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

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 p$p$ and the number of non-conformities in a product unit follows the Conway-Maxwell Poisson (COM-Poisson) distribution with location parameter lambda$\lambda$ and dispersion parameter nu$\nu$. This article presents four kinds of cumulative sum (CUSUM) charts for monitoring upward shifts in a ZICMP process. Three CUSUM schemes, namely lambda$\lambda$-CUSUM, p$p$-CUSUM, and nu$\nu$-CUSUM, have been designed to detect shift only in one parameter assuming that the other two are fixed and one CUSUM scheme, namely t$t$-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.