets of scale definitions for Severity, Stamatis (2003) and Chrysler LLC et al. (2008) generally agree very well on the definitions. Even though the wording is different, the main points are the same. The only definitions with a difference are for Rank 3 and 4. Stamatis (2003) defines rank 3 as a nonvital fault being noticed most of the time whereas Chrysler LLC et al. (2008) defines rank 3 as a nonvital fault being noticed by many customers (50 %). Regarding rank 4 Stamatis (2003) defines it as nonvital fault always being noticed whereas Chrysler LLC et al. (2008) defines rank 4 as nonvital failures being noticed by most customers (>75 %). It seems in both cases that Stamatis (2003) define the scale with a higher probability of the nonvital fault being noticed by the customers.
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Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
1
Very slight
2
Customer not annoyed. Very slight effect on product performance. Nonvital fault noticed sometimes.
None
No effect
…
… Annoyance
Slight
3
Customer experiences minor nuisance. Minor effect on product performance. Fault does not require repair. Nonvital fault always noticed. Customer slightly annoyed. Slight effect on product performance. Nonvital fault noticed most of the time.
No effect
Minor
4
…
…
…
Table 1: Definitions of Severity Scale (rank 1-4)* Rank Effect Criteria Effect Criteria Stamatis (2003) Chrysler LLC et al. (2008)
Appearance or Audible noise, vehicle operable, item does not conform and noticed by most customers (>70 %) Appearance or Audible noise, vehicle operable, item does not conform and noticed by many customers (50 %) Appearance or Audible noise, vehicle operable, item does not conform and noticed by discriminating customers ( 0, thus the RPN distribution peaks more than a normal distribution. Furthermore table 3 shows that the distribution of the RPN is right skewed because skewness > 0. The percentiles also indicate the skewness because the values are very low in relation to the maximum value of 1,000. Figure 2 shows a graphical overview of the RPN. Here it is also easy to see that the distribution is right skewed. Figure 2: The RPN distribution
RPN distribution Number of appearance
30 25 20 15 10 5 0 1
51 101 151 201 251 301 351 401 451 501 551 601 651 701 751 801 851 901 951 RPN
Output from Excel. Own contribution The RPN scale [1; 1,000] further indicates that RPN can take value of all natural numbers in between but as mentioned in chapter 2.1 the RPN can actually only take value of 120 different numbers. Figure 2 shows that a lot the S, O, D combinations
Page 14 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
result in the same RPN values e.g. a RPN of 60, 72 and 120 appears 24 times. Actually only six RPN values (1, 125, 343, 512, 729 and 1,000) are unique. Another problem about the traditional FMEA is if the team experts do not agree on the S, O, D ranking. Often the experts will not recommend the same ranks of S, O and D for a given failure mode. Hence, the Severity rank will be an average of the team experts individual severity ranks. If the experts have to agree on one rank some of team members might be more aggressive and speak well for their opinions and thereby the rank will be influenced in a specific direction. And the aggressive and loud speaking experts are not necessarily the experts with the most knowledge about the subject. There are two overall ways to calculate a simple average of the RPN; calculating the RPN based on average S, O and D or calculating the RPN as the average of the experts individual RPNs. Table 4 shows that the two ways of calculating give different results. RPN (1) based on average S, O and D is 105 and RPN (2) based on team experts individual RPNs is 127. Table 4: Average RPN Expert Ex1 Ex2 Ex3 Ex4 Ex5 Average RPN 1
S 1 2 4 3 5 3
O 2 4 7 6 6 5 105
D 9 3 6 7 10 7 RPN 2
RPN 18 24 168 126 300
127.2
Own contribution Franceschini & Galetto (2001) further criticize that the calculation of the RPN assumes that S, O and D all have the same metric (a 10-point scale). Furthermore it is assumed that the danger level for each scale value is the same for S, O and D. Beside the main points Franceschini & Galetto (2001) highlight a potential problem of using numeric scales for S, O and D. When using the numbers [1; 10] stakeholders of the FMEA will easily assume that a linear relation exists between the scale elements, hence there is a high risk that people will interpret e.g. an Occurrence at 4 as twice as bad as an Occurrence at 2. Figure 3A, 3B, 3C and 3D show the relation in the Page 15 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Occurrence scale based on different authors‟ definitions (data is available in table 3.1 in appendix 3). Figure 3A includes scale relations based on definitions from all three authors. Rank 10 and rank 1 are intentionally left out because rank 10 is defined by the use of “≥“ and rank 1 is defined by the use of “≤”. Figure 3A: Occurrence comparison
Figure 3B: Chrysler’s Occurrence
0,35 0,3 0,25 0,2 0,15 0,1 0,05 0
Likelihood of Occurrence
Chrysler LLC Stamatis
Probability
Probability
Likelihood of Occurrence
Wang et al. 2 3
0,14 0,12 0,1 0,08 0,06 0,04 0,02 0
y = 1E-07e1,5351x R² = 0,9692 Chrysler LLC
4 5 6 7 8 9
2
3
Occurrence Rank
4 5
6
7
Expon. (Chrysler LLC)
8 9
Occurrence Rank
Source: Own Contribution
Source: Own Contribution
Figure 3C: Wang et al.’s Occurrence
Figure 3D: Stamatis’ Occurrence
Likelihood of Occurrence
Likelihood of Occurrence 1
y = 7E-07e1,5339x R² = 0,9781
0,60 0,40 0,20
Wang et al.
0,00 2 3 4 5 6 7 8 9 Occurrence Rank
Source: Own Contribution
Expon. (Wang et al.)
y = 2E-07e1,6713x R² = 0,947
0,8 Probability
Probability
0,80
0,6 0,4
Stamatis
0,2 0 2
3
4
5
6
7
8
9
Expon. (Stamatis)
Occurrence Rank
Source: Own Contribution
Figure 3A shows that Stamatis (2003) and Wang et al. (2009) define the Occurrence in a very similar way. Chrysler LLC et al. (2008) on the other hand defines Occurrence at a much lower probability, e.g. if Occurrence has a rank of 8 by Chrysler (2008)‟s definition it equals a rank 6-7 by Wang et al. (2009) and Stamatis‟ (2003) definitions. This reflects the option of individualization of the Occurrence scale based on the product, in case of Chrysler; adaption to the vehicle industry. Figure 3B, 3C and 3D show that the relation between the ranks in all three cases approximates to an exponential function (R2 varies from 0.947 to 0.9781).
Page 16 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
The scales for Severity and Detection cannot be translated into a mathematical function because the definitions of the two scales are only verbal. The scale definition for Detection has been discussed by several authors. E.g. Bowles (2003) criticizes the name “Detection”. His point is that people easily misunderstand the dimension. People tend to focus on if the failure will be detected when it occurs rather than if the actual existing failures can be detected by subsequent testing. Carbone and Tippet (2004) have made the following definition of Detection: “The ability of detection technique or method(s) to detect the risk event with enough time to plan for a contingency and act upon the risk”. Also Rhee and Ishii (2004) have criticized the dimension Detection. For them the main problem about Detection is that the definition differs between two main definitions; either Detection is a measure of how easy it is to detect the failure when it occurs or it is a measure of how easy it is to prevent the failure. Abdelgawad & Fayek (2010) criticize that control is not a clear part of the Detection dimension. Abdelgawad & Fayek (2010) define Detection as: “The ability of the risk response strategy to detect and control the root causes before they lead to the occurrence of the risk event, and to control the effect given the occurrence of the risk event”. Bowles & Peláez (1995) and Gilchrist (1993) highlight the fact that RPN is calculated by a simple multiplication of S, O and D which consequently lead to a possibility of having the same danger level for completely different situations. E.g. the three failure modes (S=2, O=2, D=4), (S=1, O=4, D=4) and (S=8, O=2, D=1) will all result in a RPN at 16 and will therefore be interpreted as having the same danger level. The consequence can be that some high-risk failure modes will remain unnoticed. Pillay and Wang (2003) criticize that the formula for RPN is a function with no weighting of the inputs S, O and D. This means that the formula automatically assumes that the three dimensions all are equal of importance. According to the traditional FMEA a RPN at 35 and below is classified as a “low risk” no matter how the dimensions are ranked. Having a failure mode of S=10, O=2 and D=1. The failure mode is so severe that it should be seriously considered to take a mitigation action even though RPN is only 20.
Page 17 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Tay and Lim (2010) have dived deeper into the problem of assuming that the three dimensions are equal of importance. Tay and Lim (2010) are convinced that RPN should be modeled as a non-linear function of S, O and D. Besides being able to weight the S, O and D dimensions, the perfect RPN model should give an incremental output if any of the inputs increases. This means that if two of the dimensions are frozen and the third dimension increases then the RPN should also never decrease. To illustrate their considerations Tay and Lim (2010) undertake a case study based three FMEA techniques: the traditional RPN, a fuzzy RPN with Fuzzy Production Rules (FPR) and a fuzzy RPN with Weighted Fuzzy Production Rules (WFPR). A FPR is a rule consisting of inputs in form of previous events and an output in form of a consequence. The general formula for a FPR is (Tay and Lim, 2010): , Then Y is Gm. Instead of the FPR, Tay and Lim (2010) recommend to use the WFPR. Unlike the FPR the WFPR is capable of comparing the relative importance level of one rule with other rules in an inference path. Furthermore the WFPR is capable of showing the relative importance level of a rule when it is used in several different inference paths. Bradley and Guerrero (2011) have set up three technical axioms that multi criteria decision algorithms must satisfy in connection with FMEA: 1) Pareto optimality: if for failure mode “n” and “m”: On ≥ Om, Sn ≥ Sm and Dn ≥ Dm => then RPN(S,O,D)n ≥ RPN(S,O,D)m. 2) Transitivity: if for failure modes n, m and k: RPN(S,O,D)n > RPN(S,O,D)m and RPN(S,O,D)m > RPN(S,O,D)k => then RPN(S,O,D)n > RPN(S,O,D)k. 3) Independence of irrelevant alternatives: if RPN(S,O,D)m > RPN(S,O,D)k for failure modes m, k ∈ {1, . . . , N} => then the relative ranking of m and k will not change when an additional failure mode N + 1 is introduced. The result of Tay and Lim‟s (2010) study shows that when FMEA is performed based on a fuzzy RPN with FPR or a fuzzy RPN with WFPR then the result is equal to the experts‟ evaluations. Performing FMEA based on the traditional RPN model does not lead to the same conclusion as the experts‟ evaluations. The study further shows that the fuzzy RPN with FPR has a limitation regarding the output. The results can be seen in
Page 18 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
figure 4A, 4B and 4C, that show the outcome of the three methods when Occurrence is fixed at 10.
Figure 4A: Traditional RPN vs. Inputs at Occurrence = 10 Source: Tay & Lim (2010)
Figure 4B: Fuzzy RPN with FPR vs. inputs at Occurrence = 10 Source: Tay & Lim (2010)
Figure 4C: Fuzzy RPN with WFPR vs. inputs at Occurrence = 10 Source: Tay & Lim (2010) Figure 4A shows a clear monotone relation for the RPN. A drawback of the method is that it does not distinguish between the importance of the dimensions, hence the RPN for (S=4, O=10, D=7) is the same as for (S=7, O=10, D=4). Figure 4B shows that unlike the traditional RPN the fuzzy RPN with FPR does not have a monotone output, hence it is possible that a failure mode of (S=2, O=10, D=3) has a higher RPN than a failure mode of (S=2, 10=O, D=4). Figure 4C shows a monotone relation when using WFPR. Furthermore figure 4C shows the difference between an increase in Severity and Detection, in the given case Severity has a higher importance than Detection. An
Page 19 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
example is if Detection is fixed to 1 then the RPN will have a higher increase when Severity increases than if Severity is fixed to 1 and Detection increases. Besides the drawbacks mentioned above also more practical issues exists. Teng and Ho (1996) mention problems like: timing of the FMEA process at the product/process design stage, establishment of the FMEA expert team and coordination of getting different departments to deliver input to the FMEA simultaneously. A FMEA has a lot of different stakeholders. Therefore it is very important that the result of the FMEA can be shown in a fast and understandable way. An unambiguous result is crucial if people should use the FMEAs in their daily work. As it is today when using the traditional FMEA, people have to combine the RPN and the individual scores for S, O and D in order to be able to make a correct prioritization of the failure modes. This confuses people that are not used to work with FMEA and even though people are aware of the problems with the RPN, they often use it isolated anyway simply because it is fast and easy. According to Bradley and Guerrero (2011) one of the most important things in modifying a FMEA is to find the trade-off between simplicity and accuracy. To strengthen the traditional FMEA several fuzzy FMEA methods have been created. Most of the new fuzzy methods evaluate S, O and D according to the traditional FMEA but furthermore the fuzzy methods take importance of S, O and D into consideration during the risk prioritization. In chapter three some of the alternative FMEAs will be investigated and compared with the traditional FMEA.
