Enhancing Control: Unveiling the Performance of Poisson EWMA Charts through Simulation with Poisson Mixture DATA

Abstract

Poisson-Exponentially Weighted Moving Average (PEWMA) charts are one of the most frequently used control charts for monitoring count data. But as real-world data often shows overdispersion—prevalent in manufacturing, health care, economics, and marketing—the standard Poisson distribution falls short. One of the ways to tackle overdispersion is to use Poisson mixture distributions. Our study examines Average Run Length (ARL) performance in the presence of Poisson mixture distribution in the PEWMA control charts. Through meticulously designed experiments, we explore different control parameter combinations and employ simulation to evaluate the process. Our graphs illustrate the performance of the PEWMA control chart, offering desired in-control ARL across parameter combinations. Finally, the performance of the PEWMA control chart is presented for the real process data of fastener production.