Most of the works that propose schemes of Multivariate Statistical Process Control (MSPC) and that analyze the performance of these schemes consider changes in the observed variables. Previous authors have shown that when the shifts in the mean vector of a multivariate process typically occur in predictable directions, the most effective statistics for process monitoring are the values of the projections of the vector of observations (or of the sample average vector) in each of these directions. This paper proposes a method for the monitoring of multivariate processes in which changes in the process parameters are due to special causes that affect non-observable variables and occur in (orthogonal) known directions, and compares its performance with that of Shewharts charts on the observed variables, on the principal components, and with that of T2 charts on the vector of observed variables. In addition, it is proposed a supplementary scheme of monitoring to detect changes in new directions outside of the hyperplane formed by known directions. Results obtained by simulation show that the proposed scheme, consisting of control charts on the transformed variables (projections of the vector of observed variables on the known directions), has better performance in most of the cases analyzed. The analysis of performance is done assuming shifts in the mean of the known directions (since these are the known changes associated to special causes) and/or increases of the variance in these same directions. The comparisons are based on the in-control and out-of-control probabilities of signal.