A likelihood-based adaptive CUSUM for monitoring linear drift of Poisson rate with time-varying sample sizes

Abstract

Several weighted cumulative sum (CUSUM) and adaptive CUSUM (ACUSUM) control charts have been developed to address the challenge of time-varying sample sizes in detecting the incidence rates of Poisson count data. However, the known post-drift parameters in the CUSUM chart make it less realistic. Additionally, the adaptive component in the ACUSUM chart cannot integrate with time-varying sample sizes naturally. Furthermore, the existing charts predominantly address step drift, neglecting linear drift. Hence, this study introduces a Poisson ACUSUM chart that considers both linear drift and integration issues. Detailed comparisons are made among the proposed control chart, CUSUM control charts, and other ACUSUM control charts. Results demonstrate the proposed method's superior robustness and ability to effectively detect small drifts. Finally, the empirical results of the mortality data are employed to further validate the effectiveness of the proposed method.