EWMA Monitoring of Correlated Processes of Poisson Counts

Statistical quality control is often concerned with processes of Poisson counts. If these counts exhibit serial dependence, a popular approach is to use a Poisson INAR(1) model to describe the autocorrelation structure of the process. In this article, we develop a strategy to monitor a Poisson INAR(1) process, which is based on a combination of the c - and an EWMA chart. Since the resulting bivariate process is a Markov chain, ARLs can be computed exactly with the well-known Markov chain approach. We provide explicit design recommendations and investigate the performance of the combined EWMA chart towards a shift in one of the two model parameters.