Monitoring Zero-inflated Poisson Processes based on Model-based Cumulative Sum(CUSUM)

In this article, three monitoring approaches using cumulative sum (CUSUM) control charts in phase two for zero inflated poisson-based processes are presented. The first approach is based on the zero inflated poisson distribution, the second on, a proportional hazard regression model, and the third integrates a proportional hazard (PH) regression model and a frailty model to consider both measurable and unmeasurable covariates. The performance of all three control charts was evaluated separately and simultaneously by applying shifts to both parameters of the zero inflated poisson distribution. Extensive simulation studies were conducted to evaluate the performance of these monitoring methods in terms of the average run length (ARL) of the control charts. The proposed cumulative sum control chart with simultaneous consideration of measurable and unmeasurable variables showed superior performance. Finally, a real case study in a label printing factory has been provided to show the effectiveness of the proposed control chart.