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Module 16C

# Module 16C - IE 361 Module 16 What if the Sample Size is 1...

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IE 361 Module 16 What if the Sample Size is 1? Reading: Section 4.4, Statistical Quality Assurance Methods for Engineers (Section 3.2.3 of Revised SQAME) Prof. Steve Vardeman and Prof. Max Morris Iowa State University Vardeman and Morris (Iowa State University) IE 361 Module 16 1 / 9

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Samples of Size 1 To call n observations a "sample" or a "rational subgroup" is to implicitly assume/guarantee that they were collected under essentially constant process conditions. But there are many process monitoring contexts where it is simply not safe to assume that even two successive process outcomes are necessarily generated under the same conditions. (This is particularly the case in low volume production contexts where there is a substantial time interval between observations.) That is, sometimes the only reasonable sample size in process monitoring is n = 1. This brief module concerns two issues that arise when sample sizes are 1, namely
Charting (Individuals and) Moving Ranges (A Bad Idea) Where rational subgroups are of size n = 1 there is really only one possible choice for a plotted statistic Q , namely x . One can "transform" the most natural measurement to some other scale, but ultimately it is Q = x that is available for plotting. However, people used to making x and R chart (or x and s chart) pairs in cases where n > 1 sometimes reason that it might be useful to supplement an x chart with a chart on which one plots moving ranges MR i = j x i x i 1 j The most common version of this is one where standards given control

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Module 16C - IE 361 Module 16 What if the Sample Size is 1...

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