A progressive mean control chart for COM-Poisson distribution

Abstract

The Conway-Maxwell Poisson (COM-Poisson) distribution is a generalization of the Poisson distribution and encompasses the geometric, the Poisson and the Bernoulli distribution as special cases. This distribution can be used to model over- or under- dispersed data in manufacturing processes. For monitoring such data, a flexible memory-type control chart based on the progressive mean (PM) statistic (regarded as CMP-PM chart) is developed in the present paper. Through a simulation study, we investigate the run-length distribution of the proposed chart. The performance comparison study shows that the CMP-PM chart outperforms the Sellers, the GEWMA and the μ-CUSUM charts at almost all levels of shifts for both over- and under-dispersed data. Finally, the application of the proposed chart is given through an illustrative example.