3. Alternative FMEA approaches In this chapter several alternative methods to the traditional FMEA are investigated. For each alternative FMEA approach the theory behind is explained and an example shows the practical use of the method. Based on the theory and the example advantages and drawbacks are discussed and a comparison of the alternative and the traditional FMEA is made.
3.1. Method A – Maximization & Minimization 3.1.1. Theory
Method A is based on Francescini & Galetto‟s (2001) alternative FMEA. Francescini & Galetto (2001) made a fuzzy FMEA in the attempt to overcome the following weaknesses of the traditional FMEA: Page 20 of 85
Master Thesis 29-06-2012
-
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
The RPN does not allow different importance for S, O and D. As a consequence the dimensions influence on the RPN will always be at the same level no matter the circumstances.
-
It is not possible to distinguish between two failure modes with the same RPN.
-
The RPN scale is easily misunderstood as being on a quantitative scale.
-
Compared with the scales for S, O and D the RPN scale is too wide.
Method A consists of three overall steps to make the fuzzy FMEA. In the following formula [1] – [4] are based on Francescini & Galetto‟s (2001) FMEA approach. Step 1) Experts give Risk Levels for S, O and D. The importance is given based on a 10point scale. Table 5 shows the definitions of the scales for S, O and D as well as for the Importance (I(g)) of the dimensions. Table 5: Overview of levels – Method A Level L1 L2 L3 L4 L5 L6 L7 L8 L9 L10
Severity No Very slight Slight Minor Moderate Significant Major Extreme Serious Hazardous
Occurrence Almost never Remote Very slight Slight Low Medium Moderately high High Very high Almost certain
Detection Almost certain Very high High Moderate high Medium Low Slight Very Slight Remote Almost impossible
I (gi) No Very low Low Minor Moderate Significant Major High Very high Absolute
Source: Francescini & Galetto (2001), table 5 Step 2) Calculation of the RPC for all alternatives (am). A given alternative (ai) can be expressed by formula [1]: [1] Where: = failure mode alternatives, (i = 1, …, m) = evaluation criteria, (j = 1, …, n) = Risk Priority Code for failure mode ai = importance of each evaluation criteria = negation of importance
Page 21 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
In words formula [1] can be described as following: for each dimension the maximum level of the negation of the evaluation criteria is importance and the level of the criteria itself are chosen. From the maximum levels of the dimension the minimum level is chosen as the RPC for the failure mode. Dealing with a z-point ordinal scale formula [2] calculates the negation: [2] where Li is the i‟th level of the scale According to the 10-points scales for S, O, D and the Dimension Importance the negations will be:
In method A the importance of a dimension can have a big influence on the final result. The role of the importance can be explained as; if the criterion has a high level of importance then the negation of the level will be a low level. Because formula [1] is a minimization function the lower the importance level the bigger chance to influence the RPC result. If for instance the importance of Severity is evaluated as “very high” it will be a L9. The negation of the importance will be L2, hence the importance will potentially have a big impact on the RPC because the overall function is a minimization function. Step 3) The failure modes are prioritized. The ranking is based on formula [3] which in short terms interprets the failure mode with the highest RPC as the most dangerous failure mode. [3] Where: A = set of failure modes = Risk Priority Code for failure mode ai In case that two or more failure modes have the same RPC the indicator can be used to break down the analysis; [4] Where: = number of elements in
Page 22 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
The indicator makes it possible to rank failure modes based on the number of high evaluations for the important criterion hence the ranking of S, O and D will be compared against the RPC. For instance if RPC = L7, then the number of rankings above L7 for S, O and D for the given failure mode should be summarized and the failure mode with most rankings above the RPC level will be the most dangerous failure mode. 3.1.2. Example – method A
In the following an example will demonstrate the use of method A in practice. The three dimensions S, O and D and their corresponding importance are evaluated and levels are given in table 6. Step 1) Calculation of RPC The RPC is calculated for all failure modes by use of formula [1]. As an example the calculation for failure mode a1 is shown:
The calculation above shows that the low importance of detection does not influence the result because the negation of the importance changes it to a very high level and the final function is a minimization function. In general the calculations are made in Excel so that they are automatic. The calculations are set up as dependent functions, thus it will be possible to only change the input data in table 6 and then the rest of the calculations adjust automatically. With a few failure modes this will not make a big difference but with several FMEA reports each containing a large number of failure modes the automation can be a crucial factor. Table 6: Calculations – Method A Levels Failure Mode
a1 a2 a3 a4 I(g) Neg(I(g) )
Levels - numeric
Maximization
Minimization
S
O
D
S
O
D
RPN
S
O
D
RPC (a)
T(a)
L8
L3
L4
8
3
4
96
8
6
9
6
1
L5
L7
L2
5
4
4
80
5
6
9
5
0
L3
L2
L3
2
8
5
80
2
8
9
2
2
L9 L9
L5 L4
L8 L2
9 9
5 5
8 2
360
9
6
9
6
2
2
6
9
Ranks Met. A RPN Rank Rank
2 3 4 1
2 3/ 4 3/ 4 1
Source: Own contribution Page 23 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Excel formulas for table 6: Numeric levels: IF(Level=”L1”,”1”, IF(Level=”L1”,”1”, IF(Level=”L2”,”2”, IF(Level=”L3”,”3”, IF(Level=”L4”,”4”, IF(Level=”L5”,”5”, IF(Level=”L6”,”6”, IF(Level=”L7”,”7”, IF(Level=”L8”,”8”, IF(Level=”L9”,”9”, IF(Level=”L10”,”10”, 0) Based on formula [2]:
Neg(I(g)) = 11 – I(g)
Based on the inner formula [1]:
Maximum = MAX(
Based on the outer formula [1]:
RPC = MIN(S_leveli; O_leveli; D_leveli)
Based on formula [4]:
)
T(a) = COUNTIF(S_leveli; O_leveli; D_leveli; “>"&RPCi)
Step 2) The maximal RPC is chosen The maximal RPC is found by the use of formula [3]: ∈
Failure modes a1 and a4 are the most dangerous failure modes because they both are evaluated as L6. In order to prioritize failure mode a1 against a4 the indicator, formula [4], is used. As an example the calculation is shown for failure mode a1:
From table 6 the conclusion is that T(a4) > T(a1) hence a4 is more dangerous than a1. Using the RPC ranking together with indicator scores failure mode a4 is evaluated to be the most dangerous failure mode. The second most dangerous failure mode is a1. The example also shows how the indicator T(ai) can be used for breaking the analysis further down when two failure modes have the same RPC. Based on the RPC of the failure modes it can be concluded that a3 is the least dangerous failure mode. 3.1.3. Evaluation and comparison to traditional FMEA
Table 6 also shows the result if the traditional RPN is calculated based on the same data. The columns at the right in table 6 show how the failure modes are ranked both when using Method A and the traditional FMEA. The ranking of the failure modes are different for failure mode a2 and a3. In the traditional FMEA the two failure modes cannot be distinct from each other even though the dimension ranks are different. When
Page 24 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
two failure modes have the same RPC in method A the indicator is taken into consideration. The different prioritization by method A is a result of the weighted importance of the three dimensions. Because the importance of Severity is relatively higher than for Occurrence and Detection, Severity has a potential higher influence on the RPC. The importance weight is only given as a global weight hence only one overall weight is given to each dimension. Method A is limited to ranking the failure modes and thereby ranking the corrective actions. From the prioritization it is not possible to see when an action must be taken, when it should be considered and when it is not necessary. In other words method A does not operate with action rules as e.g. Ayyub (2003, see table 2, chapter 2.1) does. As for the traditional RPN it is important to remember that the RPC ranking is also on a relative scale. The analysis tells that failure mode a4 has a higher priority than failure mode a1 but from the analysis it cannot be concluded how much more dangerous a4 is. Method A solves several of the issues for the traditional FMEA. By method A the dimensions‟ influence on the RPC is dependent on the importance of the dimension. This means that when the importance increases the dimensions‟ influence on the failure mode increases. In case of two failure modes having the same RPC the analysis can be broken further down by using the indicator T(ai). With this second level ranking it is less likely that two failure modes cannot be differentiated from each other. Furthermore the RPC ranking is given on a relative (ordinal) scale which because of the notice (L1, L2 etc.) is less likely to be confused with a quantitative scale. And finally the RPC is given on a 10-point scale which is on the same level as the dimensions‟ scale. An advantage of the method A is that even though the method includes a ranking of the dimension‟s importance the analysis is not significantly more time consuming. The actual analysis can be automated in Excel as shown in the example by setting up maximum and minimum functions covering formula [1], [2], [3] and [4]. Other authors have created FMEA methods that reminds of method A. E.g. Selvan et al.‟s (2012) modified FMEA also builds on max/min formulas. The difference between this approach and method A is that the order of the functions is different. Selvan et al.
Page 25 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
use the following to formulas;
Student no.: 404340 Maria Bech Andersen
and
. The formulas show that instead of maximization in the inner function a minimization is used and the RPC is based on maximization across the dimensions and finally the CFM is found based on minimization across all failure modes. In 2009 Narayanagounder and Gurusami made a new Design-FMEA approach which builds on the approach by Francescini & Galetto (2001). Method A2 – an alternative to method A The main purpose of Narayanagounder and Gurusami‟s (2009) FMEA was to solve the problem of having two or more failure modes with the same RPN. In the following formula [5] – [8] are based on Narayanagounder‟s and Gurusami‟s (2009) alternative FMEA approach. Table 7 explains the set up of the structure for the calculation. Table 7: Failure mode indices – Method A2 Failure Mode a1 a2
Severity L11 L21
Occurrence L12 L22
Detection L13 L23
RPN R1 R2
. .
. .
. .
. .
. .
ai
Li1
Li2
Li3
Ri
. .
. .
. .
. .
. .
ak
Lk1
Lk2
Lk3
Rk
. .
. .
. .
. .
. .
an
Ln1
Ln2
Ln3
Rn
Source: adaption (Narayanagounder and Gurusami, 2009) The method consists of a three steps (Narayanagounder and Gurusami, 2009): 1) Calculation of the Critical Failure Mode Index (CFM Index) by the formula: [5]
Comparing formula [5] with formula [1] in method A. The maximum level is found in the same way but in a different order. Table 7 can help explain the difference. For both methods the minimum level is found across the dimensions (L11, L12, L13) and the maximum level is found from the vertical levels for each dimension across the failure
Page 26 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
modes (L11, L21, L31, L41). Where method A2 first uses the maximization formula and then the minimization formula, method A uses the minimization formula before the maximization. Method A further includes a maximization function right in the beginning between the dimension rank and the importance of the dimension. 2) Estimation of Risk Priority Code (RPC) [6] Where N(ai) = # Lij > I(a) 3) Estimation of the Critical Failure Mode (CFM) [7] CFM(a) = failure mode with the highest N(ai)
In case of equal N(ai) the CFM can be defined based on: [8] In this case: CFM(a) = failure mode with the highest T(ai) Example: The following example is based on the data from table 6 in order to make this FMEA method comparable with method A. Calculation of the Critical Failure Mode Index (CFM Index) 1)
2) Estimation of Risk Priority Code (RPC)
3) Estimation of the Critical Failure Mode (CFM) CFM(a) = Max {N(ai)} = Because three of the failure modes have the same N(ai), the T(ai) is used to prioritize them:
T(a3) > T(a2) > T(a1) Based on the calculations failure mode a4 is the most critical failure mode followed by a3, a2 and a1. Even though both method A and method A2 are based on max/min Page 27 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
functions the methods are completely different and so is the prioritization of the failure modes. In method A2 it seems as it would have been a bit more appropriate to use formula 8 without numerical value. By using numeric values it is not possible to see if the high result score is caused by a very high or a very low level for the failure mode. The preferable method seems to be method A because it weights the dimensions and thereby solves more of the problems for the traditional FMEA. And the calculation of the indicator reflects the data in a better way. Several of the alternative FMEA approaches build on the use of fuzzy if-then rules. One of the more interesting FMEAs with if-then rules is made by Abdelgawad & Fayek (2010).
