Multivariate process control charts based on the Lp depth

Even if large historical dataset could be available for monitoring key quality features of a process via multivariate control charts, previous knowledge may not be enough to reliably identify or adopt a unique model for all the variables. When no specific parametric model turns out to be appropriate, some alternative solutions should be adopted and exploiting non-parametric methods to build a control chart appears a reasonable choice. Among the possible non-parametric statistical techniques, data depth functions are gaining a growing interest in multivariate quality control. Within the literature, several notions of depth are effective for this purpose, even in the case of deviation from the normality assumption. However, the use of the Lp depth for constructing non-parametric multivariate control charts as been surprisingly neglected so far. Hence, the goal of this work is to investigate the behavior the Lp depth in the statistical process control and to compare its performances to those of the Mahalanobis depth, which is often adopted to build depth-based control charts.