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

Honghao Zhao (), Huajun Tang, Chuan Pang and Huimin Jiang
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Honghao Zhao: Department of Decision Sciences, School of Business, Macau University of Science and Technology, Macau 999078, China
Huajun Tang: Department of Decision Sciences, School of Business, Macau University of Science and Technology, Macau 999078, China
Chuan Pang: Department of Decision Sciences, School of Business, Macau University of Science and Technology, Macau 999078, China
Huimin Jiang: Department of Decision Sciences, School of Business, Macau University of Science and Technology, Macau 999078, China

Mathematics, 2022, vol. 10, issue 24, 1-12

Abstract: 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.

Keywords: average run length; exponentially weighted moving average; linear trend; poisson process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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