Adaptive CUSUM Chart for Drift Detection in Poisson Processes With Time‐Varying Sample Sizes

ABSTRACT Statistical process control (SPC) charts are widely used to detect distributional changes in sequential processes, including Poisson count data arising in applications such as healthcare surveillance, manufacturing, and service systems. Classical control charts for count data typically assume that both the in‐control (IC) and out‐of‐control (OC) parameters are known in advance. However, in many practical situations the IC parameters are unknown and must be estimated from a limited amount of historical data. Moreover, traditional SPC methods are primarily designed for abrupt shifts and often assume fixed OC parameters, whereas process changes may evolve gradually over time in the form of drifts. Detecting such drifts becomes particularly challenging for Poisson processes with time‐varying sample sizes. In this paper, we develop an adaptive self‐starting CUSUM chart for detecting drifts in Poisson processes with time‐varying sample sizes. The proposed method simultaneously estimates the IC and OC parameters during online monitoring. Specifically, initial IC estimates are obtained from historical data and are adaptively updated through a modified self‐starting mechanism when little evidence of a drift is present. Meanwhile, a locally weighted regression approach is employed to estimate the time‐varying OC parameter, enabling effective detection of gradual drift patterns. Numerical studies demonstrate that the proposed method achieves reliable monitoring performance and improved detection efficiency across a range of practical scenarios.