CUSUM Control Chart Design for Multivariate Poisson Distribution

Multiple discrete data are very common in the manufacturing industry. Most control charts are built based on the assumption of the multivariate Poisson model with a single common covariance term, which allows only equal covariance. However, this assumption may not be realistic, for the cases observed in different regions sometimes are dependent with different covariance. Besides, these control charts cannot provide fault diagnosis information. This article presents GMP-CUSUM chart based on the multivariate Poisson model with two-way covariance structure. Using Monte Carlo simulation, we compare the average running chain length (ARL) of traditional MP control chart and the new control chart considering various factors. The results show that the latter model is more suitable for modeling multivariate discrete data and the new control chart increases sensitivity to process shifts. When applied to raw data directly, the proposed method is powerful yet simple to use in practice.