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

TLDR

The Poisson distribution is widely used for count data, but its equi‑dispersion assumption limits control charts; the Conway–Maxwell–Poisson distribution relaxes this assumption and includes Poisson, geometric, and Bernoulli as special cases. The study develops a flexible control chart that generalizes classical Shewart charts to accommodate over‑ and under‑dispersed count data. This chart incorporates Poisson, Bernoulli (or binomial), and geometric (or negative binomial) distributions within the Conway–Maxwell–Poisson framework. © 2011 John Wiley & Sons, Ltd.

Abstract

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.