A Markov Chain Model for Approximating the Run Length Distributions of Poisson EWMA Charts under Linear Drifts

• Published in: Mathematics (Basel) Vol. 10; no. 24; p. 4786
• Main Authors: Zhao, Honghao, Tang, Huajun, Pang, Chuan, Jiang, Huimin
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.12.2022
• Subjects: Analysis; Approximation; average run length; Control charts; exponentially weighted moving average; False alarms; Health surveillance; Investigations; linear trend; Markov analysis; Markov chains; Markov processes; Monitoring; Monte Carlo method; Monte Carlo simulation; Poisson density functions; poisson process; Public health; Quality control; Random variables; Sensitivity analysis
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math10244786

In addition to monitoring the Poisson mean rate with step shifts, increasing attention has been given to monitoring Poisson processes subject to linear trends. The exponentially weighted moving average (EWMA) control chart has been widely implemented to monitor normal processes, but it lacks investigation for detecting the Poisson mean change under a linear trend. In this paper, we analyze the performance of the EWMA chart by extending the Markov chain model from monitoring Poisson processes under a step shift to a Poisson process with linear drift. The results demonstrate that the proposed method is able to provide accurate average run length approximation, compared with the Monte Carlo simulation. Optimal design tables and sensitivity analysis are presented to facilitate the use of the EWMA chart in practice.