Exponentially weighted moving average control charts for monitoring increases in Poisson rate

Abstract

The Exponentially Weighted Moving Average (EWMA) control chart has been widely studied as a tool for monitoring normal processes due to its simplicity and efficiency. However, relatively little attention has been paid to EWMA charts for monitoring Poisson processes. This article extends EWMA charts to Poisson processes with an emphasis on quick detection of increases in Poisson rate. Both cases with and without normalizing transformation for Poisson data are considered. A Markov chain model is established to analyze and design the proposed chart. A comparison of the results obtained indicates that the EWMA chart based on normalized data is nearly optimal.

Keywords:

• Poisson distribution
• average run length
• statistical process control
• Markov chain

Acknowledgements

The authors are grateful to the referees for many helpful suggestions that have significantly improved the quality of this article. Lianjie Shu was supported by the grants RG011/09-10S. Wei Jiang was supported in part by the grants HKUST-DAG08/09.EG10 and HKUST-RPC10EG15.