International Journal of Analysis and Applications | 2026
Authors: Wanishsakpong W.; Thaithanan J.; Hinsheranan S.
DOI: 10.28924/2291-8639-24-2026-145
Journal: International Journal of Analysis and Applications
Year: 2026
Publisher: Etamaths Publishing
Document Type: Article
Open Access: All Open Access; Gold Open Access
Cited by: 0
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. © 2026 the author(s).
Bootstrap method; Poisson INAR process, Autocorrelated count; Statistical process control