On data depth and the application of nonparametric multivariate statistical process control charts

Abstract

The purpose of this article is to summarize recent research results for constructing nonparametric multivariate control charts with main focus on data depth-based control charts. Data depth provides dimension reduction to high-dimensional problems in a completely nonparametric way. Several depth measures including Tukey depth are shown to be particularly effective for purposes of statistical process control in case that the data deviate normality assumption. For detecting small or moderate shifts in the process target mean, the multivariate version of the exponentially weighted moving average chart is generally robust to non-normal data, so that nonparametric alternatives may be less often required.