New control charts for monitoring covariance matrix with individual observations

It has recently been shown that the performance of multivariate exponentially weighted mean square (MEWMS) and multivariate exponentially weighted moving variance (MEWMV) charts of Huwang et al. (2007) 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 incontrol 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. 1 Corresponding Author