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

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 investi...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-12, Vol.10 (24), p.4786
Main Authors: Zhao, Honghao, Tang, Huajun, Pang, Chuan, Jiang, Huimin
Format: Article
Language:English
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
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10244786