Control Charts for Overdispersed Count Data: Exploring the Poisson Chris‐Jerry Distribution in Agriculture and Medicine

ABSTRACT Statistical process control (SPC) is vital for overseeing processes and ensuring quality standards, with control charts being key tools in this process. As manufacturing systems and components become more complex, there is an increasing demand for control charts built on advanced statistical distributions. The Poisson‐based count chart is commonly used to monitor nonconformities in production, but its use depends on the assumption that the mean and variance of the data are equal. In many cases, particularly in fields such as biology and medicine, overdispersion occurs, where the variance surpasses the mean. In such cases, the Poisson Chris‐Jerry (PSNCJ) distribution offers a more suitable approach for modeling count data. This study explores the development and characteristics of the PSNCJ distribution and presents control charts specifically designed for datasets that conform to this model. Its effectiveness is evaluated through both simulations and real‐world applications. Moreover, the PSNCJ count chart is applied to datasets from agriculture and biology, demonstrating its practical significance in these fields. The results validate the utility and accuracy of the proposed control charts.