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Real-life Problems and Industrial Statistics

Ronald J.M.M. Does Institute for Business and Industrial Statistics, University of Amsterdam Plantage Muidergracht 24 1018 TV Amsterdam, The Netherlands E-mail: [email protected] 1.Introduction Modern quality theory started in the Twenties when mass production was introduced in industry. In its development three phases can be distinguished, which can be characterized by: Quality by Inspection, Quality by Process Control and Quality by Design. In this paper we give a survey of the research which was initiated by consultancy projects in Dutch industry. In the examples statisticians from the Institute for Business and Industrial Statistics Inc. were involved. This institute (abbreviated by IBIS UvA) was founded in 1994 within the Department of Mathematics of the University of Amsterdam. Since 1998 IBIS UvA has been embedded in the Holding of the University of Amsterdam, in which all the commercial activities of the university are accommodated. The services that are provided by IBIS UvA deal with implementation of Statistical Process Control, Six Sigma and other quantitative quality programs, courses and general statistical consultancy. To support and constantly improve these activities, IBIS UvA aims to contribute to scientific research in industrial statistics on an international level and to promote the application of industrial statistics in all relevant parts of society. The customers of IBIS UvA cover a wide range of products and services. The purpose of this paper is to give a survey of the research, which has been done by members of IBIS UvA. Note that all research was initiated by consultancy projects and deals with real-life problems. The paper is organized as follows. In section 2 we discuss quality by inspection, in section 3 we concentrate on quality by process control and finally in the last section we briefly mention some results in the field of quality by design. 2. Quality by Inspection In certain situations inspection is inevitable, despite the generally held convictions that inspection to improve quality is equivalent to planning for defects and that one cannot inspect quality into a product. One of the first projects of IBIS UvA was to evaluate several sampling plans for testing jewelry on fineness. In practice shipments of works of precious metal have to be tested for fineness. Testing may be done by the producer such as in Germany, but for instance in the Netherlands this is done by a notified body (Waarborg Platina, Goud en Zilver N.V., Gouda). In Klaassen (1996) new sampling plans for attributes are given. In Baillie and Klaassen (1998) a general procedure is presented for switching between accept-zero attributes or variables plans to provide sampling schemes with a specified Limit on the Average Outgoing Quality (LAOQ). The switching procedure is based on the concept of credit, defined to be the total number of items accepted since the last rejection. Once credit exceeds zero, sample size is a non-decreasing function of credit, rewarding the good producer with progressively smaller sample sizes and penalizing the poor producer with large sample sizes and frequent non-acceptance of lots. The LAOQ is maintained by means of mandatory 100% inspection of lots non-accepted when the credit is zero, with acceptance of all inspected items found to be conforming in such lots.

