Design and Implementation of an EWMA Control Chart for Zero-Inflated Count Data in High-Quality Processes

The Poisson distribution is often employed to model count data, but it may not accurately represent a dataset with frequent occurrences of zero counts. This limitation often arises in high-quality processes where the production of nonconforming items is minimal. To address this issue, modified forms of existing distributions such as the zero-inflated geometric (ZIG) distributions, zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB) have been developed to more accurately capture the zero-inflated (ZI) count data. Control charts under ZIP distribution are effective for monitoring processes with zero defects. However, determining whether the data exhibit over-dispersion or under-dispersion is often challenging. To address this challenge and accommodate various dispersion patterns in zero-defect datasets, a flexible distribution called the ZI Conway-Maxwell-Poisson (ZICOMP) distribution is developed in the literature. This distribution is capable of modeling datasets that are over-dispersed, under-dispersed, or equi-dispersed. In this study, the ZICOMP distribution is integrated with the exponentially weighted moving average (EWMA) control charting structure to efficiently monitor the processes involving ZI count data, regardless of the dispersion level. Extensive Monte Carlo simulations are performed to evaluate the performance of the proposed chart under different parameter settings. Additionally, two real-life applications are provided to demonstrate the practical implementation and effectiveness of the proposed chart for both over-dispersion and under-dispersion scenarios.