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
Views 3656 Downloads 103
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
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.
Adepoju Ajibola Akeem,
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.
Hotelling, H. Multivariate Quality Control. In C. Eisenhart, M. W. Hastay and W. A. Wallis, eds. Techniques of Statistical Analysis. New York: McGraw Hill, 111-184(1947).
Sullivan, J. H. and Woodall, W. H., A Comparison of Multivariate Control Charts for Individual Observations, Journal of Quality Technology, 28 (4) 398-408 (1996).
Mason, R. L. and Young, J. C. Improving the sensitivity of the T2 statistic in multivariate process control. Journal of Quality Technology, 31(2), 155-165(1999).
Tong, L. I., Wang, C. H. and Huang, C. L., “Monitoring defects in IC fabrication using a Hotelling T2 control chart”, IEE Trans. Semiconductor Manufacturing, 18(1), 140-148(2005).
Mason R. L., Tracy N. D. and Young J. C., “Decomposition of T2 for multivariate control chart interpretation” Journal of Quality Technology 27, 99-108(1995).
Lowry, C. A. and Montgomery, D. C., A Review of Multivariate Control Chart, IIE Transactions, (27) 800 – 810.
Mason, R. L., Tracy N. D., and Young J. C. A practical application for interpreting multivariate T2 control chart signal. Journal of Quality Technology, 29(4), 396-501(1997).
Ulen, M. and Demir, I.,” Application of multivariate statistical quality control in pharmaceutical industry”, Balkan Journal of Mathematics, 1, 93-105. (2013).
Masoud, Y. and Javad E “Identification of the Out of Control Variables in Multivariate Statistical Process Control” Journal of Statistical Modeling and Analytics 1(1), 95-112(2010).
Sani, S. A., and Abubakar, Y.,” Demonstrating the Invariance Property of the Hotelling T2 Statistic”, International Journal of Innovative Research in Science, Engineering and Technology, 2(7), 2515-2519(2013).
Nathan S. A., Hussaini G. D. and Osebekwin E. A. Decomposing Hotelling’s T2 Statistic Using Four Variables International Journal of Innovative Research in Science, Engineering and Technology3(4), 2014.
Blazek, L. W., Novic B. and Scott M. D. Displaying Multivariate Data Using Polyplots. Journal of Quality Technology, 19(2), 69-74(1987).
Subramanyan, N. and Houshmand, A. A. Simultaneous representation of multivariate and corresponding univariate charts using line graph. Quality Engineering, 4, 681-682(1995).
Fuchs, C. and Benjamin, Y. Multivariate profile charts for statistical process control. Technometrics, 36(2), 182-195(1994).
Iglewicz, B. and Hoaglin, D. C. Use of boxplots for process evaluation. Journal of Quality Technology, 19(4), 180-190(1987).
Atienza, O. O., Ching L. T. and Wah, B. A. Simultaneous monitoring of univariante and multivariate SPC information using boxplots. International Journal of Quality Science, 3(2), 1988.
Woodall, W. H. and Montgomery, D. C. Research Issues and Ideas in Statistical Process Control. Journal of Quality Technology 31.376-386(1999).