3.2.Method B – Aggregated impact and if-then rules 3.2.1. Theory
Abdelgawad and Fayek (2010) define a failure mode as an uncertain event/condition that in case it occurs will impact time, cost, scope and/or quality in either a positive or negative way. Hence, even though the consequence has a positive effect, the event will still be seen as a failure mode if it is caused by an uncertain event/condition. The traditional FMEA covers those dimensions indirectly as a part of Severity. By only covering them indirectly there is a high risk that some of the sub dimensions might be forgotten in the light of some of the others. To avoid this Abdelgawad and Fayek (2010) have created a new FMEA with the main purposes: -
Fitting to the definition of a failure mode
-
Force people to evaluate time, cost and scope/quality
-
Allowing weighting of dimensions and sub dimensions
Based on their definition of a failure mode Abdelgawad and Fayek (2010) have made a new definition of the three original dimensions; Severity, Occurrence and Detection. Severity is redefined to “Aggregated Impact” and is broken down to three subgroups; Cost Impact (CI), Time Impact (TI) and Scope/Quality Impact (SI). Occurrence exists in its traditional format; the probability of occurrence of the cause. Finally, Detection is redefined to include; detection of the risk event, control of root causes and control of the consequences of the risk event. The reason for this is that even though a risk event Page 28 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
easily can be detected before it occurs, it does not necessarily mean that the risk event is under control. Abdelgawad and Fayek (2010) refer to the RPN as the Risk Criticality Number (RCN). The RCN is defined on a scale from 1 to 1,000 and can take value of any number in between and not only the natural numbers. Method B overall consists of three steps (Abdelgawad and Fayek, 2010) and in the following formula [9] and [10] are based on Abdelgawad and Fayek‟s (2010) modified FMEA approach. Step 1: Defining membership functions Abdelgawad & Fayek (2010) have defined a set of five membership functions for Occurrence, Cost Impact, Time Impact, Scope/Quality and Aggregated Impact. Figure 5 shows a graphical view of the functions. Figure 5: Membership Functions for (O), (CI), (TI), (SI), (AI) – Method B
Membership probability
M
L
100% VL
H
VH
75%
50%
25%
0%
1
2
3
4
5
6
7
8
9
10
Index value
Source: adaption of fig. 2 Abdelgawad & Fayek (2010) The membership functions are triangular except the function for VH. The reason that this function is different is to ensure that both a value of 9 and 10 is defined as very critical. From figure 5 the membership functions can be translated into formulas: Table 8: Membership functions for (O), (CI), (TI), (SI), (AI) – Method B Level
Formula
Interval ∈ ∈ ∈ ∈ Page 29 of 85
Master Thesis 29-06-2012
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
∈ ∈ ∈ ∈ ∈ Where x= index value and MP = membership probability [0;1] Source: Own contribution The membership functions for Detection are given in the reverse order. Figure 6: Membership Functions for (D) – Method B
Membership probability
100%
VH
M
H
L
VL
75%
50%
25%
0%
1
2
3
4
5
6
7
8
9
10
Index value
Source: adaption of fig. 2 Abdelgawad & Fayek (2010) The formulas for the membership functions for Detection, are the same as the ones in table 8 just with reverse definitions e.g.
∈
Step 2: Calculation of Aggregated Impact The defuzzificated value can be calculated as: [9] Where: aij = relative importance of factor i over j. a = minimum difference between factor i and factor j d = maximum difference between factor i and factor j a≤b≤c≤d In order to weight Cost, Time and Scope/Quality table 9 is used to define the relation between each of pairs of sub dimensions. The relative importance factors differ a lot from case to case. For instance in the healthcare industry it is crucial to deliver high Page 30 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
quality because the consequences of failures often will be hazardous. For companies with expensive products that are much discussed in the media, new products must also be of high quality in order to avoid scandals in the media. In this case cost will have a lower importance, whereas it often would be a very important factor later on in relation for the company to make profit. Table 9: Comparison Scale for sub dimensions – Method B Scale 1 3 5 7 9 2, 4, 6, 8
Definition Equal importance of both elements Moderate importance of one element over another Strong importance of one element over another Very strong importance of one element over another Absolute importance of one element over another Intermediate values
Source: Abdelgawad & Fayek (2010) If the relationship factor between Cost and Time is given, then the relationship factor between Time and Cost can be calculated as the inverse factor:
The formula for Aggregated Impact: [10]
Where: wj = the relative importance weight for the j‟th dimension Step 3: Estimation of RCN based on the dimensions The formulas for RCN membership functions are shown in table 10: Table 10: Membership function for RCN – Method B Level
Formula
Interval ∈ ∈ ∈ ∈ ∈ ∈ ∈ ∈ ∈ Page 31 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
∈ ∈ ∈ ∈ ∈ ∈ ∈ ∈ Where x= RCN value and MP = membership probability [0;1] Source: Own contribution For the graphical picture see figure 4 in appendix 4. Table 5.1 in appendix 5 shows how the risks are divided into nine categories based on the RCN value. According to Abdelgawad and Fayek (2010) all failure modes with a RPC on 250 and above should trigger a corrective action. 3.2.2. Example
An example based on the data in table 11 will show the use of method B in practice. The data contains an evaluation of CI, TI, SI, O and D for four failure modes. Table 11: Data – Method B Failure Mode
CI
TI
SI
O
D
a1
4
7
6
8
7
a2
9
4
2
3
6
a3
6
8
7
1
4
8 9 9 a4 Source: Own contribution
5
3
Calculation of Aggregated Impact Before calculating the Aggregated Impact the relation between the three sub dimensions; Cost Impact, Time Impact and Scope/Quality Impact must be clarified. Table 12 shows the relative importance of factor i over j. The defuzzification of the relative importance is calculated based on formula [9].
Page 32 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Table 12: Defuzzification of Impact sub dimensions – Method B a b c
SI vs. CI 2 3 3
CI vs. TI 1 2 2
SI vs. TI 6 7 7
d Defuzzy:
4 3
3 2
8 7
Source: Own contribution Table 13 shows the calculation of the factors for Aggregated Impact. Based on the relative importance between the sub dimensions the normalized importance is calculated. The average of the normalized importance for each sub dimension is calculated and used for the calculation of AI. Table 13: Relations between Impact sub dimensions – Method B Relative importance CI TI SI Sum
CI 1 0.50 3.00 4.50
TI 2.00 1 7.00 10.00
Normalized SI importance 0.33 CI 0.14 TI 1 SI 1.48 Sum
CI 0.22 0.11 0.67 1.00
TI 0.20 0.10 0.70 1.00
SI Sum Average 0.23 0.65 0.22 0.10 0.31 0.10 0.68 2.04 0.68 1.00
Source: Own contribution The averages in table 13 are used to calculate the Aggregated Impact for each failure mode in table 14 by formula [10]. Table 14: Aggregated Impact – Method B Failure Mode
a1 a2 a3 a4
CI
TI
SI
AI
4 9 6
7 4 8
6 2 7
5.67 3.72 6.89
8
9
9
8.78
Source: Own contribution The calculation of AI for failure mode a1 is shown as an example:
Page 33 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Estimation of RCN based on the dimensions Figure 7 shows a complete set (125 rules) of fuzzy if-then rules based on the 5-point scales for AI, O and D. It should be noticed that the order of the linguistic terms is reverse for Detection. Figure 7 shows that Aggregated Impact in general is weighted more heavily than Occurrence and Detection. The rules are created in such a way that if two dimensions are frozen and the third dimension increases then the RCN will never decrease.
O - VL O-L O-M O-H O - VH O - VL O-L O-M O-H O - VH O - VL O-L O-M O-H O - VH O - VL O-L O-M O-H O - VH O - VL O-L O-M O-H O - VH
AI - VL VL VL VL/L L L/M VL VL/L L L/M M/H VL L L/M M M/H VL/L L L/M L/M M VL/L L L/M M M
Aggregated Impact AI - L AI - M AI - H VL VL/L M VL/L L/M M/H L M H L/M M/H H/VH M H H/VH VL/L L M L M M/H L/M M/H H M/H H H/VH H H/VH VH L M M/H L/M M H M M/H H/VH M/H H VH H VH VH L M H M M/H H M/H H H/VH H H/VH VH H/VH VH VH L/M M/H H/VH M H H/VH H H/VH VH H/VH VH VH H/VH VH VH
AI - VH M/H H H/VH VH VH H H/VH H/VH VH VH H/VH H/VH VH VH VH H/VH VH VH VH VH VH VH VH VH VH
D - VH
D- H
D- M
Detection/Control
Probability of Occurrence
Figure 7: Fuzzy if-then-rules – Method B
D- L
D - VL
Page 34 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Scale Definitions Very Low Low / Medium High Very Low / Low Medium High / Very High Low Medium / High Very High
Source: Own contribution In table 15 four failure modes are evaluated based on the if-then rules from figure 7 and the membership functions for the RCN (chapter 3.2.1). The rule for failure mode a1 is: Because of a “66.5% Medium and 33.5% High Aggregated Impact”, a “50% High and 50% Very high Probability” and a “100% Low Detection” the RCN is “40% High/Very high and 60% Very high”. As an example the calculation of the RCN value for a1 is shown: V/VH:
membership value =
The result will naturally be the same if the RCN is calculated based on the membership function for VH instead: VH:
membership value =
Table 15: Evaluation of failure modes – Method B
Failure mode a1 a2 a3 a4
AI 66.5% M, 33.5% H 64% L, 36% M 5.5% M, 94.5% H 11% H, 89% VH
O 50% H, 50% VH
D 100% L
50% M, 50% L 50% H, 100% VL 50% M 100% L
100% M
100% H
RCN
RCN value
40% H/VH, 736.31 60% VH 40% L/M, 260.00 60% M 52% M, 348.00 48% M/H 11% H, 636.25 89% H/VH
Source: Own contribution Table 15 shows that a1 is the most dangerous failure mode followed by a4, a3 and finally a2. According to Abdelgawad & Fayek (2010) all failure modes with a RCN value at 250 and above should trigger a mitigation action. Thus, in the case above all four failure modes trigger an action. Page 35 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
3.2.3. Evaluation and comparison to traditional FMEA
In order to compare the results by the use of method B with the results from a traditional FMEA, the RPN values for the four failure modes are calculated in table 16 based on the classic formula: RPN = S * O * D. Table 16: Results of traditional FMEA – Method B Failure Mode
a1 a2 a3 a4
392 54 28
RPN Rank 1 3 4
Met. B Rank 1 4 3
135
2
2
S
O
D
RPN
7 3 7
8 3 1
7 6 4
9
5
3
Source: Own contribution C.f. chapter 3.2.2 all failure modes would trigger an action if method B is used. If the traditional RPN is used with three intervals; Low risk: RPN ϵ [1; 35], Medium risk: RPN ϵ [36; 124] and High risk: RPN ϵ [125; 1000], failure mode a1 and a4 would for sure trigger an action, it would be considered if a2 should trigger one and a3 would not. Furthermore table 16 shows that the prioritization of the failure modes is different. The two methods agree on failure mode a1 as the most dangerous and a4 as the next coming. The disagreement about the ranking of failure mode a2 and a3 is because a2 has a higher RPN than a3 if the dimensions are not weighted. If the dimensions are weighted as in method B the high Aggregated Impact results in a higher RCN for failure mode a3 than a2. An advantage of method B is that besides ranking the failure modes the method also shows when it is recommended to take a mitigation action. One of the advantages of method B is that more information is used. Breaking Impact down in sub dimensions forces the experts to evaluate how big contribution Cost, Time and Scope/Quality should have to the Impact dimension. In this way the difference between the importance of three sub dimensions is highlighted. Furthermore it is an advantage that method B is more specific in the definition of Detection and includes the controlling parts. It should be considered to use the three elements; detection of the risk event, controlling the root causes and controlling the consequences of the risk event as sub dimensions with an individual rank like for Aggregated Impact. In this way the
Page 36 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
elements are allowed to have different ranks and the experts can decide how much each sub dimension should weight in the Aggregated Detection. A big advantage of using if-then rules is that they can include all kinds of weights; e.g. threshold values for instance for a very high Severity, which should always lead to at least a medium/high RCN. Global weights can be included if one dimension always should be weighted higher than the other dimensions. Furthermore local weights can be included if the weight of a given dimension increases and decreases depending on the dimension level. A huge disadvantage of method B is that an if-then-rule must be made for all potential failure modes. Furthermore it is not necessarily possible to use the same if-then rules across all projects. Depending on the scope of the project and the phase of the development process, the if-then rules should be designed differently. Hence, the experts have to make several sets of 125 if-then rules, which will be very time consuming. Other authors have also developed FMEA approaches based on a set of fuzzy if-thenrules. Two of them are Sankar and Prabhu (2001). To overcome the problem of having a situation with similar RPN values, they let an expert evaluate all 1,000 possible S, O, D combinations and rank them based on increasing risk from 1 to 1,000. Sankar and Prabhu (2001) were operating with the thought of an ideal FMEA model. But the problem is that it is very unrealistic since no expert would have time for thinking 1,000 situations through. And even if an expert did have the time, the large amount of logical coherences would probably also lead to some illogical results. Tay and Lim (2010) also created an alternative FMEA based on if-then rules. Tay and Lim (2010) used a 5-point scale for Severity and 6-point scales for Occurrence and Detection. This gives a total of 180 rules which they believed was too time consuming. Therefore Tay and Lim (2010) investigated the opportunity of reducing the set of fuzzy rules. Tay and Lim‟s (2010) study showed that a 50 % reduction of the fuzzy rules is possible. Because a rule only contributes to a specific area of the inputs it will only affect the given area associated with the rule, hence removing less important rules can lead to big changes but only in areas that have a very small impact on the fuzzy RPN. Page 37 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Wang et al. (2007) warns against reducing the if-then-rule base because a reduction of the if-then-rule base means that two failure modes will be bundled together. This is only possible because an expert cannot distinguish between them. And since experts have a different basis for bundling it will be impossible to agree on a reduction of the rules. In section 2.2 the traditional FMEA was criticized for having the scale [1; 1,000] for RPN when the RPN could only take value of 120 numbers. Method B solves the problem by defining the RCN in such way that it can take value of any number in the interval. At the same time this of course strengthens the problem about the too high resolution regarding prioritization of the failure modes. In the attempt to overcome the problem with fuzzy if-then rules being too time consuming; other authors have created fuzzy FMEAs without the use of if-then rules. Wang et al. (2007) have developed an alternative FMEA based on a fuzzy weighted geometric mean.
