Bootstrap EWMA and CUSUM Charts for Monitoring Mean Shifts in Poisson INAR Processes

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DOI: https://doi.org/10.28924/2291-8639-24-2026-145
Published: May 11, 2026
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Wandee Wanishsakpong, Jeeraporn Thaithanan, Sawaporn Hinsheranan, Bootstrap EWMA and CUSUM Charts for Monitoring Mean Shifts in Poisson INAR Processes, Int. J. Anal. Appl., 24 (2026), 145.

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Wandee Wanishsakpong, Jeeraporn Thaithanan, Sawaporn Hinsheranan

Abstract

Autocorrelated count data commonly arise in applications where classical control charts assuming independence may not be appropriate. This paper develops bootstrap-calibrated one-sided EWMA and CUSUM charts for detecting upward mean shifts in Poisson INAR(p) processes. Two bootstrap procedures are considered: a Discrete (D) approach that refits the model in each replication to account for parameter estimation variability, and a Model-Based (MB) approach that conditions on a single fitted in-control model. Detection performance is evaluated using expected detection delay and detection reliability. Simulation results show that EWMA charts generally provide faster detection, whereas CUSUM charts may achieve slightly higher detection reliability. As the shift magnitude increases, performance differences diminish. The D approach performs better for small shifts, while the MB approach provides a computationally efficient alternative with comparable performance for moderate and large shifts. A real-data example using road-traffic injury counts illustrates the practical relevance of the method.

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