Control Charts for Poisson Counts based on the Stein-Chen Identity

Abstract: If monitoring Poisson count data for a possible mean shift (while the Poisson distribution is preserved), then the ordinary Poisson exponentially weighted moving-average (EWMA) control chart proved to be a good solution. In practice, however, mean shifts might occur in combination with further changes in the distribution family. Or due to a misspecification during Phase-I analysis, the Poisson assumption might not be appropriate at all. In such cases, the ordinary EWMA chart might not perform satisfactorily. Therefore, two novel classes of generalized EWMA charts are proposed, which utilize the so-called Stein-Chen identity and are thus sensitive to further distributional changes than just sole mean shifts. Their average run length (ARL) performance is investigated with simulations, where it becomes clear that especially the class of so-called "ABC-EWMA charts" shows an appealing ARL performance. The practical application of the novel Stein-Chen EWMA charts is illustrated with an application to count data from semiconductor manufacturing.