Detecting mean increases in Poisson INAR(1) processes with EWMA control charts

Abstract

Processes of serially dependent Poisson counts are commonly observed in real-world applications and can often be modeled by the first-order integer-valued autoregressive (INAR) model. For detecting positive shifts in the mean of a Poisson INAR(1) process, we propose the one-sided s exponentially weighted moving average (EWMA) control chart, which is based on a new type of rounding operation. The s-EWMA chart allows computing average run length (ARLs) exactly and efficiently with a Markov chain approach. Using an implementation of this procedure for ARL computation, the s-EWMA chart is easily designed, which is demonstrated with a real-data example. Based on an extensive study of ARLs, the out-of-control performance of the chart is analyzed and compared with that of a c chart and a one-sided cumulative sum (CUSUM) chart. We also investigate the robustness of the chart against departures from the assumed Poisson marginal distribution.

Keywords:

• Poisson INAR(1) model
• s-EWMA chart
• c chart
• CUSUM chart
• ARL performance
• Markov chain approach
• robustness

Acknowledgements

The author would like to thank the referees for their useful comments on an earlier draft of this article.