Change-Point Methods for Overdispersed Count Data

A control chart is often used to detect a change in a process. Following a control chart signal, knowledge of the time and magnitude of the change would simplify the search for and identification of the assignable cause. In this research, emphasis is placed on count processes where overdispersion has occurred. Overdispersion is common in practice and occurs when the observed variance is larger than the theoretical variance of the assumed model. Although the Poisson model is often used to model count data, the two-parameter gamma-Poisson mixture parameterization of the negative binomial distribution is often a more adequate model for overdispersed count data. In this research effort, maximum likelihood estimators for the time of a step change in each of the parameters of the gamma-Poisson mixture model are derived. Monte Carlo simulation is used to evaluate the root mean square error performance of these estimators to determine their utility in estimating the change point, following a control chart signal. Results show that the estimators provide process engineers with accurate and useful estimates for the time of step change. In addition, an approach for estimating a confidence set for the process change point will be presented.