Misleading signals (MS) are likely to happen while using a simultaneous scheme to control the mean vector (\mu) and the covariance matrix (\Sigma) of a bivariate process. They correspond to valid signals that lead to a misinterpretation of a shift in \mu (resp. \Sigma) as a shift in \Sigma (resp. \mu). Following previous work, focused on the quantitative assessment of the probabilities of misleading signals (PMS) in simultaneous schemes for bivariate processes, we now make use of stochastic ordering to qualitatively assess the impact of changes in \mu and \Sigma in those probabilities.