On the variable contributions to the D-statistic

Abstract

The D-statistic is widely used in Statistical process control to reliably detect the out of control status, but by itself it offers no assistance as fault identification tool. Some strategies, that work in the original or in the latent variable space, have been proposed to show the contribution of each process variable to the calculated statistic. Nevertheless it is still an open research subject. In this work, a straightforward strategy to decompose the D-statistic as a unique sum of each variable contribution is presented, that is applied in the space of the original variables. Also an explanation is provided regarding the physical meaning of the negative contributions to the statistic. The results of the proposed strategy are compared with those obtained in the latent variable space using other methods. As the new strategy works in the original variable space, the selection of an appropriate method to calculate the number of retained latent variables which reduce the lost of significant information, is avoided.