The general procedure is developed and illustrated by applying it in three situations: one for sampling by attributes; and two for sampling by variables from a normal distribution with known and unknown process standard deviation, respectively. 3. Quality by Process Control In our approach (cf. Does, Roes and Trip (1999a)), Statistical Process Control (SPC) is implemented on the shop floor by cross-disciplinary teams, which we call Process Action Teams (PAT's). Such a team consists of operators, foreman, process engineer, maintenance engineer, other technical personnel involved with the process, and a statistician. A PAT implements SPC for a specific process following ten steps of an activity plan. The main phases are: definition of the process to be dealt with; diagnosis of the process; design of control charts and out-of-control action plans; and implementation. From a statistical point of view the following issues are important: the choice of the quality characteristic which will be monitored, the way this quality characteristic is measured, the analysis of the variance components and the set-up for the control chart. In the last five years IBIS UvA has implemented SPC in several companies in the Netherlands. These companies cover the complete range from mass-production, low volume production and small series (or one off) production. We mention ASM Lithography (wafer steppers), Sara Lee | Douwe Egberts (coffee and tea), Fokker Aerostructures (cable harnesses and machining), Thomson CSF Hollandse Signaalapparaten (printed circuit boards), Philips Semiconductors (diodes), and Stork Digital Imaging (nozzles), among others. In this section we discuss our research related to measurement evaluation, search for variance components and control charts. 3.1 Evaluation of measurement systems Within quantitative quality programs, such as SPC but also Six Sigma, it is important to evaluate the measurement system or method. When a good measurement system is in place the measurements of a quality characteristic are precise and therefore, the variation in the quality characteristic under consideration can be controlled and improved. The usual way to investigate the precision of the measurement system is to conduct a well described experiment. The variability is often divided into two components, the first caused by the operators who do the measurements, the other by the measurement device itself. Since these components are called "Reproducibility" and "Repeatability", respectively, the above experiment is also known as a Gage R&R study (cf. Automotive Industry Action Group (1990)). In general, a random effects model is used for the experiment. However, in practice, operators are not always a sample from a large number. Instead, there are only a few, e.g. in the situation that a measurement requires expertise that just a few operators possess. Instead of assuming a general operator effect, which is normally distributed, the assumption that each operator measures a fixed distance from the true value makes more sense. In Van den Heuvel and Trip (1999) a new method for this situation is proposed. They also give a reallife example to show that the standard model indeed needs modification. 3.2 Analysis of variance components In SPC it is good practice to carefully study the behavior of the process under consideration prior to any control charting. In such a preliminary investigation the data are collected from the running process without deliberate intervention. From the collected data one can obtain a basic understanding of the main statistical features of the quality characteristic. For this study the multi-vari chart is a useful graphical tool. It provides a graphical display of the behavior of the quality characteristic in the running process. Variance components and patterns in the data are easily recognized. Seder (1950) introduces the multi-vari chart and compares it with the traditional ( X , R)-control chart. The multi-vari chart presents an analysis of the variation in the process by differentiating three main sources: 1. Intra-piece (the variation within a piece, batch or lot); 2. Inter-piece (the additional variation between pieces); and 3. Temporal variation (variation which is related to time).

In De Mast, Roes and Does (1999) formal statistical tests for the analysis of multi-vari charts are established. They state a number of hypotheses that can be used to evaluate what is going on with the running process. Examples of a fruitful combination of an analysis of variance using F-tests and a multi-vari study using the new tests are also given. 3.3 Designing control charts The control chart is the basic tool in SPC to detect the presence of special causes. Originated by Shewhart in 1924, the effectiveness of control charts is due in part of their simplicity. It is a chart indicating the time at which a quality characteristic is measured on the horizontal axis, and the value of the quality characteristic on the vertical axis. By charting a quality characteristic as a function of time we can judge whether or not a process is statistically under control. The charts are usually constructed using 20 to 30 initial samples of about 5 units. In general, these samples are supposed to arise from pure random sampling, when chosen rationally. A thorough treatment of statistical aspects of control charts in this typical textbook situation was given by Does and Schriever (1992). The case of subgroup size n=1 was treated in Roes, Does and Schurink (1993). The textbook situation referred to is seldom encountered in real-life. In most applications, control charts have to be tailored to the nature of the running process. Research on SPC by IBIS UvA statisticians has been dedicated to control charting methods that accommodate the situation of actual applications. The first concerns the presence of multiple components of variation actually present in the process inherent variation, dealt with extensively by Roes and Does (1995) and Does, Roes and Trip (1999b). Secondly, today's manufacturing hardly resembles the high volume production environment at the time of introduction of control charting methods. Low volume manufacturing requires adapted control charting methods, e.g., as developed by Quesenberry (1995). Adaptations and alternatives to enhance the power of these charts are given by Roes, Does and Jonkers (1999). Thirdly, the most commonly reported effect on control charts of violating one of the fundamental assumptions is the erroneous placement of the control limits. Especially, in situations where the independence assumptions is not true, control limits needs adjustment. In the Ph.D. thesis of Wieringa (1999) the application of control charts to cases where serially correlated observations are allowed is treated. Finally, another effective technique to control an industrial process was developed by Page (1954). He proposed the so-called Cumulative-sum (Cusum) chart. This technique plots the cumulative sums of deviations of the sample values of a quality characteristic from a target value against time. In Koning and Does (1999) Cusum charts for individual observations are considered. A new Cusumtype chart has been developed for the detection of linear trends based on the uniformly most powerful test. This chart is compared with the Likelihood Ratio Test control chart of Sullivan and Woodall (1996), the Cusum and Shewhart charts of the Q-statistics from Quesenberry (1995) and the traditional Shewhart control chart for individuals. 4. Quality by Design Designing processes and products so that they are insensitive to variation in conditions is known as robust design. It means that a process or product must be designed so that it is robust against potential causes of variability, that may occur before, during or after production. Since these causes are often hard or expensive to control, they are called noise factors (cf. Taguchi (1987)). The socalled Taguchi experiments include both design and noise factors as fixed and quantitative factors. There is a lot of discussion about the way the experiments are set up and the experimental data are analyzed (cf. Nair (1992) for a panel discussion and more than 100 references about this subject). In the Ph.D. thesis of Huele (1998) the response surface approach to analyze the data, is extensively treated. He considers both the parameter and the tolerance design.

