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