A generalized statistical control chart for over‐ or under‐dispersed data

Abstract The Poisson distribution is a popular distribution used to describe count information, from which control charts involving count data have been established. Several works recognize the need for a generalized control chart to allow for data over‐dispersion; however, analogous arguments can also be made to account for potential under‐dispersion. The Conway–Maxwell–Poisson (COM‐Poisson) distribution is a general count distribution that relaxes the equi‐dispersion assumption of the Poisson distribution, and in fact encompasses the special cases of the Poisson, geometric, and Bernoulli distributions. Accordingly, a flexible control chart is developed that encompasses the classical Shewart charts based on the Poisson, Bernoulli (or binomial), and geometric (or negative binomial) distributions. Copyright © 2011 John Wiley & Sons, Ltd.