Acknowledgement I thank my colleagues Jeroen de Mast, Freek Huele, Chris Klaassen, Kit Roes, Albert Trip, Edwin van den Heuvel, and Jaap Wieringa for their contributions.

REFERENCES Automotive Industry Action Group (1990). Measurement Systems Analysis Manual. Automotive Industry Action Group. Detroit MI. Baillie, D.H. and Klaassen, C.A.J. (1999). Credit-based accept-zero sampling schemes for the control of outgoing quality. Submitted for publication. De Mast, J., Roes, K.C.B. and Does, R.J.M.M. (1999). The multi-vari chart a systematic approach. Submitted for publication. Does, R.J.M.M., Roes, K.C.B. and Trip, A. (1999a). Statistical Process Control in Industry. Kluwer Academic. Dordrecht, the Netherlands. Does, R.J.M.M., Roes, K.C.B. and Trip, A. (1999b). Handling multivariate problems with univariate control charts. Accepted for publication in the Journal of Chemometrics. Does, R.J.M.M. and Schriever, B.F. (1992), Variables control chart limits and test for special causes. Statistica Neerlandica 46, 229-245. Huele, A.F. (1998). Statistical Robust Design. Ph.D. thesis. University of Amsterdam. Amsterdam. Klaassen, C.A.J. (1999). Bonus-Malus in acceptance sampling on attributes. Tentatively accepted for publication in Technometrics. Koning, A.J. and Does, R.J.M.M. (1999). Cusum charts for prelimanary analysis of individual observations. Tentatively accepted for publication in the Journal of Quality Technology. Nair, V.N. (1992). Taguchi's parameter design: a panel discussion. Technometrics 34, 127-161. Quesenberry, C.P. (1995). On properties of Q charts for variables. Journal of Quality Technology 27, 184-203. Page, E.S. (1954). Continuous inspection schemes. Biometrika 41, 100-115. Roes, K.C.B. and Does, R.J.M.M. (1995). Shewhart-type charts in nonstandard situations (with discussion). Technometrics 37, 15-40. Roes, K.C.B., Does, R.J.M.M. and Jonkers, B.S. (1999). Effective application of Q(R) charts in low volume manufacturing. Accepted for publication in Quality & Reliability Engineering International. Roes, K.C.B., Does, R.J.M.M. and Schurink, Y. (1993). Shewhart-type control charts for individuals. Journal of Quality Technology 25, 188-198. Seder, L.A. (1950). Diagnosis with diagrams. Part I and II. Industrial Quality Control 6, January (Part I) 11-19, March (Part II) 7-11. Sullivan, J.H. and Woodall, W.H. (1996). A control chart for preliminary analysis of individual observations. Journal of Quality Technology 28, 265-278. Taguchi, G. (1987). Systems of Experimental Designs 1 and 2, American Supplier Institute, Dearborn. Van den Heuvel, E.R. and Trip, A. (1999). Evaluation of measurement systems for models with fixed operators. Submitted for publication. Wieringa, J.E. (1999). Statistical Process Control for Serially Correlated Data. Ph.D. thesis. University of Groningen, Groningen, the Netherlands. RÉSUMÉ Dans cet article un résumé est donné de la recherche de statisticiens employés à un institut commercial de l'Université d'Amsterdam. Les sujets sont: qualité par sélection, qualité par processus contrôlés et qualité par développement.

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