Leveraged Plans for Measurement System Assessment
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In manufacturing, measurement systems are used to control processes and inspect parts with the goal of producing high quality product for the customer. Modern Quality Systems require the periodic assessment of key measurement systems to ensure that they are functioning as expected. Estimating the proportion of the process variation due to the measurement system is an important part of these assessments. The measurement system may be simple, for example, with one gauge automatically measuring a single characteristic on every part or complex with multiple characteristics, gauges, operators etc. Traditional assessment plans involve selecting a random sample of parts and then repeatedly measuring each part under a variety of conditions that depend on the complexity of the measurement system. In this thesis, we propose new plans for assessing the measurement system variation based on the concept of leveraging. In a leveraged plan, we select parts (non-randomly) with extreme initial values to measure repeatedly. Depending on the context, parts with initial measurements may be available from regular production or from a specially conducted baseline study. We use the term leveraging because of the re-use of parts with extreme values. The term leverage has been used by the proponents of the problem solving system initially proposed by Dorian Shainin. Parts with relatively large and small values of the response are compared to identify the major causes of the variation. There is no discussion of the theory of leveraging in the literature or its application to measurement system assessment. In this thesis, we provide motivation for why leveraging is valuable and apply it to measurement system assessments. We consider three common contexts in the thesis: Simple measurement systems with one gauge, no operator effects and no external information about the process performance; Measurement systems, as stated above, where we have external information, as would be the case, for example, if the measurement system was used for 100% inspection; Measurement systems with multiple operators. For each of these contexts, we develop new leveraged assessment plans and show that these plans are substantially more efficient than traditional plans in estimating the proportion of the process variation due to the measurement system. In each case, we also provide methodology for planning the leveraged study and for analysing the data generated. We then develop another new application of leveraging in the assessment of a measurement system used for 100% inspection. A common practice is to re-measure all parts with a first measurement outside of inspection limits. We propose using these repeated measurements to assess the variation in the measurement system. Here the system itself does the leveraging since we have repeated measurements only on relatively large or small parts. We recommend using maximum likelihood estimation but we show that the ANOVA estimator, although biased, is comparable to the MLE when the measurement system is reliable. We also provide guidelines on how to schedule such assessments. To outline the thesis, in the first two chapters, we review the contexts described above. For each context, we discuss how to characterize the measurement system performance, the common assessment plans and their analysis. In Chapter 3, we introduce the concept of leveraging and provide motivation for why it is effective. Chapters 4 to 7 contain the bulk of the new results in the thesis. In Chapters 4, 5 and 6, which correspond to the three contexts described above, we provide new leveraged plans, show their superiority to the standard plans and provide a methodology to help design leveraged plans. In Chapter 7, we show how to assess an inspection system using repeated measurements on initially rejected parts. In the final chapter, we discuss other potential applications of leveraging to other measurement system assessment problems and to a problem in genetics.