New control charts for monitoring covariance matrix with individual observations

Ahmad Ostadsharif Memar · Seyed Taghi Akhavan Niaki

23 citations0/0 files storedQuality and Reliability Engineering International

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Advanced Statistical Process Monitoring Fault Detection and Control Systems Management Systems and Quality Improvement

Abstract

Abstract 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 L1‐norm and a L2‐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.

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References

1992Introduction to Statistical Quality Control 1992A Multivariate Exponentially Weighted Moving Average Control Chart 2005Introduction to Statistical Quality Control 1993The Exponentially Weighted Moving Variance 198817 Multivariate process control 2006Multivariate Control Charts for Monitoring Covariance Matrix: A Review 2007Monitoring Multivariate Process Variability for Individual Observations 2006Multivariate Control Charts for Monitoring the Mean Vector and Covariance Matrix

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2017Monitoring multivariate process variability via eigenvalues 2021A new multivariate CUSUM chart for monitoring of covariance matrix with individual observations under estimated parameter 2018A control scheme for monitoring process covariance matrices with more variables than observations 2013Robust Control Charts for Monitoring Process Variability in Phase I Multivariate Individual Observations 2011Multivariate variability monitoring using EWMA control charts based on squared deviation of observations from target

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