Dynamic Probability Control Limits for the Multivariate Poisson EWMA Control Chart With Time‐Varying Sample Sizes

ABSTRACT In statistical process control, the multivariate Poisson (MP) control chart is a satisfactory tool for efficient online monitoring of multivariate correlated count data. Unfortunately, there are three main problems with the traditional MP control chart: (1) The assumption of the MP model with a single common covariance is too strict in reality; (2) its conditional false alarm rate varies over time, which may lead to unexpected and undesirable chart performance; (3) it requires the sample size to remain constant. In order to improve the applicability of this control chart with time‐varying sample sizes and to ensure its in‐control performance, this paper introduces dynamic probability control limits to design an exponentially weighted moving average (EWMA) chart based on the MP model with a two‐way covariance structure, which has a marginal Poisson distribution in each dimension and allows for pairwise correlations. The simulation results show that the control limits of the proposed control chart can automatically adapt to changes in the sample size. In addition, the proposed control chart not only has an ideal in‐control performance, but it also has a better ability to detect out‐of‐control cases than the traditional control chart. Finally, a real example is used to demonstrate the implementation and superiority of the proposed control chart.