Multivariate Nonparametric Control Charts Based on Ordered Samples, Signs and Ranks

Nonparametric control charting techniques have attracted the interest of the researchers during the past decades. However, the studies in the multivariate case are not equally weighted as the ones that have already been done in the univariate case. In the present work, we firstly review the recent literature of nonparametric control charts, giving emphasis on multivariate schemes, which make use of order statistics, signs or ranks for the computation of the test statistic that is exploited for the decision-making whether the process is in- or out-of-control. In addition, we carry out a simulation study in order to evaluate the performance of these charts when compared with each other, as well as to their parametric counterparts. The numerical results take into account different shift scenarios for the location parameter, the scale parameter or both. Finally, some concluding remarks are given, as well as some ideas and directions for future work.