Likelihood-Based EWMA Charts for Monitoring Poisson Count Data with Time-Varying Sample Sizes∗

Many applications involve monitoring incidence rates of the Poisson distribution when sample size varies over time. Recently, a couple of cumulative sum and exponentially weighted moving average (EWMA) control charts have been proposed to tackle this problem by taking the varying sample size into consideration. However, we argue that some of these charts, which perform quite well in terms of average run length (ARL), may not be appealing in practice because they have rather unsatisfactory run length distributions. With some charts the specified in control (IC) ARL is attained with elevated probabilities of very short and very long runs, as compared with a geometric distribution. This is reflected in a larger run length standard deviation than that of a geometric distribution and an elevated probability of false alarms with short runs, which in turn hurt an operators confidence in valid alarms. Furthermore, with many charts the IC ARL exhibits considerable variations with different patterns of sample ∗The authors thank the editor, associate editor, and three anonymous referees for their many helpful comments that have resulted in significant improvements in the article. This research was supported by the NNSF of China Grants 11001138, 11071128, 11131002, 11101306, 71172131 and the RFDP of China Grant 20110031110002. Zhou’s work is partially supported by PAPD of Jiangsu Higher Education Institutions. Zou also thanks for the support of the National Center for Theoretical Sciences, Math Division. The first two authors contributed equally to this work. Wang is the corresponding author: [email protected]