Design of Combined CUSUM Charts for Monitoring Zero‐Inflated Poisson Processes Using the Conditional False Alarm Rate

ABSTRACT

Statistical process monitoring of zero‐inflated count data has received increasing attention because of its applications in healthcare surveillance, reliability studies, and high‐quality manufacturing processes. In many practical situations, the observed counts contain an excessive number of zeros and are collected under time‐varying sample sizes, making conventional Poisson‐based monitoring procedures inadequate. In this paper, dynamic probability control limits (DPCLs) are developed for the combined CUSUM (PL‐CUSUM) chart to monitor zero‐inflated Poisson (ZIP) processes with time‐varying sample sizes. The proposed approach maintains a constant conditional false alarm rate (CFAR) over time, regardless of whether the sample size is fixed or time‐varying. Monte Carlo simulations are used to estimate the CFAR and investigate the in‐control run‐length properties of the PL‐CUSUM chart. The results show that, unlike the conventional PL‐CUSUM chart with fixed control limits, the DPCL‐based PL‐CUSUM chart successfully stabilizes the CFAR over time and produces run‐length properties that closely follow those of a geometric distribution. A real‐data healthcare application involving needle‐stick injury counts is presented to illustrate the practical implementation of the proposed monitoring scheme.