Using SPSS for Process Quality Control – A Critical Review Alexander Naidenov, PhD, Assist. Prof., Statistics and Econometrics Department, UNWE, Sofia, Bulgaria, [email protected]

Abstract. The pursuit of high quality production is one of the main topics of our modern world society. The great variety and complexity of the production characteristics lead to the need for use of the specific software products in order to control for the production process quality. There are many software solutions to this issue but one of the most famous is SPSS. Although the latter is a wide range purposed software tool it also provides great opportunities for a basic quality control analysis. The paper is a critical review of SPSS quality control functions and features. Keywords: SPSS, quality, control, process, tools

1. Introduction Our contemporary society is dedicated to the mass production and consumption of incredible wide variety of products. Some manufacturers prefer to produce low cost products with low quality but other pursuit the excellence in all directions. When we talk about quality products we understand different things. The consumer imagines a quality good or service as such that would satisfy his/hers physical, emotional and mental needs. But if we ask the manufactures they will replay: ‘Our quality products (services) are such because they meet the required standards’. When these two viewpoints collide the concept of production process quality is born. The manufacturers who follow their production standards and strive to satisfy consumer needs are obliged to observe a great number of rules concerning the product or service characteristics and features. In order to achieve a certain level of ‘perfection’ in these quality characteristics (e.g. weight of a biscuit, length of a knife blade, smoothly working tablet PC operating system, etc.) we need to probe continuously the status of these. This is due to the fact that principle ‘everything changes’ holds for the production characteristics too. The variation of the latter is caused by different kind of sources e.g. tired worker makes more mistakes, worn machine produces poor output, bad raw materials lead to bad products, etc. So if we can reduce this variation in the characteristics we will achieve easier the standard requirements and finally we will have production with certain level of quality. The first step to manage the variation of production characteristics is to survey and observe their changes in time. If we are able to measure and control the levels of these characteristics we will be able to provide assurance of good production quality. There are many statistical and non-statistical tools for production process quality control but one of the most popular ones, even now - ninety years after their invention, are so called Shewhart control charts. Generally speaking they are a special graphical visualization of certain product characteristic temporal dynamics. These charts provide the possibilities for observation of characteristics’ changes in the time and interference in the production process, if there is a warning for product quality worsening. Unfortunately one product or service doesn’t have only one dimension of quality. Even the one-piece type products, such as the kitchen knife, have more than one characteristic – blade length, hardness, sharpness, handle comfort and etc. In order to control

for all the quality features of a given product, we usually use modern technologies such as computers, sensors, lasers and so on. Nowadays every product, subject to quality control, is an object of detailed measurements which are stored as a raw data in big databases. The latter are then imported in specialized software products to deepen the analysis of the process dynamics and variation. Many of today’s statistical packages, which are multi-purposed ones, include a set of statistical methods for quality control of production process data. This paper considers the most famous and widely used software for broad-range analysis Statistical Package for Social Science (or SPSS) and its usage for basic quality control analyses. Next sections are dedicated to a short description of the software capabilities in the quality control field and also a critical review of its features.

2. SPSS quality control features and functions Nowadays many scientists and researchers in Bulgaria count on SPSS for their analysis and problem solving and that is why it is a logical reason to test the capabilities of this software for quality control problem solvation too. Even though initially SPSS is social science oriented software, over the course of time it became a Swiss-army-knife type tool. Its capabilities include manipulating raw data from different sources and many formats, basic statistical descriptive analysis (including graphical presentation), advanced techniques such as non-parametric tests, regression, correlation, factor analyses, multiple imputation, distribution simulation, sampling, survival analysis and many more. Since version 14th (at the time of writing this paper 22nd version of SPSS is the latest available and this paper is based on it) SPSS team implemented quality control functionality and became an easy tool for basic quality control analysis. Let us present its quality control features at the following diagram: SPSS Quality control features

Fig.1. Main SPSS quality control features.

