Monitoring variability of multivariate processes

Abstract

The paper focuses on determining changes in process variability of multivariate processes. The problem is compounded by the fact that any of the elements in the variance-covariance matrix of variables could change, leading to a change in the process variability. While it may not be feasible to maintain individual control charts for each element of the variance-covariance matrix, some aggregate measure of the variability criteria could be monitored to initially determine if a change has occurred in the process variability. A couple of aggregate measures are proposed and the performance of these suggested measures is explored through a simulation procedure. Compared to the traditional method, which monitors the determinant of the variance-covariance matrix, these alternatives perform well. The performance measure used is the mean time to first detection of a change in the process variability.