A new approach to estimate variable contributions to Hotelling's statistic

Abstract

Hotelling's statistic, also called T 2-statistic, is widely used in statistical process control as an extension of the univariate student's chart to reliably detect out of control status in multivariate processes. Although it is a very efficient tool for detection purposes, by itself, it offers no assistance about the origin of the declared faulty status. Several different approaches have been proposed to estimate the variable values' effect on the overall statistic's value. Some of these strategies work in the original measurement space, while others interpret the results coming from the analysis in latent variable spaces using for example Principal Component Analysis or Independent Component Analysis. With the same purpose, we present a novel approach, based on finding the nearest in-control neighbor of the observation point, in this work. The distance between both points is used to determine the contribution of each variable to the out of control state. Those variables whose distance measures exceed a certain threshold value are considered as suspicious. The results of the proposed strategy are compared with those obtained using other strategies that work both the original and latent variable spaces for case studies extracted from the literature.