IE 361 Module 24. Introduction to Shewhart Control Charting Part 1 (Statistical Process Control, or More Helpfully: Statistical Process Monitoring)

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1 IE 361 Module 24 Introduction to Shewhart Control Charting Part 1 (Statistical Process Control, or More Helpfully: Statistical Process Monitoring) Reading: Section 3.1 Statistical Methods for Quality Assurance ISU and Analytics Iowa LLC (ISU and Analytics Iowa LLC) IE 361 Module 24 1 / 9

2 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." (ISU and Analytics Iowa LLC) IE 361 Module 24 2 / 9

3 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 inherent to a system configuration due to system/common/universal causes random short term that which can be eliminated due to special/assignable causes nonrandom long term (ISU and Analytics Iowa LLC) IE 361 Module 24 3 / 9

4 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 (ISU and Analytics Iowa LLC) IE 361 Module 24 4 / 9

5 Shewhart Charting-Generalities For a generic plotted statistic, Q (different 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 unspecified type) to find and take action on the physical source of any assignable cause. (ISU and Analytics Iowa LLC) IE 361 Module 24 5 / 9

6 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 fixed 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 + 3σ Q and LCL Q = µ Q 3σ Q. and it is common to draw a "center line" on a Shewhart control chart at CL Q = µ Q. (ISU and Analytics Iowa LLC) IE 361 Module 24 6 / 9

7 Shewhart Charting for Means To make this more concrete, consider the sample mean of n individual measurements, Q = x. If individuals can be modeled as random draws from a process distribution with mean µ and standard deviation σ, elementary probability implies that Q = x has a distribution with mean µ Q = µ x = µ and standard deviation σ Q = σ x = σ/ n. It follows that typical control limits for x are UCL x = µ + 3 σ n and LCL x = µ 3 σ n with a center line drawn at CL x = µ. This illustrates that very often process parameters appear in formulas for control limits... and values for them must come from somewhere. (ISU and Analytics Iowa LLC) IE 361 Module 24 7 / 9

8 Two Modes of Control Charting Sometimes past experience with a process, engineering standards, or other considerations made prior to a particular application specify what values should be used. (This is a standards given situation.) In other circumstances, one has no information on a process outside a series of samples that are presented along with the question "Is it plausible that the process was physically stable over the period represented by these data?" This is sometimes called an as-past-data or retrospective scenario. Here all that one can do is tentatively assume that, in fact, the process was stable, make provisional estimates of process parameters and plug them into formulas for control limits, and apply those limits to the data in hand as a means of criticizing the provisional assumption of stability. (ISU and Analytics Iowa LLC) IE 361 Module 24 8 / 9

9 Two Questions Answered by Control Charting In a standards given context, with each new sample one faces the question "Are process parameters currently at their standard values?" In a retrospective context, one can only wait until a number of samples have been collected (often, using data from a minimum of time periods is recommended) and then looking back over the data ask the question "Are these data consistent with any fixed set of process parameters?" The greatest importance of control charts is in standards given applications to real-time process monitoring. Textbooks, however, are full of problems involving retrospective charts. (Of course, what other kinds of data sets could be in a textbook???!!) (ISU and Analytics Iowa LLC) IE 361 Module 24 9 / 9

IE 361 Module 25. Introduction to Shewhart Control Charting Part 2 (Statistical Process Control, or More Helpfully: Statistical Process Monitoring)

IE 361 Module 25. Introduction to Shewhart Control Charting Part 2 (Statistical Process Control, or More Helpfully: Statistical Process Monitoring) IE 361 Module 25 Introduction to Shewhart Control Charting Part 2 (Statistical Process Control, or More Helpfully: Statistical Process Monitoring) Reading: Section 3.1 Statistical Methods for Quality Assurance