3.3. Method C – Geometric mean 3.3.1. Theory
The main purpose of Wang et al.‟s (2007) FMEA based on a fuzzy weighted geometric mean is: -
Allowing importance weights for S, O and D
-
Having a fuzzy FMEA that do not need to have experts to judge hundreds of possible situations in order to create a complete if-then rule base
-
Allowing the expert team members to have different evaluations of S, O and D
-
Assuring that the experts‟ evaluations are weighted according to their relative knowledge about the given subject
In Method C several expert team members evaluate S, O and D based on the fuzzy ratings from table 17, 18 and 19. In the following formula [11] - [21] are based on Wang et al.‟s (2007) alternative FMEA approach. The rating of Occurrence is based on five trapezoidal membership functions. The membership functions all follow the rules in formula [11]:
[11]
MDO =
Page 38 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Where: MD = membership degree [0;1] and x is the index value For each membership function the following is true: - MD = 0 for x [a;d] - MD is monotonic increasing for x ∈[a;b] - MD is monotonic decreasing for x ∈[c;d] - MD = 1 for x ∈ [b;c] For the trapezoidal membership functions the centroid can be calculated as: [12] Table 17: Fuzzy Rating of Occurrence – Method C Rating Very high (VH) High (H) Moderate (M) Low (L) Remote (R)
Probability of Occurrence Failure is almost inevitable Repeated failures Occasional failures Relatively few failures Failure is unlikely
Fuzzy Number (8, 9, 10, 10) (6, 7, 8, 9) (3, 4, 6, 7) (1, 2, 3, 4) (1, 1, 2)
Source: Wang et al. (2007) The membership functions in figure 8 are made based on the fuzzy ratings in table 17
Figure 8: Membership functions for fuzzy Occurrence rating b
c
75%
Rem
50%
Low
ote
Membership degree
100%
Moderate
High
Very high
25% 0%
1
2
a
3
4
5
6
d 7
8
9
10
Index value
Source: Adaption of figure 1, Wang et al. (2007) Figure 8 demonstrates the above mentioned rules for the membership functions. Looking at the membership function for Moderate, the function is always increasing in the interval [a; b] and decreasing in the interval [c; d]. In the interval [b; c] the membership degree is constant 1 and outside the interval [a; d] the membership degree is constant 0.
Page 39 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
The rating of Severity and Detection are based on ten triangular membership functions. In this case b=c and the functions are based on formula [13]:
[13]
MDS,D =
Table 18: Fuzzy rating of Severity – Method C Rating
Severity of effect
Hazardous without warning (HWOW) Hazardous with warning (HWW) Very high (VH) High (H) Moderate (M) Low (L) Very low (VL)
Very high severity ranking without warning
Fuzzy number (9, 10, 10)
Very high severity ranking with warning
(8, 9, 10)
System inoperable with destructive failure (7, 8, 9) System inoperable with equipment damage (6, 7, 8) System inoperable with minor damage (5, 6, 7) System inoperable without damage (4, 5, 6) System operable with some degradation of (3, 4, 5) performance Minor (MR) System operable with some degradation of (2, 3, 4) performance Very minor (WMR) System operable with minimal inference (1, 2, 3) None (N) No effect (1, 1, 2) Source: Wang et al. (2007) The membership functions for the Severity rating are all triangular. Because b=c the centroid is calculated as: [14] centroidtriangular = Figure 9: Membership functions for fuzzy Severity rating N
VM
MR
VL
b=c L
M
H
VH
2
3
a 4
5
d 6
7
8
HWW HWOW
Membership degree
100% 75%
50%
25% 0%
1
9
10
Index value
Source: Adaption of figure 2, Wang et al. (2007)
The basic rules for the membership functions still exist. Looking at the membership function for Low as an example, the membership deegree is monotonic increasing in the Page 40 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
interval [a;b] and monotonic decreasing in the interval [c;d]. Outside the interval [a;d] the membership degree equals 0. For the triangular membership functions the interval [b;c] only consists of one value; 1. Table 19: Fuzzy Rating of Detection – Method C Rating
Likelihood of detection Absolute uncertainty (AU) No chance Very remote (VR) Very remote chance Remote (R) Remote chance Very low (VL) Very low chance Low (L) Low chance Moderate (M) Moderate chance Moderately high (MH) Moderately high chance High (H) High chance Very high (VH) Very high chance Almost certain (AC) Almost certainty Source: Wang et al. (2007)
Fuzzy number (9, 10, 10) (8, 9, 10) (7, 8, 9) (6, 7, 8) (5, 6, 7) (4, 5, 6) (3, 4, 5) (2, 3, 4) (1, 2, 3) (1, 1, 2)
Figure 10: Membership functions for fuzzy Detection rating AC
VH
H
MH
b=c M
L
VL
R
VR
AU
2
3
a 4
5
d 6
7
8
9
10
Membership degree
100% 75%
50%
25% 0%
1
Index value
Source: Adaption of figure 3, Wang et al. (2007) For the three dimensions S, O and D fuzzy weights are given in order to let the dimensions have different level of impact on the FRPN. In total there are five membership functions for the fuzzy weights. They are triangular like the ones for S and D and the same rules apply for those as for the other triangular functions from above. Table 20: Fuzzy weights – Method C Linguistic term Very low (VL) Low (L) Medium (M) High (H)
Fuzzy number (0, 0, 0.25) (0, 0.25, 0.5) (0.25, 0.5, 0.75) (0.5, 0.75, 1) Page 41 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Very high (VH) (0.75, 1, 1) Source: Wang et al. (2007) Figure 11: Membership functions for fuzzy weights Very low
Low
b=c Medium
High
0
a 0.25
0.5
d 0.75
Very high
Membership degree
100% 75%
50%
25%
0%
1
Fuzzy weights
Source: Adaption of figure 4, Wang et al. (2007) The expert team members‟ opinions are aggregated by the following formulas: Formulas for aggregated S, O, D ratings For Failure Mode (i): [15] [16] [17] Where: hj(j=1,…,m) is the relative importance of the weights , and are the fuzzy ratings of the i'th failure mode on S, O and D Formulas for aggregated fuzzy weights for S, O, D [18] [19] [20] Where: hj(j=1,…,m) is the relative importance of the weights ,
and
are the fuzzy weights for S, O and D provided by the j‟th team member.
Page 42 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Formula [21] shows the calculation of the Fuzzy Risk Priority Number as a fuzzy weighted geometric mean of S, O and D: [21] Where: , and
are aggregated S, O, D ratings from formula [15], [16] and [17]. are aggregated fuzzy S, O and D weights from formula [18], [19] and
[20]. The FRPN is used for ranking the failure modes based on weighted indices for S, O and D. Furthermore the FRPN weights the experts‟ knowledge in such way that the indices given by the most competent expert will have the relative highest importance on the final FRPN rank. 3.3.2. Example
The following example is based on five failure modes a1, a2, a3, a4 and a5 evaluated by four expert team members. The team members‟ influence on the result is weighted in accordance to their assumed relative knowledge on the subject. The ratings are based on the definitions from table 17, 18, 19 and 20. Table 21: Team members’ evaluation – Method C
Detection
Occurrence
Severity
Risk Factor
Team member
Factor weight
a1
a2
a3
a4
a5
TM1 (10%) TM2 (45%)
H
L
HWW
L
M
MR
VH
VL
VH
MR
H
VH
TM3 (30%)
M
M
HWOW
MR
L
M
TM4 (15%)
H
L
VH
VL
L
H
TM1 (10%)
M
H
VL
H
L
H
TM2 (45%)
L
M
M
H
M
VH
TM3 (30%) TM4 (15%)
H H
M VH
L M
M H
R L
H M
TM1 (10%)
VL
L
H
VH
AU
VL
TM2 (45%)
L
VR
M
AC
VR
M
TM3 (30%)
M
R
MH
VH
AU
H
TM4 (15%)
L
VR
M
H
R
MH
Source: Own contribution Page 43 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Table 22: Severity Calculations – Method C
Severity
TM
TM Factor Weight Weight Weight a - a1 - a1 a1 1 weight weight Low Med Up Low Med Up
TM1
10%
H
0.5
0.75
TM2 TM3
45% 30%
VH
0.75 0.25
1 0.5
0.5
0.75
0.538
0.788
M TM4 15% H Weighted ratings TM weight
a3
TM1
10%
L
4
5
TM2
45%
MR
2
TM3
30%
MR
TM4
15%
VL
TM
a3 Low
Weighted ratings
a3 Med
1 L 1 VL 0.75 M 1 L 0.925 a3 Up
a2
4
5
6 HWW
8
9
10
3 5
4 6
7 9
8 10
9 10
4
5
5 VH 7 HWO W 6 VH
7
8
9
3.85 4.85 5.85 a4
a4 - a4 - a4 Low Med Up 5
6
3
6 M 4 H
6
2
3
4 L
3
4
5 L
2.35
3.35
4.35
a2 - a2 a2 Low Med Up
7.70 a5
8.70 9.40
a5 - a5 a5 Low Med Up 2
3
4
7
7 MR 8 VH
7
8
9
4
5
6
M
5
6
7
4
5
6
H
6
7
8
5.00 6.00 7.00
5.75
6.75 7.75
Source: Own contribution The index values in table 22 are produced by the IF-formulas in Excel. The formulas are based on the definitions for Severity (table 18) and the Fuzzy Weights (table 20). As an example the Excel functions for the medium factor weight and the medium rank for failure mode a1 are shown. Factor Weight – Medium =IF(FW="VH";1;IF(FW="H";0.75;IF(FW ="M";0.5;IF(FW ="L";0.25;IF(FW ="VL";0;0))))) Where FW is the factor weight a1 - Medium =IF(a1="N";1;IF(a1="VMR";2;IF(a1="MR";3;IF(a1="VL";4;IF(a1="L";5;IF(a1 ="M";6;IF(a1="H";7;IF(a1="VH";8;IF(a1="HWW";9;IF(a1="HWOW";10;0)))))))))) The Excel functions for the upper and lower factor weights and factor values can be found in appendix 6. Based on the team members‟ ratings a lower, medium and upper value are calculated. The weighted ratings in table 22 are calculated based on the formula [15] for aggregated Severity ratings and formula [18] for aggregated fuzzy weights. The calculation of the Medium Severity value for a1 is shown as example:
Page 44 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
The same calculations are made for Occurrence in table 23 based on the definitions for Occurrence in table 17 and formula [16] for aggregated Occurrence ratings and formula [19] for aggregated fuzzy weights. Table 23: Occurrence Calculations – Method C
10%
TM2 TM3
45% 30%
M L
H TM4 15% H Weighted ratings TM
a1 Weight a - a1 a1 a1 1 Up Low Med1 Med2 Up
TM Factor Weight Weight weight weight Low Med
TM1
TM weight
a3
TM1 10% H TM2 45% H TM3 30% M TM4 15% H Weighted ratings
0.25
0.5
0 0.5
0.25 0.75
0.5 0.250 a3 Low
0.75 H 0.5 M 1 M
0.75
1 VH
0.500 a3 – a3 – Med1
6 6 3 6
7 7 4 7
5.10
6.10
0.750
a3 Med2 Up 8 8 6 8 7.40
6
7
8
3 3
4 4
6 6
9 VL 7 M 7 L
8
9
10
10 M
4.05
5.05 6.80 7.65 a4 - a4 – a4 – a4 Low Med1 Med2 Up 1 2 3 4 3 4 6 7 1 1 1 2 1 2 3 4
a4 9 9 7 9
a2
L M R L
8.40
1.90
2.60
a2 – a2 - a2 – a2 Low Med1 Med2 Up 0
0
0
0
3 1
4 2
6 3
7 4
3
4
6
7
2.10
3.00 4.50 5.40 a5 – a - a5 – a3 a5 3 Low Med1 Med2 Up 6 7 8 9 H 8 9 10 10 VH 6 7 8 9 H M 3 4 6 7
3.75 4.75
6.45
7.45
8.60 9.15
Source: Own contribution Table 24 is based on the definitions for Detection in table 19 and formula [17] for aggregated Occurrence ratings and formula [20] for aggregated fuzzy weights. The Excel functions for Occurrence and Detection calculations can be found in appendix 7. Table 24: Detection Calculations – Method C TM
Detection
Occurrence
TM
TM Factor Weight Weight Weight a - a1 - a1 a1 1 weight weight Low Med Up Low Med Up
TM1
10%
TM2
45%
TM3
30%
VL L
0 0
0 0.25
0.25 L 0.5 VR
5 8
6 9
M L
0.25 0 0.075
0.5 0.25 0.300
0.75 R 0.5 VR 0.550
7 8 7.4
8 9 8.4
TM4 15% Weighted ratings TM
TM weight
a3
a3 Low
TM1 10% VH TM2 45% AC TM3 30% VH H TM4 15% Weighted ratings
1 1 1 2 1.15
a3 Med 2 1 2 3 1.7
a3 Up
a4 3 2 3 4 2.7
AU VR AU R
a2 7 10
H M
9 MH 10 M 9.4
a4 - a4 - a4 a5 Low Med Up 9 10 10 VL 8 9 10 M 9 10 10 H 7 8 9 MH 8.25 9.25 9.85
a2 - a2 a2 Low Med Up 2 4
3 5
4 6
3 4 5 4 5 6 3.5 4.5 5.5 a5 - a5 a5 Low Med Up 6 4 2 3 3.5
7 5 3 4 4.45
8 6 4 5 5.5
Source: Own contribution Table 25 summarizes the weighted ratings for the medium cases for both S, O and D for all five failure modes. Page 45 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Table 25: Calculations for centroids – Method C Factor weight Severity Occurrence Detection
a1
a2
a3
4.85 5.89 8.40
8.60 3.75 4.50
3.35 6.75 1.85
6.00 3.25 9.12
6.75 7.91 4.45
5.75
5.80
3.73
5.35
6.54
0.750 0.500 0.308
Centroid
a4
a5
Source: Own contribution In the bottom row of table 25 the centroid is calculated for the five failure modes based on formula [21]. Calculation of the Failure Mode a1‟s centroid is shown as an example:
In appendix 8 the corresponding upper and lower limits are calculated. The centroids and lower and upper limits are summarized in table 26. Table 26: Prioritization of failure modes – Method C a1
