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Abstract:
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When in-control parameters are unknown, they have to be estimated using a reference sample. The control chart performance in Phase II, which is generally measured in terms of the Average Run Length (ARL) or False Alarm Rate (FAR), will vary across practitioners due to the use of different reference samples in Phase I. This variation is especially large for small sample sizes. Although increasing the amount of Phase I data improves the control chart performance, others have shown that the amount required to achieve a desired in-control performance is infeasibly high. Thus, in order to deal with this variation, new corrections for Shewhart control charts are proposed that guarantee a minimum in-control performance with a specified probability. However, a minimum in-control performance guarantee generally lowers the out-of-control performance. To balance the tradeoff between in-control and out-of-control performance, the minimum performance threshold and specified probability can be adjusted as desired. The corrections are given in a closed form.
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