GENERALIZATION OF THE HOTELLING’S T2 DECOMPOSITION METHOD TO THE R-CHART - Piña-Monarrez, Manuel Roman (International Journal of Industrial Engineering: Theory, Applications and Practice, 2018)
The purpose of this paper is to provide the multivariate statistical control process (MSPC) with an efficient method to decompose the out-of-control (signal) when the non-parametric R-chart signals. The method determines the contribution of each variable as a linear combination of the p variables. And it is efficient in the sense, that the observed signal value and its decomposition always hold, and in the fact that it determines the contribution of each variable due to its variance and due to its covariance with each one of the other p–1 variables. The method has already been applied in the Hotelling T2 chart, where the Mahalanobis distance (MD) is decomposed. However, in the R-chart, the signal is measured by using the Mahalanobis depth function (MDF), which is based on the MD too. Thus, in this paper, due to the direct relationship between the MD and the MDF, the Hotelling’s T2 decomposition method is generalized to be used in the R-chart. Results show that because decomposing either the MD or the MDF is equivalent, the method works efficiently in the R-chart too. To see how it numerically works, an application to a set of three variables is presented.