Misleading signals in joint schemes for the mean vector and covariance matrix

Abstract

In multivariate statistical process control, it is recommendable to run two individual charts: one for the process mean vector and another one for the covariance matrix. The resulting joint scheme provides a way to satisfy Shewhart's dictum that proper process control implies monitoring both process location and spread. The multivariate quality characteristic is deemed to be out of control whenever a signal is triggered by either individual chart of the joint scheme. Consequently, a shift in the mean vector can be misinterpreted as a shift in the covariance matrix and vice versa. Compelling results are provided to give the quality control practitioner an idea of how joint schemes for the mean vector and covariance matrix are prone to trigger misleading signals that will likely lead to a incorrect diagnostic of which parameter has changed.

Monitoring the covariance matrix of bivariate processes with the DVMAX control charts

“…Ning and Li 20 proposed a simulation comparison of some distance‐based EWMA control charts for monitoring the covariance matrix with individual observations. Cabral Morais et al 21 investigated how joint schemes for the mean vector and covariance matrix are prone to trigger misleading signals.…”