As it can be seen in the Fig.1, SPSS has two main tools for quality control: control charts and Pareto charts. Control charts include such as these for variables (quantitative characteristics measures at interval or ratio scale e.g. temperature in Celsius, weight in grams, length in cm, etc.) and for attributes (qualitative characteristics measured at nominal or ordinal scales e.g. defective and non-defective items). Measurements of a given product characteristic is based on a random selection (a.k.a. sample) of one individual item (unit) or a subgroup (sample) of items (units) from the all produced items called a lot. The reasons for the unit sampling are rooted in the great number of produced items (usually in hundreds of thousands, even millions) and the lack of resources (time, personnel, space, etc.) for the measurement of all characteristics for given units. Also it is imposed by the “unreal” variation in the individual unit characteristics (individual values variation is greater than sample means variation). Using the measurements of the sampled units and based on the statistical sampling theory [3], we can be sure at a certain level that almost all items (99,7%) will fall in ±3 standard errors (standard deviation divided by squared number of sampled items) from the target value (the mean of all measurements). This gives us the possibility by the use of control charts (which implement the sampling theory) to test if there are measurements outside these limits (also called control limits) and if there are such to act in order to avoid manufacturing of out of specification (the specification limits are defined by the quality standards considering the natural variation (not caused by and special events) in the item characteristics and are described in details in the product documentation) items (e.g. if the knife blade became too short of too long). When we encounter such out of control limit measurements it is a warning that may be there are special (non-natural) causes influencing the production process that may lead to a low quality production [4]. All these assumptions are considered in the control chart functionality of the SPSS software. First let us describe the software features concerning the variable charts. There are two types of them: charts for subgroup (sample) of units and charts for individuals (in Data organization option you define the structure of the file and not the data collection type). For subgroups

For individuals

Fig.2. Screenshots of the software windows for variable control charts. When data are available for a sample of units we use so called X-bar (mean), R (range) and s (standard deviation from a sample) charts. By the combined use of these we can simultaneously account for the change in the accuracy (sample means) and for the

precision (sample range and standard deviation) of a given the production process. In Fig.2 (the left part) we can see the required fields for control chart building. These are: Process Measurement (defines the variable that contains the measurements of interest), Subgroups Defined by (defines the variable which account for the identification of each sample) and Identify points by (defines the variable which identify each and every measurement in order to expose for which of them we should worry about). At this step we can choose how we will measure precision – by R or by s charts. Also there are additional options available for each control chart given as buttons: Titles (user defined chart titles), Options (defines the number of sigmas (standard error boundaries) to use in testing and the size of each sample (subgroup), Control Rules (specific rules used to perform quality control using control charts features [6]) and Statistics (control chart capability analysis features using indexes [5]). Titles

Options

Control Rules

Statistics

Fig.3. Screenshots of software windows for variable charts options.

Using example data from the production process of terracotta tiles (21 random samples of 7 units) we attain the following control charts:

X-bar control chart

R control chart

Control chart rule violations

Fig.4. Screenshots of SPSS output results for variable control charts (an example).

As it can be seen in Fig.4, control charts are presented visually in order to find out if there are any warnings or rules violations. For every chart also we can see the average of sample means (average is given with solid line and means with diamonds), upper and lower control limits (given with dotted lines). Automatically the possible rule violations (presented as circled points) are described in tables too with additional information for the ID of the problematic measurement(s). An extra feature is the capability analysis which shows the production process possibilities in the scope of manufacturing production in the specification limits:

Fig.5. Screenshots of SPSS output results for capability analysis (process statistics). The features for the control charts for individuals are almost the same but considering the fact that here we do not have samples of a number of units we cannot calculate sample means, ranges and standard deviations. In this case we use so called moving range or the difference between two consecutive measurements. The use of those kind of control charts is imposed by the peculiarities of some manufacturing or servicing process that have for example only one unit at random time intervals (e.g. customer claims in a bank). When there are no possibilities for quantitative measurement of production items (e.g. we have only a description of the item quality features) we usually define the units only as defective (non-conforming) and fit-to-use (conforming) ones i.e. we use so called attribute control charts. If we are interested in the number of defects per item then we call these issues non-conformities. In SPSS we can use np (number of non-conforming units from all produced) and c (number of non-conformities) chart – if each sample used has an equal size, and p (proportion of non-conforming units from all produced) and u (number of nonconformities per unit) – for the unequal size samples.

