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New control charts for monitoring covariance matrix with individual observations
Author(s) -
Memar Ahmad Ostadsharif,
Niaki Seyed Taghi Akhavan
Publication year - 2009
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.998
Subject(s) - control chart , scatter matrix , covariance matrix , estimator , multivariate statistics , statistics , covariance , mathematics , statistical process control , estimation of covariance matrices , matrix (chemical analysis) , diagonal , norm (philosophy) , computer science , process (computing) , materials science , geometry , political science , law , composite material , operating system
It has recently been shown that the performance of multivariate exponentially weighted mean square and multivariate exponentially weighted moving variance charts of Huwang et al. (J. Qual. Technol. 2007; 39:258–278) in monitoring the variability of a multivariate process for individual observations is better than existing schemes. Both of these control charts monitor a distinct matrix which is an estimator of the in‐control covariance matrix. Instead of using the trace, in this paper, we propose a L 1 ‐norm and a L 2 ‐norm‐based distance between diagonal elements of the estimators from their expected values to design new control charts in monitoring the covariance matrix of a multivariate process. The results of simulations show that employing the new control statistics significantly improve the ability of the change detection process in the covariance matrix. Copyright © 2009 John Wiley & Sons, Ltd.