Misleading signals in simultaneous schemes for the mean vector and covariance matrix of a bivariate process

Abstract

In a bivariate setting, misleading signals (MS) correspond to valid alarms which lead to the misinterpretation of a shift in the mean vector (resp. covariance matrix) as a shift in the covariance matrix (resp. mean vector). While dealing with bivariate output and two univariate control statistics (one for each parameter), MS occur when: The individual chart for the mean vector triggers a signal before the one for the covariance matrix, although the mean vector is on-target and the covariance matrix is off-target.The individual chart for the variance triggers a signal before the one for the mean, despite the fact that the covariance matrix is in-control and the mean vector is out-of-control. Since MS can be rather frequent in the univariate setting, as reported by many authors, this chapter thoroughly investigates the phenomenon of MS in the bivariate case.