a2
a3
a4
a5
Lower Centroid
4.45 5.75
4.34 5.80
2.62 3.73
4.05 5.35
5.39 6.54
Upper
7.00
7.08
4.89
6.61
7.62
Rank
3
2
5
4
1
Source: Own contribution Table 26 shows that failure mode a5 is most dangerous followed by failure mode a2 and a1. Furthermore the result shows the upper and lower bound of each failure mode. 3.3.3. Evaluation and comparison to traditional FMEA
By weighting S, O and D in accordance to their relative importance, method C overcomes one of the biggest weaknesses of the traditional FMEA. The weighting is with global weights; hence the weight for e.g. Severity does not change depending on if the Severity rank is high or low. In the traditional FMEA a single risk level for each dimension is given by the expert team. It can often be difficult for people to give just one number. In method C the scale
Page 46 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
for S, O and D are defined by membership functions, so when a dimension is evaluated as being “high” for a failure mode, it covers several possible number values. Dong, C. (2007) also created an alternative FMEA method with the use of triangular fuzzy membership functions for S, O and D. Instead of the RPN Dong, C. (2007) operates with a Risk Priority Index which is a function of the utilities for S, O and D. Furthermore method C allows the team members to have different evaluations of the dimensions. The different evaluations are weighted based on the relative knowledge of the expert. This has two main advantages; the experts have a controlled impact on the result and their evaluations can be made independent of time and place. To have the experts evaluating by themselves and afterwards weight their answers will be faster than having them all in the same room trying to agree on the ranks. When the experts evaluate individually it is also assured that all experts will be heard and not just the ones ahead of the curve. A drawback of the individual evaluations is that the synergy effect of having the experts discussing might be lost. Another advantage of method C is that the FMEA does not build on if-then rules hence the experts do not need to judge hundreds of possible combinations of S, O and D. One of the important things for method C is to automate the calculation e.g. by shown in the examples by using Excel. Method C deals with the different expert evaluations in the following way; the weighted average for each dimension is found across all expert evaluations. Based on average dimensions the weighted centroid is calculated. Another approach for dealing with the different expert evaluations would be to calculate weighted centroid based on the data from each expert and then based on the individual centroids, calculate the overall centroid weighted on the experts‟ knowledge. When weighting the team members evaluations based on their relative knowledge it should be considered if the weight for a given team member should be split into three independent weights, so the team member will get a separate weight for each dimension. The team member, with highest relative knowledge regarding Severity of the given failure mode, is not necessarily the team member with the highest relative knowledge regarding Occurrence and Detection. By weighting the dimensions one by one, it will be possible to always weight the knowledge in the best possible way. Page 47 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Some authors have also made alternative FMEAs with a specialization in something more specific. An example is Sawhney et al. (2010) whom modified the FMEA to fit to enhance reliability of LEAN systems.
3.4.Method D – Reliability of LEAN systems 3.4.1. Theory
Sawhney et al. (2010) have created a FMEA approach intended for enhancing reliability of LEAN systems. The purpose of the modified FMEA is to have a tool that can be used for highlighting the gap between the actual business conditions and the ideal conditions. The approach builds on the four main resources for sustaining LEAN. The resources are translated into a definition of the ideal reliable LEAN system (Sawhney et al., 2010); 1) Personnel: workforce’s capabilities and skills required to implement LEAN. In order to meet product quality and delivery requirements the personnel must be available and qualified to perform the standard operating procedures. 2) Equipment: primary and secondary equipment used in LEAN systems. Equipment should not unexpectedly fail but if it fails the repair time should be minimized. 3) Materials: raw materials, work in progress and finished goods. Materials should be delivered in/at the right quantity, time and location. 4) Schedules: the ability to forecast, plan and schedule production system. The schedule should be attained without variance, rescheduling and expediting. Method D consists of a three step procedure (Sawhney et al., 2010): 1) Performance of gap analysis in order to narrow the focus to the major weaknesses of the LEAN system. 2) Identification of potential failure modes and root causes for the four resources 3) Prioritization of the failure modes based on the evaluations of S, O and D Instead of using the traditional RPN a new parameter, Risk Assessment Value (RAV), is introduced (Sawhney et al., 2010); [22]
Page 48 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Based on the 10-points scales for S, O and D, RAV can take values from 0.101 to 100, where RAV=0.10 represents the lowest risk and RAV=100 represents the highest risk. 3.4.2. Example
In table 27 the RAV is calculated based on formula [22] and the RPN as the traditional: S·O·D Table 27: Results – Method D LEAN Resource
Failure mode
S
O
D
a1
2
9
10
1.80
10
180
5
Personnel a2
8
4
7
4.57
7
224
2
a3
6
6
6
6.00
6
216
3
a4
5
8
4
10.00
3
160
7
Equipment a5
9
2
2
9.00
4.5
36
10.5
a6
2
3
8
0.75
12
48
9
a7
9
8
1
72.00
1
72
8
a8
3
6
9
2.00
9
162
6
a9
1
9
1
9.00
4.5
9
12
a10
3
2
6
1.00
11
36
10.5
Schedules a11
5
5
8
3.13
8
200
4
a12
10
8
6
13.33
2
480
1
Materials
RAV
RAV Rank
RPN Rank
RPN
Source: Own contribution Table 27 shows that according to the RAV failure mode a7 is the most dangerous followed by a12 and a4. The relation between RAV and RPN is: 3.4.3. Evaluation and comparison to traditional FMEA
By prioritizing the failure modes based on RAV the failure modes will be prioritized based on their ability to detect and control the failure via LEAN tools. In the formula for RAV only Detection can be directly and immediately impacted by implementing LEAN. The lean tools for improving Detection are e.g. production boards which monitor the progress and output of a process against plan, 5S representing sorting, straightening, systematic cleaning, standardizing and sustaining, supermarkets where the stock is divided into small containers with the purpose of reducing the Muda caused by transport and unnecessary movement, proactive maintenance meaning a maintenance strategy for stabilizing the reliability of machines and equipment and moving lines 1
In case S= 1, O=1, D=10. It should be mentioned that Sawhney et al. (2010) refers to the RAV interval as having the scale [1; 100]. It is assumed this is a mistake.
Page 49 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
where the productions steps are divided into specialized process sequences (Sawhney et al., 2010). One of the drawbacks of method D is that it is possible for different failure modes to have the same RAV values. Table 27 shows that it as expected is not the same failure modes that have identical RAV values and RPN values. Because of the identical RAV values there will still be situations where it is not possible to distinguish between two failure modes. Furthermore table 27 shows that the prioritization of the failure modes is completely different for method D and the traditional FMEA. Another drawback of the RAV is that it like the traditional RPN has a scale that easily can be misunderstood. The RAV scale [0.1; 100] gives the impression that the mean of the RAV should approximately be 50. C.f. table 28 the actual mean of RAV for the 1,000 possible combinations of S, O and D is 8.86. The RAV scale further gives the impression that the median is approximately 50. C.f. table 28 the actual median is only 5.00. As for the distribution of the traditional RPN the RAV distribution is also very right skewed and the very high kurtosis indicates that the RAV distribution peaks much more than a normal distribution. The percentiles show that more than 75 % of the RAV values are in the interval [0.1; 10]. Where the RPN could take value of 120 different numbers the RAV can take value of 202 different numbers and 34 of those are unique values. The most frequent RAV value is 2.00, this value covers 34 different S, O, D combinations. Table 28: Statistics for the RAV – Method D
Page 50 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Output from IBM SPSS. Own contribution Some of the alternative FMEAs created are handling the RPN as being qualitative in the interpretation but quantitative during the calculations for the prioritization. Narayanagounder & Gurusami (2009) are some of the authors handling the RPN in this way in order to use an analysis of variance to interpret the RPN results.
3.5. Method E – Experts average and ANOVA 3.5.1. Theory
In 2009 Narayanagounder & Gurusami presented a new Design-FMEA approach with the goal of dealing with two main problems for the traditional Design-FMEA: -
The problem of having two or more failure modes with the same RPN.
-
Situations where the team members disagree on the ratings of the three dimensions.
In the following two of Narayanagounder and Gurusami‟s (2009) alternative FMEA approaches will be investigated. Method E1
The first method is developed in order to deal with the problem of the expert team disagreeing on the ranks for S, O and D. In method E1 the RPN is calculated as the mean of the team members individual RPNs. In case that two failure modes will have the same RPN, the failure mode with the smallest RPN range will be the most critical failure mode. Formula [23] – [25] are based on Narayanagounder and Gurusami‟s (2009) alternative FMEA. [23] Where k = k‟th expert,
i = i'th failure mode
[24] Where n = # of expert team member, [25]
i = i'th failure mode
RPN range(ai) = Max(RPN(ai)) – Min(RPN(ai))
Where i = i'th failure mode In table 29 an example of method E1 is shown with three failure modes (a1, a2 and a3). The RPN is calculated based on each team members evaluation of the given failure Page 51 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
mode. The overall RPN for the failure mode is calculated as the average of the team members RPNs. Table 29: RPN – Method E1 Failure Mode a1 tm 1
S
O
D
RPN
Mean (RPN)
Range (RPN)
7
5
2
70
123.67
248
a1 tm 2
4
2
6
48
a1 tm 3
8
7
5
280
a1 tm 4
9
4
2
72
Rank
a1 tm 5
5
6
8
240
2
a1 tm 6
4
2
4
32
a2 tm 1
2
5
6
60
a2 tm 2
4
6
5
120
a2 tm 3
6
7
8
336
a2 tm 4
3
5
4
60
Rank
a2 tm 5
4
6
4
96
3
a2 tm 6
2
7
5
70
a3 tm 1
9
8
8
576
a3 tm 2
7
9
4
252
a3 tm 3
9
7
5
315
a3 tm 4
6
6
4
144
Rank
a3 tm 5
8
8
6
384
1
a3 tm 6
9
6
7
378
123.67
341.50
276
328
Source: Own contribution The calculations in table 29 show that failure mode a3 is the most critical because this failure mode has the highest RPN. Failure mode a1 and a2 both have a RPN on 123.67, therefore the range of the RPN is used for prioritizing the risks. Because a1 has the smallest RPN range it is evaluated to be more critical than a2. Method E2 builds on Narayanagounder and Gurusami‟s (2009) modified FMEA which is an alternative to method E1, but it can also be used in extension in order to verify the result of E1. The basic set up of the methods are the same; S, O and D are evaluated on the traditional 10-point scales and a RPN value is calculated for all failure modes for each team member. Based on the different RPNs an analysis of variance is made in order to test statistically if the means for the failure modes are equal or not.
