Title: Multivariate control charts based on the $L^p$ depth
Authors: Giuseppe Pandolfo - University of Naples Federico II (Italy) [presenting]
Carmela Iorio - University of Naples, Federico II (Italy)
Michele Staiano - University Of Naples Federico II (Italy)
Massimo Aria - University of Naples Federico II (Italy)
Roberta Siciliano - University of Naples Federico II (Italy)
Abstract: When monitoring key quality features of a process via multivariate control charts, previous knowledge may not be enough to adopt a unique model for all the variables. In the case no specific parametric model turns out to be appropriate, alternative solutions have to be considered and adopting nonparametric methods to build control charts appears a reasonable choice. Among the existing non-parametric 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 $L^p$ depth has been surprisingly neglected so far. Hence, the goal is to investigate the behaviour of the $L^p$ 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.