Hotelling’s T2 Decomposition: Approach for Five Process Characteristics in a Multivariate Statistical Process Control
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 6, November 2015, Pages: 432-437
Received: Aug. 27, 2015; Accepted: Sep. 13, 2015; Published: Sep. 28, 2015
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Authors
Adepoju Ajibola Akeem, Department of Mathematics, Ahmadu Bello University, Zaria, Kaduna State, Nigeria
Abubakar Yahaya, Department of Mathematics, Ahmadu Bello University, Zaria, Kaduna State, Nigeria
Osebekwin Asiribo, Department of Mathematics, Ahmadu Bello University, Zaria, Kaduna State, Nigeria
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Abstract
Multivariate statistical process control (MSPC) is the most acceptable monitoring tool for several variables, and it is advantageous when compare to the simultaneous use of univariate scheme. However, there are some disadvantages in this scheme which include identification of influential variable(s). The Mason, Young and Tracy (MYT) decomposition diagnosis is one of the approaches commonly use to identify the influential variables. This approach aid the breaking down, the overall T square value and show the individual variable contribution, while their joint contributions is also revealed. The challenges of this approach include rigorous derivation of model, computation and complexity more especially when the size of the process characteristics is large. In this research paper we extend the decomposition derivation to five variables. One hundred and twenty (120) models (decomposition partitions) are obtained from the decomposition, revealing the invariance property of the Hotelling’s T square statistic, and eighty (80) unique terms.
Keywords
Decomposition Chart, Hotelling’s T square, Invariance Property, Matrix Permutation, Multivariate Statistical Process Control (MSPC), MYT Decomposition
To cite this article
Adepoju Ajibola Akeem, Abubakar Yahaya, Osebekwin Asiribo, Hotelling’s T2 Decomposition: Approach for Five Process Characteristics in a Multivariate Statistical Process Control, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 6, 2015, pp. 432-437. doi: 10.11648/j.ajtas.20150406.13
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