Page 52 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Method E2
Hypothesis: H0: μ1 = μ2 = μ3 H1: at least two means are different Assumptions: 1) Normal distribution of the RPN for each failure mode 2) Variance homogeneity: s2a1 = s2a2 = s2a3 The skewness and kurtosis in table 30 indicates that the RPN is not normal distributed. Table 30: Skewness and Kurtosis N
Skewness
Statistic
Statistic
Kurtosis
Std. Error
Statistic
Std. Error
FM1
6
.945
.845
-1.515
1.741
FM2
6
2.198
.845
4.982
1.741
FM3
6
.446
.845
.959
1.741
Output from IBM SPSS. Own contribution In appendix 9 histograms for the three failure modes also indicate that RPN is not normally distributed. All three failure modes are right skewed, failure mode a2 most heavily. Even though assumption 1 is not fulfilled the ANOVA test will be completed.
Table 31: Test of homogeneity
Output from IBM SPSS. Own contribution Because the p-value is above 0.05 in the test of homogeneity of variance the assumption of equal variance can be accepted. Table 32: ANOVA
Output from IBM SPSS. Own contribution Page 53 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
C.f. table 32 the analysis of variance shows that the H0 can be rejected hence the means are different for the failure modes. Table 33: Bonferroni’s test
Output from IBM SPSS. Own contribution Table 33 shows Bonferroni‟s test which indicates that a significant difference exists between the RPNs for failure mode a3 and a2. A significant difference also exists between a3 and a1. 3.5.2. Evaluation and comparison to traditional FMEA
Method E1 and E2 overcome two of the main problems of about the traditional FMEA. First of all they solve the problem with failure modes that cannot be distinguished from each other based on the RPN. Secondly the methods can handle situations with team members disagreeing on the ratings of the dimensions. One of the disadvantages of method E1 and E2 is that these approaches like the traditional FMEA assume that the importance is equal of S, O and D. Method E1 and E2 take basis in the same principles. The main difference between them is that E1 is built on simple calculations such as average and range where E2 is based on a statistical approach. There are pros and cons for both methods. E1 is easier to implement in companies because of the simple calculations. E2 gives a bit more refined result but to deliver a reliable result the assumptions for the test must be fulfilled. In method E1 it was possible to rank the failure modes. Method E2 shows when the difference in the ranks is actually significant.
Page 54 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Using the ANOVA analysis in method E2 is critical because the one-way ANOVA should only be used when dealing with more than two independent sample sizes on interval/ratio scales (Keller, 2009). Furthermore the assumption of normality is not fulfilled. The assumption says that for each failure mode the RPN should be normally distributed. This will most likely never happen because there will only be a small number of experts to evaluate the dimension scores, hence the sample size will be very small. Instead of using ANOVA a non parametric test could be used. When dealing with more than two independent samples on ordinal scales the Kruskall Wallis test can be used (Norheim, 1986). The performance of the test will be demonstrated in the following. Hypothesis: H0: μ1 = μ2 = μ3 H1: at least two means are different Assumptions: 1) Independent samples 2) Simple random sampling Assumption 1 is fulfilled because there is no relation between the samples. Assumption 2 is assumed correct. Table 34: Kruskal-Wallis Test
Output from IBM SPSS. Own contribution Table 34 shows that the Kruskal-Wallis test is significant meaning the null hypothesis can be rejected hence the distribution of the RPN is not the same across the failure modes. More results regarding the Kruskal-Wallis test can be found in appendix 10.
Page 55 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
4. Comparison of alternative FMEA methods In chapter 3 several alternative FMEA approaches were investigated. The purpose of looking at the alternative FMEAs was to find a solution for how to overcome the drawbacks of the traditional FMEA in order to find a FMEA approach that gives a better ranking of the risks and thereby a better prioritization of the actions. At the same time it is crucial that the modified FMEA is easy to use and gives an unambiguous result that cannot be misunderstood. The main methods investigated are: Method A, based on Francescini & Galetto‟s (2001) fuzzy FMEA with max/min functions. Method A2, an alternative to method A based on Narayanagounder and Gurusami‟s alternative FMEA (2009). Method B, based on Abdelgawad and Fayek‟s (2010) FMEA with if-then rules and new definitions for Severity and Detection. Method C, based on Wang et al.‟s (2007) FMEA based on a fuzzy weighted geometric mean and weights based on the experts‟ relative knowledge. Method D, based on Sawhney et al.‟s (2010) FMEA approach intended for enhancing reliability of LEAN systems with the new risk parameter; RAV. Method E1 and E2, based on Narayanagounder and Gurusami‟s (2009) alternative FMEAs with focus on calculation of mean RPN and ANOVA. One of the biggest drawbacks of the traditional FMEA and therefore one of the most discussed subjects is how to weight the dimensions. Method A, B and C include a weighting of the three dimensions. Method A and C only include a global weight for the dimensions hence the same weight for S, O and D respectively will be used no matter if the dimension rank is high or low. Method B allows all types of weights because they can be built indirectly into the if-then rules. An if-then rule can e.g. cover a threshold weight, a global weight and a local weight. In method A the dimensions are given an importance level. In the calculations of the RPC the importance level figures on equal basis with the rating of the dimension, hence the importance level can potentially have a very high influence on the RPC. In this way it is possible when using method A to get the worst level for the dimension even though the dimension rank is the lowest possible. In method C the dimension weights figure as exponents for the dimension ratings in the calculation of FRPN.
Page 56 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
That method B builds on if-then rules is not an unconditional improvement of the traditional FMEA. A big drawback of the use of if-then rules is that it is very time consuming to set up the rules. An expert needs to think about any possible combination of the dimensions. If 10-points scales are used the expert needs to go through 1,000 situations as Sankar & Prabhu (2001) suggest. It would definitely be an ideal situation to have the 1,000 rules because then every possible situation would be thought through, but it would not be a realistic approach. If 5-points scales are used instead as in method B the expert still needs to go through 125 rules. This is still very much work for an expert to do, but in a very large company with a wide use of FMEA it could be a possibility. The usefulness of a set of if-then rules also depends a lot on the possibility to reuse the rules across different FMEA reports, this e.g. depends on the types of products and different product development stages. Another focus of improvement regarding the traditional FMEA is the scale for RPN. Method A and A2 overcome most of the issues related to the scale. By renaming the scale values from numbers to levels (L1, L2 etc.) the scale is less likely to be misinterpreted as being quantitative. Furthermore the RPN scale is limited to the same interval as the dimension scales, in this way the RPN ranking can be better justified. Method D operates with the parameter RAV (S*O/D) instead of the RPN. It is the only method investigated that calculates the prioritization of the failures based on a fraction relation between S, O and D. The relation between the RPN and the RAV is: RPN = RAV*D2. The RAV has many of the same drawbacks as the RPN. The scale [0.1 ; 100] for RAV is also covering non natural numbers but the RAV can only take value of 202 different numbers because it is defined by S, O and D which can only take value of 10 different numbers. The RAV scale is even more likely to be confused with a quantitative scale than the RPN because of the non real numbers. With a mean of 8.86, a median of 5.00 and a 75 % percentile at 10.00 the RAV distribution is very right skewed. Method B and E1 & E2 still operate with a RPN on the scale [1;1,000]. But due to the calculation of the RPN‟s they can now take can now take the value of any number in the interval.
Page 57 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Method C does not operate with a RPN but calculates Centroids. From formula [21] it can be seen that the centroids always will be in the same interval as the scales for the dimensions. In this way the problem of the too wide RPN scale is solved. Method D is very different from the other alternative FMEA methods. First of all it is based on a System-FMEA, second it focuses directly on reliability of LEAN systems and third it uses the fraction relation, RAV, to rank the risks. The reason for using RAV instead of one of the other risk priority values is that the RAV prioritizes the failure modes based on their ability to detect and control the failure via LEAN tools Method B initiates a bigger redefining of Severity into Aggregated Impact, which is split into three sub dimensions; Cost Impact, Time Impact and Scope/Quality Impact. By operating with the three sub dimensions the experts are forced to evaluate the dimensions separately and to define how to weight the dimensions against each other. In the traditional FMEA and the other alternative FMEAs there is a high risk that one of the impact sub dimensions will be forgotten in the light of one of the others. Furthermore method B has redefined Detection to include three elements; detection of the risk event, controlling the root causes and controlling the consequences of the risk. The other alternative FMEA methods are not specific about the content of the Detection. The traditional FMEA most often operates with a tripartite categorization of the RPN values, where a high risk should always trigger a mitigation action and for a medium risk it should be considered if an action needs to be taken. According to method B an action should be taken if the RCN is evaluated as a moderate risk (RCN=250) or higher. The rest of the methods investigated do not have a definition for when an action should be taken. In chapter 3 it was also investigated how to handle the situation when the expert team members were disagreeing on the rating of the dimensions. Method C, E1 and E2 allow the team members to give an individual evaluation of all failure modes. In method C an average of each dimension is calculated by weighting each team members rank according to his relative knowledge. Afterwards the rank for the risk priority is calculated based on the average dimension ranks. In method E1 the team members‟ ranks are not weighted based on the team members‟ relative knowledge. Instead the
Page 58 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
RPN is calculated for each team member and the mean of the RPNs is used as the overall RPN. In method C it will be possible to split the weighting of the team members into a separate weight for S, O and D in case the experts‟ relative knowledge is not the same for all dimensions. This will not be possible in method E1 and E2 since it is only possible to have an overall weight for the RPN value. The critical fact about method C, E1 and E2 is that they, when calculating the average of either the dimension rank or the risk priority rank, treat the scales as being quantitative. The following example will demonstrate the problem: Five team members have rated the Occurrence of a failure mode both the rank and the corresponding definition of the rank are shown in table 35. The scale definition used is from Wang et al. (2007). Table 35: Average of Occurrence ranks Team (O) Definition member Rank Rank TM1 3 1 / 15,000 TM2 2 1 / 150,000 TM3 4 1 / 2,000 TM4 7 1 / 20 TM5 3 1 / 15,000 Source: Own contribution
Simple mean rank 3.80
Mean Definition value 1 / 98.74 (rank 5 – 6)
Table 35 shows how the result differs depending on the method to calculate the mean rank. The simple mean rank is an average of the five Occurrence ranks. The mean definition value is an average of the definitions of Occurrence by Wang et al. (2007). In the example above the mean definition probability is 1/98.74 which equals a rank between 5 and 6, closest to 6. This means that depending on whether the average is calculated based on the ranks or on the definitions of the ranks, then the mean rank varies 2 levels. The reason for the big difference is that the definitions are exponential (c.f. chapter 2.2) but the ranks are treated as linear. Method A and A2 calculate the RPN by the use of maximization and minimization functions. The main difference between the methods is the order of the functions. Both methods minimize across the dimensions S, O and D and maximize across the failure modes. The calculation in method A is a maximization between the negation of the Page 59 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
impact and the dimension rank, then a minimization across the dimensions and finally maximization across the different failure modes. Method A2 maximizes across the failure modes first and then minimizes across the dimensions. Both methods can be broken one step further down in case of equal prioritization of two or more failure modes. Method A evaluates the failure mode with most levels above the risk priority level as being most dangerous. Method A2 evaluates the most dangerous failure mode to be the one that compared to the other failure modes has the relative highest S, O or D evaluation. Among the investigated alternative FMEAs method E1 also uses a two level break down. This method uses the range of the RPN as the second level. Method E2 is the only method that evaluates if the risk prioritization ranks differ significantly. The original test chosen, the ANOVA, seems to be quite problematic because the ANOVA is only meant for use with interval/ratio scaled data. And besides that the assumption about normal distribution is not fulfilled. Instead the non parametric test Kruskal-Wallis is used. This test fits with a test on several independent samples on ordinal scales and there is no assumption regarding normal distribution.
5. The combined FMEA None of the alternative FMEA methods investigated in chapter 3 can be used as “the perfect FMEA”. Most of the methods focus on one or two specific things that are improved compared with the traditional FMEA. In order to get the traditional FMEA improved more widely a new combined FMEA will be presented in the following chapter. The Combined FMEA will be based on parts from each of the FMEA approaches investigated in this thesis. Throughout the construction of the Combined FMEA the purpose of the new FMEA is kept in mind; a FMEA approach that ranks the failure modes in a better way than the traditional FMEA but is still easy to use, has an unambiguous result and in general has a minimal risk of being misinterpreted. When designing the FMEA the company should consider a few basic but very important things. First of all the ambition level should be set; will the FMEA be a small project with few resources or is it a larger ongoing project? Secondly it should be evaluated which type of data will be available; quantitative data, qualitative data or qualitative data than can approximate to quantitative.
