GENERALIZATION OF THE HOTELLING’S T2 DECOMPOSITION METHOD TO THE R-CHART

Authors

  • Manuel Roman Piña-Monarrez Universidad Autonoma de Ciudad Juarez

DOI:

https://doi.org/10.23055/ijietap.2018.25.2.2053

Keywords:

R-chart, Hotelling T2 chart, Mahalanobis depth function, Decomposition method

Abstract

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 p1 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.

Author Biography

Manuel Roman Piña-Monarrez, Universidad Autonoma de Ciudad Juarez

Researcher of the Postgraduate Department at the Engineering and Technology Institute in the Autonomous University of Ciudad Juarez.

Published

2018-04-26

How to Cite

Piña-Monarrez, M. R. (2018). GENERALIZATION OF THE HOTELLING’S T2 DECOMPOSITION METHOD TO THE R-CHART. International Journal of Industrial Engineering: Theory, Applications and Practice, 25(2). https://doi.org/10.23055/ijietap.2018.25.2.2053

Issue

Section

Quality, Reliability, Maintenance Engineering