ARL-unbiased geometric and CCCG control charts

Abstract

ABSTRACTIn order to control increases and decreases in a parameter in a timely fashion, a chart should be set in such way that the average run length (ARL) curve attains a maximum in the in-control situation.This article proposes not only a geometric (or cumulative count of conforming, CCC) chart but also a CCC chart under group inspection (CCCG) for which all out-of-control ARL values are smaller than the in-control ARL and thus provides an improvement on the designs described in L. Zhang et al. (2004) and C. W. Zhang et al. (2012). Moreover, by exploring the notions of uniformly most powerful unbiased tests with randomization probabilities, we are able not only to eliminate the bias of the ARL function of the geometric charts but also to bring their in-control ARL exactly to a prespecified value.Instructive examples are provided to illustrate the efficiency of the proposed charts.