A nonparametric multivariate phase I location control chart based on data depth

In this paper, we propose a new depth-based nonparametric multivariate control chart for phase I to detect location changes. The proposed depth-based is affine invariant and asymptotically nonparametric over a broad family of distributions and also does not require any symmetric assumption. Simulation studies are provided to analyze the performance of the proposed control chart based on various depth functions. We apply the proposed control chart to a real data set for illustrative purposes. Our proposed statistic performs well and in some cases better than competitors.