On Constructing Retrospective X Control Chart Limits

摘要

In this paper, we address the issue of constructing retrospective X control chart limits so as to control the overall probability of a false alarm at a desired level. The standard approach for constructing limits is shown to result in a large overall probability of a false alarm. We propose that an established technique, the analysis of means (ANOM), be used for constructing the retrospective control limits, especially when the subgroup size is small. We compare the performance of the ANOM control limits with that of Bonferroni-adjusted standard limits through Monte Carlo simulation experiments, and make recommendations as to when each approach can be used.