Page 60 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
The benefit of redefining Severity into Aggregated Impact with three sub dimensions; Cost Impact, Time Impact and Scope/Quality Impact is very high. In most cases Severity is seen as the most important dimension and by breaking the dimension down, more specific information will be gained. The expert team members should decide the weights between the three sub dimensions. The dimension Detection should also be redefined in order to be more specific and to include; detection of the risk event, controlling the root causes and controlling the consequences of the risk. The scales for S, O and D should still be adjustable in the definitions based on the industry the FMEA is used in. The new FMEA method should allow the expert team members to give different ranks for the dimensions of a given failure mode. If the company performing the FMEA is very sensitive to failures the recommendation will be to use the worst case scenario, hence the highest individual rank for S, O and D should represent the given failure mode. If the company using the FMEA is not extraordinarily sensitive to failures the recommendation will be to weight the ranks of a given expert in accordance to the expert‟s relative knowledge when calculating the overall ranks. Because an expert has not necessarily the same relative knowledge regarding Severity, Occurrence and Detection, three different weights should be used in the weighting. The way of calculating the average RPN is quite important for the result. Calculating the average dimension ranks separately and based on those calculate the RPN give most flexibility and in case of if-then rules this is the only option since it is not possible to take the average of the risk prioritizations. When calculating an average of a dimension‟s ranks, the overall understanding of the dimension must be defined first. If the scale, like most Occurrence scales, is defined as an exponential distribution, the average rank should not be calculated as a simple mean of the ranks. If the scale is defined by probabilities the probabilities should be used for calculating the average and from the average probability the corresponding rank can be chosen. Even though if it is not clearly defined, it should be decided what distribution the scale most likely represents e.g. exponential or linear. In order to keep the synergy effect from the expert team meetings a preliminary FMEA meeting can be held where the experts are brainstorming about potential failure modes and all failure modes can be described clearly. Afterwards the experts individually can Page 61 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
give ranks and weights for Severity, Occurrence and Detection. The scores will then be collected and weighted in accordance the expert‟s relative knowledge. After the failure modes are prioritized a second expert meeting should be held in order to discuss the situation and which actions to take. In case that the data is qualitative with no possibility to approximate it to quantitative data the scale values should be changed to levels (L1, L2 etc.) and a maximization/minimization function can be used to determine the risk levels of the failure modes. In this way the problems of people misunderstanding the dimension scales and the RPN as being quantitative would be eliminated. The FMEA should be seen as a flexible tool, which can be adjusted to the needs of the company. In case of small companies with limited resources it is very important to keep the FMEA simple and non-time consuming. That said, the traditional FMEA should at a minimum be extended to include global weights for the dimensions. Furthermore it should be considered to automate some calculations which can compensate for a more complex calculation of the RPN. The expected cost of performing a FMEA should always be weighted against the benefit of reducing the failure modes.
6. Conclusion In general the procedure of the FMEA is to identify and then rank the potential failure modes in order to prioritize mitigation actions. The traditional FMEA classifies the failure modes based on the three dimensions; Severity of the failure effect, frequency of Occurrence and likelihood of Detecting if the failure mode occurs. Based on the RPN (S*O*D) mitigation actions can be planned and prioritized. The traditional FMEA uses 10-points scales for S, O and D. The definitions of the scales transfer a verbal evaluation of the failure mode into an ordinal number which is used for the calculation of the RPN. There are four overall types of FMEAs. The System-FMEA analyzes systems and subsystems in the beginning of the concept and design stage. The Design-FMEA analyzes the failure modes caused by deficiencies in the design and is used to analyze products before going to production. The Process-FMEA is used for analysis of
Page 62 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
manufacturing and assembly processes. And finally in the Service-FMEA the service is analyzed before it reaches the customer. During the last decade the traditional FMEA approach has been greatly criticized. The main points of the criticism are in regard to the definitions of the scales for S, O and D and regarding the calculation of the RPN. One of the advantages of the RPN is that it includes three dimensions where most other risk assessments only evaluate Severity and Occurrences. Another advantage is that the RPN is very easy to calculate. One of the problems about the RPN is that it assumes that S, O and D all have the same metric (a 10-point scale) and the same danger level for each scale value. When using the natural numbers [1; 10] it is easy to misunderstand the scale and assume that a linear relation exists between the scale elements, hence there is a high risk that people will interpret e.g. an Occurrence at 4 as twice as bad as an Occurrence at 2. Even though the definition of Occurrence differs from author to author, they seem to agree that the scale should reflect an exponential distribution. Because the definitions of Severity and Detection are only verbal they cannot be translated into mathematical functions. The scale definition for Detection has been discussed by several authors. The definition of Detection often differs between two main definitions; either Detection is a measure of how easy it is to detect the failure when it occurs or it is a measure of how easy it is to prevent the failure. The RPN has a scale from 1 to 1,000 but the indices of S, O and D operate with a scale from 1 to 10. The much wider scale for the RPN results in that the failure modes will be ranked with a much higher resolution than can be justified. The RPN scale is easily misunderstood. Having the RPN on a scale from 1 - 1,000 gives the impression that the mean of the RPN should approximately be 500 but the actual mean is 166.38. The RPN scale further gives the impression that the median is approximately 500 but the actual median is 105. The distribution of the RPN is in general very right skewed. Only six RPN values are unique the rest of the values represent more than one (S, O, D) combination. For each failure mode the expert team members are forced to find one rank for each of S, O and D. Often the experts will disagree about the ranks and consequently the dimension rank will be a compromise of the team experts‟ individual opinions. The Page 63 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
more aggressive and loud speaking experts will often have a very high influence on the specific ranks even though they are not necessarily the experts with the biggest knowledge about the subject. Overall there are two ways to calculate a simple average of the RPN; calculating the RPN based on average S, O and D or calculating the RPN as the average of the experts‟ individual RPNs. Another possibility is to “play safe” and choose the highest rank for each dimension. The formula for RPN does not weight the input S, O and D. This means that it is assumed that the three dimensions are of equal importance. To not weight the dimensions is a problem because a “low risk” with a RPN below 36 can e.g. be (S=10, O=2, D=1) which is a so severe risk that it should trigger a mitigation action no matter the low ranks for O and D. Furthermore the non-weighting results in a lot of failure modes with the same RPN which cannot be distinguished from each other. Besides being able to weight the dimensions, the perfect RPN model should give an incremental output if any of the dimensions increase. This means that if two of the dimensions are fixed and the third dimension increases then the RPN should never decrease. An advantage of the traditional RPN is that it has a clear monotone relation. The problem of the RPN is that it is not capable of distinguishing between the importance of S, O and D. Both criteria will be possible by the use of weighted fuzzy production rules. In this thesis some of the alternative FMEA methods have been investigated and compared with the traditional FMEA and with each other respectively. Method A is based on Francescini & Galetto‟s (2001) fuzzy FMEA with maximization and minimization functions. In method A the expert team members first give Risk Levels for S, O, D and the Importance levels for the dimensions. Then the Risk Priority Code is calculated as a maximization and minimization function. If the importance of a dimension is high the importance level has a potentially high impact on the RPC. The failure mode with the highest RPC is evaluated as the most dangerous failure mode. In case of equal RPC values the analysis can broken further down; the failure mode with most rankings above the RPC level will be the most dangerous failure mode.
Page 64 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Method A2 is based on Narayanagounder and Gurusami‟s (2009) alternative FMEA which is similar to method A. The Critical Failure Mode Index (CFM Index) is calculated by a max/min formula. The failure mode with the highest number of levels above the CMF Index is the most dangerous failure mode. In case of equal prioritization of two or more failure modes, the most dangerous failure mode is the one that compared to the other failure modes has the relative highest S, O or D evaluation. Method B is based on Abdelgawad and Fayek‟s (2010) modified FMEA. The method is based on a bigger redefinition of Severity and Detection. Severity is redefined to “Aggregated Impact” and is broken down to three subgroups; Cost Impact, Time Impact and Scope/Quality Impact. Detection is still one single rank but is redefined to include three elements; detection of the risk event, controlling the root causes and controlling the consequences of the risk event. In method B the membership functions for all dimensions are first defined. Then the Aggregated Impact is calculated based on the relation between each of pairs of sub dimensions. And finally the RCN is estimated based on a fuzzy set of if-then rules. Method C is based on Wang et al.‟s (2007) alternative FMEA based on a fuzzy weighted geometric mean. The method allows importance weights for S, O and D and that the expert team members have different evaluations of S, O and D. For each dimension membership functions are made based on fuzzy ratings. The fuzzy RPN ranks the failure modes based on the weighted dimensions. Furthermore the FRPN weights the experts‟ rankings according to their relative knowledge about the subject. Method D builds on Sawhney et al.‟s (2010) FMEA approach intended for enhancing reliability of LEAN systems. The purpose of the modified FMEA is to highlight the gap between the actual business conditions and the ideal conditions. The method builds on the four main resources for sustaining LEAN; Personnel, Equipment, Materials and Schedules. Instead of using the traditional RPN a new parameter, Risk Assessment Value (RAV), is used which prioritizes the failure modes based on their ability to detect and control the failure via LEAN tools. Method E1 and E2 are based on Narayanagounder and Gurusami‟s (2009) alternative FMEAs. The methods are developed in order to deal with the problem of the expert team disagreeing on the ranks for the dimensions. In method E1 the RPN is calculated
Page 65 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
as the mean of the team members individual RPNs. In case of equal mean RPNs the failure mode with the smallest range of RPNs is the most dangerous failure mode. In method E2 the RPN value is calculated for all failure modes by all team members. Based on the different RPNs an analysis of variance (ANOVA) is made in order to test if the RPN means for the failure modes are significantly different. The alternative FMEA methods have some common features but do also differ a lot from each other. Method A, B and C weight the three dimensions based on importance. Method A and C use global weights for the dimensions hence the same weight for S, O and D respectively are used independently on if the dimension rank is high or low. Method B can have all different types of weights built indirectly into the if-then rules. The if-then rules can e.g. cover a threshold weight, a global weight and a local weight. Method A includes the importance level for the dimension on equally basis with the dimension rank when calculating the RPC; hence the importance level can potentially have very high influence on the RPC. In method C the dimension weights are used as exponents for the dimension ranks in calculation of FRPN. That method B builds on in-then rules is not an unconditional improvement from the traditional FMEA. The main concern about using if-then rules is that it is very time consuming to set up the rules. If case of 10-points scales for S, O and D the expert needs to go through 1,000 situations as Sankar & Prabhu (2001) suggest. Even though 5-points scales are used as in method B the expert still needs to go through 125 rules. If deciding to use if-then rules, the usefulness of the rules depends a lot on the possibility to reuse the rules across different FMEA reports. Method A overcomes most of the issues related to the scales. By having the scale values named as levels (L1, L2 etc.) the scales are less likely to be misinterpreted as being quantitative. Furthermore the scale interval for the RPN is limited to the same interval as the dimension scales, in this way the RPN ranking can be better justified. Method D is the only method investigated that rank the failures based on a fraction relation of the dimensions (S*O/D). A drawback of the RAV is that the scale, just as the RPN scale, can easily be misunderstood as being quantitative. By redefining Severity into Aggregated Impact Method B makes sure that the experts evaluate the sub dimensions separately and weight them. This reduces the risk of Page 66 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
forgetting one of the sub dimensions in the light of one of the others. Furthermore method B is the only FMEA method investigated that has also redefined Detection. Normally the traditional FMEA operates with a tripartite categorization of the RPN values with high risks as action triggers. According to method B an action should be taken if the RCN is as minimum evaluated as a moderate risk (RCN=250). The other methods investigated do not have defined when an action should be taken. Method C, E1 and E2 allow the team members to give an individual evaluation of all ranks. Afterwards a mean rank is calculated. A problematic about method C, E1 and E2 is that they treat the scales as being quantitative when they calculate the averages ranks. Method A and A2 calculate the RPN by the use of maximization and minimization functions. Both methods minimize across dimensions and maximize across the different failure modes but the order of the functions differs for the two methods and this causes a difference in the final prioritization of the failure modes. Method E2 is the only method investigated that statistically evaluates if the risk prioritization ranks differ significantly. The use of ANOVA is problematic because the test is only meant for use with interval/ratio scaled data. Instead the non parametric test Kruskal-Wallis can be used. This test fits with a test on several independent samples on ordinal scales and there is no assumption regarding normal distribution. In chapter 5 a combined FMEA is made in order improve the traditional FMEA more widely than any of the alternative FMEA methods investigated in chapter 3 did. The construction of the Combined FMEA is done with focus on creating a FMEA approach that ranks the failure modes in a better way than the traditional FMEA but is still user friendly, has an unambiguous prioritization of the risks and in general has a minimal risk of being misinterpreted. The most important thing is to find a balance between accuracy and cost of performing the FMEA and this depends on the type of company and the level of resources. Furthermore it is important to be aware of type of the data; should it be handled as quantitative data, qualitative data or qualitative data than can approximate to quantitative?
