This article proposes a methodology that helps to predict the main mean shifts, denoted as principal alarms, in a non-normal multivariate process using the available in-control data. The analysis is based on the transformation of the observed correlated variables into independent factors using independent component analysis. These independent components allow us to simulate shifts preserving the covariance structure. The graphical representations of those simulated shifts are helpful in improving the design and control of the process. Two real manufacturing processes are presented showing the advantage of the proposed methodology.