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Register a new userA Review of Dispersion Control Charts for Multivariate Individual Observations
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Added by
Jimoh Olawale Ajadi
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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A multivariate control chart is designed to monitor process parameters of multiple correlated quality characteristics. Often data on multivariate processes are collected as individual observations, i.e. as vectors one at the time. Various control charts have been proposed in the literature to monitor the covariance matrix of a process when individual observations are collected. In this study, we review this literature; we find 30 relevant articles from the period 1987-2019. We group the articles into five categories. We observe that less research has been done on CUSUM, high-dimensional and non-parametric type control charts for monitoring the process covariance matrix. We describe each proposed method, state their advantages, and limitations. Finally, we give suggestions for future research.
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Monitoring several correlated quality characteristics of a process is common in modern manufacturing and service industries. Although a lot of attention has been paid to monitoring the multivariate process mean, not many control charts are available for monitoring the covariance matrix. This paper presents a comprehensive overview of the literature on control charts for monitoring the covariance matrix in a multivariate statistical process monitoring (MSPM) framework. It classifies the research that has previously appeared in the literature. We highlight the challenging areas for research and provide some directions for future research.
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A multivariate dispersion control chart monitors changes in the process variability of multiple correlated quality characteristics. In this article, we investigate and compare the performance of charts designed to monitor variability based on individual and grouped multivariate observations. We compare one of the most well-known methods for monitoring individual observations -- a multivariate EWMA chart proposed by Huwang et al -- to various charts based on grouped observations. In addition, we compare charts based on monitoring with overlapping and nonoverlapping subgroups. We recommend using charts based on overlapping subgroups when monitoring with subgroup data. The effect of subgroup size is also investigated. Steady-state average time to signal is used as performance measure. We show that monitoring methods based on individual observations are the quickest in detecting sustained shifts in the process variability. We use a simulation study to obtain our results and illustrated these with a case study.
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