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Abstract:
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Tolerance intervals were first introduced by Wilks (1941), a decade after Walter Shewhartintroduced the famous ??? control chart. The most common metric control char performance is the average run length (ARL). The classical Shewhart ???chart assumes known mean and known variance, however, in reality, they are often estimated; thus, variability in the performance of the (Phase II) control charts, from practitioner to practitioner, is inevitable. A recently proposed alternative chart performance measure is the probability that the in-control ARLexceeds some desired fixed value, with a high probability, which is referred to as the exceedance probability criteria (EPC). We examine the connections between the EPC based control limits and the limits of a suitable tolerance interval and explain how to interpret the tolerance limits when they are usedas control limits.
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