Copula-based control charts for monitoring multivariate Poisson processes with application to hepatitis C counts

In this article, we study attribute control charts for monitoring correlated multivariate Poisson processes that are adequately described by copula models. The work is motivated by the need to study multivariate models for correlated count data with less restrictive assumptions on the correlation structure. We consider copula models that allow for varying levels of correlation between Poisson variables. In particular, we identify which of multivariate elliptical and mixtures of max-infinitely divisible copulas best describes the correlated multivariate Poisson process based on model selection criteria. Our primary objective in this article is to study mainstream attribute monitoring schemes based on this model structure and assess their average run length performance through numerical and simulation procedures.