A Markov Chain Model for the Adaptive CUSUM Control Chart

Abstract

In practice, when the magnitude of a future mean shift is unknown, it is always desired to design a control chart to perform reasonably well over a range of shifts rather than to optimize the performance at detecting a particular level of shifts. Compared with the conventional cumulative sum (CUSUM) control chart designed based on a prespecified mean shift, the adaptive CUSUM (ACUSUM) chart proposed by Sparks (2000) can detect a broader range of mean shifts. This paper develops a two-dimensional Markov chain model to analyze the performance of ACUSUM charts. Moreover, a more general operating model is suggested for the current ACUSUM chart to simplify its implementation.

• Average Run Length
• EWMA
• Statistical Process Control

Additional information

Notes on contributors

Lianjie Shu

Dr. Shu is an Assistant Professor in the Faculty of Business Administration. His email address is [email protected].

Wei Jiang

Dr. Jiang is an Assistant Professor in the Department of Systems Engineering & Engineering Management. His email address is [email protected].