p and np control charts

c and u control charts

Fig.6. Screenshots of software windows for attributes control charts. Similarly to the variable control chart we should define: subgroups and point (units) identifiers but also specific variables for the nonconforming items and the nonconformities. It is important to indicate if we have used equal (constant) or unequal (variable) sample sizes. The options and control rules are exactly the same as those for the variable control charts. Using sample data for quality control of the color pencil production we obtain the following results for the four types of attribute charts:

p control chart

u control chart

(cont.) np control chart

c control chart

Fig.7. Screenshots of SPSS output results for attribute control charts. In this case we can also notice the presence of information about the center line (target value), upper and lower control limits (at ±3 standard errors), sample non-conforming items and non-conformities too. In case of need for rules violation analysis an output for these is also available: For the p control chart

For np control chart

For the u control chart

For c control chart

Fig.8. Screenshots of SPSS output results for attribute control charts (rules violations). When we deal with attribute data a lack of capability analysis is evident, so in this case it is omitted. However we have additional capabilities for defect items analysis and it is based on so called Pareto charts, named after the Italian economist Vilfredo Pareto (18481923) who discovered that 80% of the land in Italy was owned by 20% of the population (see Fig.1 - right part). They are useful if we’d like to find out what are the major reasons for non-conforming units production. For example if execute quality control for a call-center service, indicating reasons for eventual client claims, we could get the following results by summarizing the collected data:

SPSS Pareto Chart window

Output results

Fig.9. Screenshots of SPSS Pareto charts function and output results. Depending on the information collected it is possible to use and visualize individual cases or aggregated data. At the figure above (in the right) we could see the Pareto chart for our example that states that the main reasons for call-center issues (see left part of the chart) are the ‘Operator bad attitudes’, ‘Too long waiting time’ and ‘Not qualified operator’. The chart shows not only the number of claims (counts) but also the cumulative present of different types of issues. We can see that Pareto principle is held that about 80% of the claims are due to the first three reasons. Although SPSS includes the most frequently used basic tools for quality control it lack some of most powerful techniques implemented in specialized software products such as Statistica and Minitab. Some of these missing functionalities are: • Design of Experiments; • Cause-and-effect (fishbone) diagram; • EWMA and CUSUM charts; • Rare event control charts: G, T; • Multivariate control charts: T-squared, generalized variance, MEWMA; • Custom tests for special causes; • Process capability for non-normal, attribute, batch type of data; • Six Sigma analysis; • Acceptance sampling and OC curves; • Measurement Systems Analysis (Gage Repeatability/Reproducibility Analyses); • Automatic updating of quality control charts and process capability statistics as new data becomes available (real-time online process analysis and monitoring); • Sampling techniques for quality control. The abovementioned functions are not obligatory but they are essential especially when the statisticians or researchers want to do more elaborate analysis of the quality status of a given production process.

3. Conclusion Even though SPSS is not a ‘real’ quality control tool it provides a sufficient amount of basic functionalities for the quality issues management. Unlike its qualified and specialized competitors (Minitab and Statistica), which provide sophisticated and elaborated quality

control instruments, this software product gives a limited options for quality analyses mainly by the use of control and Pareto charts. However we hope that our favorite universal all-inone tool for the data processing will continue developing in the scope of its quality control functions and soon we will be able to do more powerful and complex quality statistical analyses.

References 1. IBM Corporation: IBM SPSS Statistics 22 Core System User's Guide (2013). 2. IBM Corporation: IBM SPSS Online Help (2013). 3. Lohr, S.: Sampling: Design and Analysis, Duxbury Press (2010) 4. Mitra, A.: Fundamentals of quality control and improvement, John Wiley & Sons (2008) 5. Montgomery, D.: Introduction to Statistical Quality Control, Sixth Edition, Wiley & Sons Inc. (2009). 6. Oakland, J.: Statistical Process Control, Sixth Edition, Butterworth-Heinemann (2008).