Multivariate ELR control chart with estimated mean vector and covariance matrix

Recently, simultaneous monitoring of multivariate process mean and variability has received increasing attention in the literature of statistical process monitoring (SPM). However, the deleterious impact of parameter estimation on the capability of control charts designed for simultaneous monitoring...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2023-12, Vol.52 (24), p.8814-8827
Main Authors: Maleki, Mohammad Reza, Salmasnia, Ali, Yousefi, Sahand
Format: Article
Language:English
Subjects:
Control chart
Control charts
Covariance matrix
Error analysis
Error detection
Error reduction
False alarms
Likelihood ratio
Mathematical analysis
Mean
Monitoring
Multivariate analysis
multivariate process
Parameter estimation
Phase II
run length
simultaneous monitoring
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Summary:Recently, simultaneous monitoring of multivariate process mean and variability has received increasing attention in the literature of statistical process monitoring (SPM). However, the deleterious impact of parameter estimation on the capability of control charts designed for simultaneous monitoring of the mean vector and covariance matrix of multivariate processes has been clearly neglected. In this paper, we study the effect of estimation error on both in-control and out-of-control properties of the multivariate exponentially weighted moving average (EWMA)-based generalized likelihood ratio (MELR) chart. Simulation studies in terms of the average run length (ARL), the standard deviation of run length (SDRL), and the median run length (MRL) metrics are conducted to explore how the amount of Phase I reference samples affects the performance of the MELR chart. The results show that extra variability due to estimation error reduces the detecting capability of the MELR chart while increases its false alarm rate. Meanwhile, a real-life data is provided to illustrate poor Phase I estimation results in more false alarms than expected.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2022.2076116