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

Abstract

The performance of a product often depends on several quality characteristics. Simultaneous schemes for the process mean vector $$(\varvec{\mu })$$ and the covariance matrix ( $$\varvec{\Sigma }$$ ) 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 $$\varvec{\mu }$$ (resp. $$\varvec{\Sigma }$$ ) as a shift in $$\varvec{\Sigma }$$ (resp. $$\varvec{\mu }$$ ). 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 $$\varvec{\mu }$$ and $$\varvec{\Sigma }$$ in the probabilities of misleading signals in simultaneous schemes for these parameters while dealing with multivariate normal i.i.d. output.