Two Moments May Not Be Enough

Article

Demskey, Sidney   (1991, ASQC)   Statistical Investigation Directorate, Inc., Broomall, PA

Annual Quality Congress, Milwaukee WI    Vol. 45    No. 0
QICID: 9629    May 1991    pp. 931-937
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Article Abstract

This abstract is an edited version of the author's original.

This paper discusses the problem of specifying risk magnitude and/or risk criteria incurred with statistical methods. For example, with Statistical Process Control (SPC) charts, the error of diagnosing a stable process as unstable is approximately 0.001 for each chart, X-bar, and R or S. If Run Theory is used to supplement the above SPC chart, the risk is increased.The author asserts that the risk for the IX/Process Average Chart is approximately 0.05 (�.025), and the risk for the MR chart is approximately 0.001. To illustrate this IX/MR risk problem the author reviews the interpretation of X-bar/Range (XB/R) charts and statistically tests periodic or successive averages and ranges of rational subgroups against their respective standard values with a false alarm risk of approximately 0.001.

When, due to cost, limited production rates, timing, etc. only one datum per subgroup is available for SPC analysis, one expedient approach is to apply the IX/MR chart. The single X datum for each subgroup sample is treated as the process average. Since there is only one datum per group, the measure of process variability cannot be calculated for that subgroup; the general approach is to calculate the moving range (MR) between successive X values. Then the process variability is calculated as the average of the MRs.

Given the limitations of the process mean and variance in the case presented, one method for overcoming the problem is given.

Keywords

Statistical process control (SPC),Statistics,X-bar control charts,Individuals charts


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