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Misleading Signals in Simultaneous Schemes for the Mean Vector and Covariance Matrix of a Bivariate Process

Ramos, Patrícia F.; Morais, M. C. ; Pacheco, António; Schmid, W.

Recent Developments in Modeling and Applications in Statistics Studies in Theoretical and Applied Statistics, Springer Berlin Heidelberg, (2013), 225–235

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.