Monitoring Multivariate Process Variability for Individual Observations

Abstract

Most of the existing control charts for monitoring multivariate process variability are based on subgroup sizes greater than one. In many practical applications, however, only individual observations are available and the usual control charts are not applicable in these cases. In this paper, two new control charts are proposed to monitor multivariate process variability for individual observations. The proposed control charts are constructed based on the traces of the estimated covariance matrices derived from the individual observations. When there is only one quality characteristic, these two charts respectively reduce to the exponentially weighted mean squared deviation and exponentially weighted moving variance charts. It is shown based on the simulation studies that the proposed charts are superior to the existing ones in detecting increases in variance and changes in correlation. An example from the semiconductor industry is also presented to illustrate the applicability of the proposed charts.