Generalization of the Hotelling’s t2 decomposition method to the r-chart

Abstract

In this paper, the decomposition of the Mahalanobis distance (MD) and the proportional contribution that each one of the p monitored variables has on the estimated Mahalanobis depth function (MDF) of the R-chart are determined. And because the p monitored variables are correlated each other, then the contributions are determined due to their variances and due to their covariances. On the other hand, since 1) the decomposition’s method of the Hotelling T2 chart, by decomposing MD, efficiently determines the contribution of each variable due to its variance and due to its covariance, and 2) because a direct relationship between MD and MDF exists, then in this paper the Hotelling T2 decomposition method is used to determine the proportional contribution that each one of the p monitored variables has on the observed MDF value when in the R-chart, an out of control is detected. A numerical application to a set of three non-normal variable behavior is also presented.