The zero-inflated Conway-Maxwell Poisson (ZICOMP) distribution models count data with many zero observations. This distribution assumes that zero observations occur with probability \(\:p\) , and the count of nonconformities in a product unit follows the Conway-Maxwell Poisson (COMP) distribution with parameters \(\:\mu\:\) and \(\:\gamma\:\) . The ZICOMP distribution is flexible in accommodating various dispersion patterns in zero-inflated (ZI) datasets and effectively models over-dispersed, under-dispersed, or equi-dispersed data. This study provides an in-depth analysis of the ZICOMP-Shewhart control chart, as discussed by Alevizakos and Tasias1, to assess its effectiveness in detecting shifts in the rate parameter ( \(\:\mu\:\) ) while assuming constant dispersion and zero-inflation parameters. The key focus of this research is the selection of the limit coefficient to achieve the desired in-control (IC) average run length and assessing Type II error sensitivity for improved out-of-control (OOC) detection. Through extensive simulations, we examine the comparative efficiency of the ZICOMP-Shewhart chart against the traditional Shewhart chart under the COMP distribution. Additionally, the effectiveness of the ZICOMP-Shewhart control chart is demonstrated through a real-life example.
