Efficient monitoring of autocorrelated Poisson counts

Statistical surveillance for autocorrelated Poisson counts has drawn considerable attention recently. These works are usually based on a first-order integer-valued autoregressive model and focus on monitoring separately either the marginal mean or the autocorrelation coefficient. Inspired by multivariate statistical process control, this article transforms autocorrelated Poisson counts into a bivariate representation and proposes an efficient control chart. By borrowing the power of the likelihood ratio test, albeit surprisingly, this chart demonstrates almost uniformly stronger power than the existing alternatives in simultaneously detecting shifts in both the marginal mean and the autocorrelation coefficient. In addition, the robustness of the proposed chart against overdispersion encountered often in counts is also verified. It is shown that this chart also has superiority in monitoring autocorrelated overdispersed counts.