Statistical Performance of Control Charts

Average run length is the most popular measure to assess the statistical performance of a control chart procedure. This paper discusses the limitations of the traditional average run length measure and introduces the concept of ‘unity’ average run length which is the ratio of the expected run length to the number of points plotted. The use of overall probability of acceptance for a set of plotted points is recommended as a supplementary performance measure. The background theory for using the overall probability acceptance is borrowed from the field of acceptance sampling. A discussion on how to improve the efficiency of the control chart signal rule is also made.