Controlling jumps in correlated processes of Poisson counts

Processes of autocorrelated Poisson counts can often be modelled by a Poisson INAR(1) model, which proved to apply well to typical tasks of SPC. Statistical properties of this model are briefly reviewed. Based on these properties, we propose a new control chart: the combined jumps chart. It monitors the counts and jumps of a Poisson INAR(1) process simultaneously. As the bivariate process of counts and jumps is a homogeneous Markov chain, average run lengths (ARLs) can be computed exactly with the well-known Markov chain approach. Based on an investigation of such ARLs, we derive design recommendations and show that a properly designed chart can be applied nearly universally. This is also demonstrated by a real-data example from the insurance field. Copyright (C) 2008 John Wiley & Sons, Ltd.