Cumulative sum control charts for monitoring zero‐inflated COM‐Poisson processes

Abstract The zero‐inflated Conway‐Maxwell Poisson (ZICMP) distribution models count data with many zero observations. ZICMP model has been developed assuming that zero observations exist with probability and the number of non‐conformities in a product unit follows the Conway‐Maxwell Poisson (COM‐Poisson) distribution with location parameter and dispersion parameter . This article presents four kinds of cumulative sum (CUSUM) charts for monitoring upward shifts in a ZICMP process. Three CUSUM schemes, namely ‐CUSUM, ‐CUSUM, and ‐CUSUM, have been designed to detect shift only in one parameter assuming that the other two are fixed and one CUSUM scheme, namely ‐CUSUM, has been designed to detect shifts in all the parameters. The performance of the proposed charts has been evaluated in terms of the average run‐length (ARL). Finally, a numerical example is given to demonstrate the application of the proposed charts.