Page 67 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
Severity should be redefined into Aggregated Impact with the three sub dimensions; Cost Impact, Time Impact and Scope/Quality Impact. By breaking Severity down more specific information will be gained. Detection should also be redefined in order to be more specific and include control. The sub dimensions for Detection are; detection of the risk event, controlling the root causes and controlling the consequences of the risk. In case the data should be understand and handled as purely qualitative data the scale values should be changed to levels and a maximization/minimization function can be used to determine the risk levels of the failure modes. In this way the problems of people misunderstanding the scales for the dimensions and the RPN as being quantitative will be reduced. In case the data can adjust to quantitative data the new FMEA method should allow the expert team members to give different ranks for the dimensions of a given failure mode. If the company using the FMEA is not extraordinarily sensitive to failures the recommendation will be to weight the ranks of a given expert in accordance to the expert‟s relative knowledge of the dimension when calculating the overall ranks. In case of sensitivity the worst case scenario for all dimensions should be chosen. Calculating the RPN based on average ranks of the dimensions gives most flexibility. Neither the dimensions nor the risk prioritization rank are designed for average calculation because they are ordinal scaled. But even though if it is not clearly defined, it should be decided if it is more likely that the distribution is e.g. exponential instead of linear. The mean rank should then be calculated based on the distribution, e.g. Occurrence can be calculated based on the exponential definition. It is important to keep the synergy effect from the expert team meetings and that all experts are aligned about the content of the given failure modes. Therefore a preliminary FMEA meeting should be held where the experts indentify the potential failure modes. Afterwards the experts should individually rank and weight the dimensions; S, O and D. After the prioritization an expert meeting should be held in order to discuss the situation of the highest failure modes and the corresponding actions. It is here important to make sure that the FMEA process does not stop when the report is delivered to the management. The report should be a living document and the FMEA should be a part of continues improvement.
Page 68 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
7. Perspective In the thesis only FMEA approaches based on qualitative data has been investigated. Quantitative data would be a very interesting foundation for FMEA because it gives some different possibilities regarding calculations. The prioritization of the failure modes will be more reliable and it will be possible to include costs in the calculations e.g. as the final prioritization parameter. C.f. chapter 1.2 qualitative data will most likely be available in the Control phase of the DMAIC process. Several authors have investigated the possibilities for making a more quantitative costbased FMEA. In the following an extract of the existing research literature about costbased FMEAs is made. In 1993 Gilchrist proposed an alternative FMEA where the failure modes were prioritized based on expected costs. Later Kementa and Ishii (2000) presented a scenario-based FMEA with use of expected costs. The method works as a cost based decision making tool but requires quantitative data and the experts are not allowed to have different opinions. Based on the scenario-based FMEA from 2000, Rhee & Ishii (2003) introduced the Life Cost-Based FMEA. This FMEA measures risks as cost over life cycle. When the origin and detection occur in the same stage the failure cost is minimal. The further apart the origin and detection stages become, the higher is the increase in the failure cost. The failure costs are broken down in three major components: labor cost, material cost and opportunity cost. The labor and opportunity costs can be broken further down into: detection time, fixing time, delay time and recovery time. In 2001 Tarum presented the FMERA on the SAE world congress. The FMERA analyzes process failures and prioritizes corrective actions based on financial risk to the operation. Regarding Service-FMEA Arunachalam & Jegadheesan (2006) have introduced a cost based Service-FMEA approach with focus on reliability. With the purpose of creating a FMEA with focus on costs but at the same time also based on qualitative data, Dong (2007) presented a fuzzy FMEA based on utility theory and fuzzy membership functions for S, O and D. The failure modes are prioritized based on the Risk Priority Index (RPI) which reflects the failure cost. The disadvantage of a cost-based FMEA is that all focus will be on costs. Some costs are very hard to anticipate but still they are just as important as any other costs. This can e.g. be costs regarding injury to the company‟s reputation if its quality fails. Another Page 69 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
drawback of the cost-based FMEAs is that they rely on quantitative data which does not always exist. On the other hand using cost-based FMEA can have some huge advantages e.g. the analysis will use more information than a traditional FMEA and should therefore be more reliable in the ranking of the failure modes. Another big advantage is that the prioritization is more logical for the stakeholders. The management usually takes decisions based on costs, hence it will be more rational to prioritize based on costs instead of RPN values.
Page 70 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
8. Literature Articles 1) Abdelgawad, M. & Fayek, A. R., September 2010, „Risk Management in the Construction Industry Using Combined Fuzzy FMEA and Fuzzy AHP‟, Journal of Construction and Management, Vol. 136, No. 9 2) Arunachalam V.P. & Jegadheesan, C., 2006, Failure Mode and Effects Analysis: A Reliability and Cost-based Approach, The IUP Journal of Operations Management, pp. 7-20 3) Bowles, J.B. & Peláez, C.E., 1995, „Fuzzy logic prioritization of failures in a system failure mode, effects and criticality analysis’, Reliability Engineering and System Safety, Vol. 50, pp. 203-213 4) Bradley, J.R. & Guerrero, H.H., August 2011, „An Alternative FMEA Method for Simple and Accurate Ranking of Failure Modes’, Decision Sciences Journal, Vol. 42, No. 3 5) Carbone, T.A. & Tippett, D.D., 2004, „Project Risk Management Using the Project Risk FMEA’, Engineering Management Journal, Vol. 16, No. 4 6) Dong, C., 2007, „Failure mode and effects analysis based on fuzzy utility cost estimation’, International Journal of Quality & Reliability Management, Vol. 24 Iss: 9 pp. 958-971 7) Franceschini, F. & Galetto, M., March 2001, „A new approach for evaluation of risk priorities of failure mode in FMEA’, International Journal of Production Research, Vol. 39, No. 13, pp. 2991-3002 8) Gilchrist, W., 1993, „Modelling Failure Modes and Effects Analysis’, International Journal of Quality & Reliability Management, Vol. 10, No. 5, pp. 324-336 9) Kmenta, S. & Ishii, K., September 2000, Scenario-based FMEA: A life cycle cost perspective, ASME Design Engineering Technical Conferences
Page 71 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
10) Narayanagounder, S. & Gurusami, K., 2009, „A New Approach for Prioritization of Failure Modes in Design FMEA using ANOVA’, World Academy of Science, Engineering and Technology Vol. 49 11) Norheim, E.T., 1986, „Kruskal-Wallis test: BASIC computer program to perform nonparametric one-way analysis of variance and multiple comparisons on ranks of several independent samples’, Computer Methods and Programs in Biomedicine, Vol. 23, pp. 57-62 12) Pillay, A. & Wang, J., 2003, „Modified failure mode and effects analysis using approximate reasoning’, Reliability Engineering and System Safety vol. 79, pp. 69-85 13) Rhee, S.J. & Ishii, K., 2003, „Using cost based FMEA to enhance reliability and serviceability’, Advanced Engineering Informatics Vol. 17, pp. 179-188 14) Sankar N.R. & Prabhu B.S., 2001, „Modified approach for prioritization of failures in a system failure mode and effects analysis’, International Journal of Quality and Reliability Management, Vol. 18, No. 3, pp. 324-336 15) Sawhney R., Subburaman, K., Sonntag, C. Rao, P.R.V. & Capizzi, C., 2010, „A modified FMEA approach to enhance reliability of lean systems’, International Journal of Quality & Reliability Management, Vol. 27, No. 7, pp. 832-855 16) Selvan et al., 2012, „Continuous Quality Improvement in Investment Castings: An Experimental Study using a Modified FMEA Approach Called FEAROM’, European Journal of Scientific Research, Vol. 74, No. 2, pp. 308-325 17) Tay, K.M. & Lim, C.P., 2010, „Enhancing the Failure Mode and Effect Analysis methodology with fuzzy inference techniques’, Journal of Intelligent and Fuzzy Systems 21, pp. 135-146 18) Tarum, C.D., March 2001, FMERA – Failure Mode and Effects (Financial) Risk Analysis, SAE Technical Paper Series, SAE 2001 World Congress 19) Teng, S.H. & Ho, S.Y., 1996, „Failure mode and effects analysis: An integrated approach for product design and process control’, International Journal Quality & Reliability Management, Vol. 13, No. 5, pp. 8-26 Page 72 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
20) Wang, Y.M., Chin, K.S., Poon, G.K.K. & Yang, J.B., 2007, „Risk evaluation in failure mode and effects analysis using fuzzy weighted geometric mean’, Expert Systems with Applications Vol. 36, pp. 1195-1207 Books 21) Brassard, M., 1991, The Memory Jogger, GOAL/QPC, 2nd edition 22) Chrysler LLC, Ford Motor Company & General Motors Corporation, June 2008, Potential Failure Mode and Effects Analysis (FMEA), Reference Manual, 4th edition 23) Ginn, D. et al., 2004, The Design for Six Sigma Memory Jogger, GOAL/QPC, 1st edition 24) Gitlow, H.S. & Levine, D.M., 2010, Sig Sigma for Green Belts and Champions, Pearson Education, 8th edition 25) Guba, E.G. & Lincoln, Y.S., 1994, Competing paradigms in qualitative research. In: Denzin N.K. & Lincoln Y.S. (eds), Handbook of Qualitative Research. Thousand Oaks, CA: Sage, pp. 105–117. 26) Heldbjerg, G., 1997, Grøftegravning i metodisk perspektiv, Samfundslitteratur 27) Keller, G., 2009 Managerial Statistics, South-Western Cengage Learning, 8th edition 28) Kubiak, T.M. & Benbow, D.W., 2009, The Certified Six Sigma Black Belt Handbook, America Society for Quality - Quality Press, 2nd edition 29) Stamatis, D. H., 2003, Failure Mode and Effects Analysis: FMEA from Theory to Execution, America Society for Quality - Quality Press, 2nd edition
Software Programs -
Microsoft Office Excel 2007
-
IBM SPSS Statistics 19
Page 73 of 85
Master Thesis Date
M. Sc. Business Intelligence
Student no.: 404340 Maria Bech Andersen
9. Appendices 9.1. Appendix: Definition of the Severity scale
Hazardous
Table 1.1: Severity definitions Rank Effect Criteria Stamatis (2003) 10 Hazardous effect .Safety related-sudden failure. Noncompliance with government regulation.
Serious
9
Extreme
8
6
Significant
Major
7
Moderate
5
Minor
4
Potential hazardous effect. Able to stop product without mishap-timedependent failure. Compliance with government regulation is in jeopardy. Customer very dissatisfied. Product inoperable but safe. System inoperable. Customer dissatisfied. Product performance severely affected but functionable and safe. Subsystem inoperable. Customer experiences discomfort. Product performance degraded, but operable and safe. Nonvital part inoperable. Customer experiences some dissatisfaction. Moderate effect on product performance. Fault on nonvital part requires repair. Customer experiences minor nuisance. Minor effect on product performance. Fault does not require repair. Nonvital fault always noticed.
Effect Criteria Chrysler LLC et al. (2008) Failure to Potential failure mode meet safety affects safe vehicle and/or operation and/or regulatory involves requirenoncompliance with ments government regulation without warning Potential failure mode affects safe vehicle operation and/or involves noncompliance with government regulation with warning Loss of Loss of primary degradation function (vehicle of primary inoperable, does not function affect safe vehicle operation) Degradation of primary function (vehicle operable, but at reduced level of performance) Loss or degradation of secondary function
Annoyance
Loss of secondary function (vehicle operable, but comfort/ convenience functions inoperable) Degradation of secondary function (vehicle operable, but comfort/ convenience functions at a reduced level of performance) Appearance or Audible noise, vehicle operable, item does not conform and noticed by most customers (>70 %)
Page 74 of 85
Master Thesis Date
Slight
3
Very slight
2
Customer slightly annoyed. Slight effect on product performance. Nonvital fault noticed most of the time. Customer not annoyed. Very slight effect on product performance. Nonvital fault noticed sometimes. No effect
No effect
Student no.: 404340 Maria Bech Andersen
Appearance or Audible noise, vehicle operable, item does not conform and noticed by many customers (50 %) Appearance or Audible noise, vehicle operable, item does not conform and noticed by discriminating customers (
