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Module 10C - IE 361 Module 10 Introduction to Shewhart...

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IE 361 Module 10 Introduction to Shewhart Control Charting (Statistical Process Control, or More Helpfully: Statistical Process Monitoring) Reading: Section 3.1 Statistical Quality Assurance Methods for Engineers Prof. Steve Vardeman and Prof. Max Morris Iowa State University Vardeman and Morris (Iowa State University) IE 361 Module 10 1 / 18
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Generalities About Shewhart Control Charting SPC (SPM) is process watching for purposes of change detection. Figure: SPC (SPM) is About "Process Watching" One famous statistician has called it "organized attention to process data." Vardeman and Morris (Iowa State University) IE 361 Module 10 2 / 18
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Shewhart Charting-Generalities Walter Shewhart, working at Bell Labs in the late 20°s and early 30°s reasoned that while some variation is inevitable in any real process, the variation seen in data taken on a process can be decomposed as overall observed variation = baseline variation + variation that can be eliminated baseline that which can be eliminated inherent to a system con±guration due to system/common/universal causes due to special/assignable causes random nonrandom short term long term Vardeman and Morris (Iowa State University) IE 361 Module 10 3 / 18
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Shewhart Charting-Generalities If one accepts Shewhart°s conceptualization .... how is one to detect the presence of the second kind of variation so that appropriate steps can be taken to eliminate it? The hope is to leave behind a process that might be termed physically stable (not without variation, but consistent in its pattern of variation). The point of Shewhart control charting is to provide a detection tool. Shewhart°s charting idea was to periodically take a sample from a process and compute the value of a statistic meant to summarize process behavior at the period in question plot against time order of observation compare to so-called control limits Vardeman and Morris (Iowa State University) IE 361 Module 10 4 / 18
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Shewhart Charting-Generalities For a generic plotted statistic, Q (di/erent kinds of Shewhart charts correspond to various choices of Q ), this looks like Figure: A Generic Shewhart Control Chart Points plotting "out of control" indicate process change, i.e. the presence of variation of the 2nd kind, and signal the need for intervention (of some unspeci±ed type) to ±nd and take action on the physical source of any assignable cause. Vardeman and Morris (Iowa State University) IE 361 Module 10 5 / 18
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Shewhart Charting-Setting Limits A basic question is how to set the control limits, UCL Q and LCL Q . Shewhart°s answer was essentially: If one models process output (individual measurements from the process) under stable conditions as random draws from a °xed distribution, then probability theory can often be invoked to produce a distribution for Q and corresponding mean μ Q and standard deviation σ Q . For many distributions, most of the probability is within three standard deviations of the mean. So, if μ Q and σ Q are respectively a "stable process" mean and standard deviation for Q, common generic control limits are UCL Q = μ Q + 3
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