On the misleading signals in simultaneous schemes for the mean vector and covariance matrix of multivariate i.i.d. output

The performance of a product often depends on several quality characteristics. Simultaneous schemes for the process mean vector and the covariance matrix are essential to determine if unusual variation in the location and dispersion of a multivariate normal vector of quality characteristics has occurred.

Misleading signals (MS) are likely to happen while using such simultaneous schemes and correspond to valid signals that lead to a misinterpretation of a shift in mean vector (resp. covariance matrix) as a shift in covariance matrix (resp. mean vector).

This paper focuses on numerical illustrations that show that MS are fairly frequent, and on the use of stochastic ordering to qualitatively assess the impact of changes in th emean vector and covariance matrix in the probabilities of misleading signals in simultaneous schemes for these parameters while dealing with multivariate normal i.i.d. output.

(Joint work with: Manuel Cabral Morais, António Pacheco, CEMAT-IST; Wolfgang Schmid, European University Viadrina.)