Statistical process control and the joint monitoring of multivariate through the zonoid region parameter depth

A new concept of depth for central regions is introduced. The proposed depth notion assesses how well an interval fits a given univariate distribution as its zonoid region of level 1/2, and it is extended to the multivariate setting by means of a projection argument. Since central regions capture information about location, scatter, and dependency among several variables, the new depth evaluated on an empirical zonoid region quantifies the degree of similarity (in terms of the features captured by central regions) of the corresponding sample with respect to some reference distribution. Statistical process control and the joint monitoring of multivariate and interval-valued data in terms of location and scale are proposed by exploiting the above-mentioned depth notion