Two approaches to monitoring multivariate Poisson counts: Simple and accurate
针对多元相关计数数据，提出两种控制图来同时监控均值向量和协方差矩阵，一种简单快速，另一种准确可靠，并给出选择建议。
We consider the monitoring of multivariate correlated count data, which have many applications in practice. Although there are quite a few methods for the statistical process control of Multivariate Poisson (MP) counts, they are either too complicated or too simple to provide a satisfactory tool for efficient online monitoring. In addition, they mostly focus on only the mean vector of multivariate counts and ignore the correlations among them. In this article, we adopt the multivariate Poisson distribution with a two-way covariance structure for modeling MP counts, which has marginal Poisson distributions in each dimension and allows for pairwise correlations. Based on this, we develop two control charts to simultaneously monitor the mean vector and covariance matrix of MP counts. The first chart enjoys a simple charting statistic and is computationally fast, whereas the second one is accurate and provides a gold standard for monitoring MP counts. We also give recommendations on choice between them. Numerical simulations have demonstrated the advantages of the proposed two charts, and in non-Poisson cases we also test their robustness against underdispersion and overdispersion that are encountered often in count data.