Control Charts for Poisson Count Data with Varying Sample Sizes

Various cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been recommended to monitor a process with Poisson count data when the sample size varies. We evaluate the ability of these CUSUM and EWMA methods in detecting increases in the Poisson rate by calculating the steady-state average run length (ARL) performance for the charts. Our simulation study indicates that the CUSUM chart based on the generalized likelihood-ratio method is best at monitoring Poisson count data at the out-of-control shift for which it is designed when the sample size varies randomly. We also propose a new EWMA method that has good steady-state ARL performance.