An enhanced adaptive CUSUM control chart

Abstract

Adaptive CUSUM charts, referred to as ACUSUM charts, have attracted considerable attention from the research community. By adjusting the reference parameter k dynamically, an ACUSUM chart may achieve a better performance over a range of mean shifts than conventional CUSUM charts that are designed for maximal detection effectiveness at a particular level of process shift. This article studies a new feature of the ACUSUM chart related to an additional charting parameter w, i.e., the exponential of the sample mean shift in (x t – μ 0) w . The ACUSUM chart can be enhanced by adapting this parameter w according to the on-line estimated value of the mean shift, in conjunction with the reference parameter k. The testing cases reveal that this new adaptive CUSUM chart not only outperforms the earlier ACUSUM chart to a substantial degree, but also works as well as the most effective combined schemes consisting of a few CUSUM and/or charts. Furthermore, this enhanced ACUSUM chart is easier to design and implement in a computerized environment compared with those combined schemes. In addition, a general-purpose optimization algorithm is proposed to assist the designs of various CUSUM charts. This paper demonstrates that this algorithm can significantly improve the performance of many CUSUM charts over the entire process shift range. Moreover, a systematic performance comparison of eight CUSUM charts is presented. The findings from this comparison are useful aids for SPC practitioners to select an appropriate CUSUM chart for real applications. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplementary resource: Appendix]