The L^P data depth and its application to multivariate process control charts

Control charts are used to identify non-random behaviours of a manufacturing process by monitoring changes in the distribution of the quality characteristics of the tested product. Process monitoring of related variables is usually referred to as a multivariate quality control problem. In many applications there is not enough information to justify the assumption of a specific form for the underlying process distribution. Thus, a non-parametric approach is a valid tool in a quality control process. Among possible non-parametric statistical techniques, data depth functions are gaining increasing interest in multivariate quality control. The aim of this work is to investigate the behaviour of a non-parametric approach based on the notion of the L^p depth in the statistical process control.