A new control chart based on proportional hazards and frailty regression models for monitoring high‐quality processes with censored observations

Abstract Improving quality and reducing defects in various processes have led to the design of numerous control charts for monitoring count data. These charts are characterized by a large number of zero defects and are modeled with zero‐inflated distributions. Besides, it is important to consider the influence of key factors on the number of defects in some processes. This paper presents three monitoring scenarios that utilize cumulative sum (CUSUM) control charts in Phase II. These scenarios are valuable for monitoring high‐quality processes, particularly with censored observations. The first scenario uses a zero‐inflated Poisson (ZIP) distribution while the second one employs a proportional hazards regression model to account for observed variables. The third scenario combines the proportional hazards and frailty regression models to consider both observed and unobserved variables. The performance of all three control charts is evaluated by applying shifts to both parameters of the ZIP distribution separately and simultaneously. Extensive simulation studies are conducted and the effects of low, moderate, and high censoring rates are thoroughly studied. The results highlight the importance of considering influential variables for detecting early shifts, as neglecting them significantly impairs the control chart performance. Finally, a real case study, involving defect counts in printed rolls at a label printing factory, has been provided and discussed to show the application of the monitoring procedures.