ON TECHNIQUES FOR IDENTIFICATION OF OUT-OF-CONTROL VARIABLE(S) IN MULTIVARIATE T2 CONTROL CHART ON CABLE PRODUCTION

AKANINYENE UDO UDOM *

Department of Statistics, University of Nigeria, Nsukka, Enugu State, Nigeria.

ONYINYE MARYJANE EZEANI

Department of Statistics, University of Nigeria, Nsukka, Enugu State, Nigeria.

NNAMDI PASCHAL ODOH

Department of Statistics, University of Nigeria, Nsukka, Enugu State, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

Multivariate statistical process control charts are used for process monitoring and control of two or more variables simultaneously for quality and quality improvement. A popular multivariate control chart is used to monitor the mean vector of the process. A usual problem in the multivariate control chart is the identification and interpretation of variable(s) for an out-of-control signal that occurred in the chart. This has brought many developed techniques from many researchers to aid in finding the responsible variable(s) that caused the out-of-control signal in the chart. This work is aimed at a comparative study of some developed techniques for identifying and interpreting an out-of-control signal, in the multivariate control chart when applied on the cable production process. The techniques are Mason-Tracy-Young, Donganaksoy-Faltin-Tucker, Univariate -chart using Bonferroni control limits by Alt and Principal component analysis by Jackson. A performance criterion, the power of the test was used to ascertain the most satisfactory technique that explained the out-of-control signal that occurred in -chart. From the results and discussions, Mason Tracy-Young and Doganaksoy-Faltin-Tucker techniques are the most satisfactory for identifying and interpreting an out-of-control signal in the multivariate control chart.

Keywords: Multivariate statistical process control chart, multivariate control chart interpretation, power of a test, cable products


How to Cite

UDOM, A. U., EZEANI, O. M., & ODOH, N. P. (2022). ON TECHNIQUES FOR IDENTIFICATION OF OUT-OF-CONTROL VARIABLE(S) IN MULTIVARIATE T2 CONTROL CHART ON CABLE PRODUCTION. Asian Journal of Mathematics and Computer Research, 29(2), 7–22. https://doi.org/10.56557/ajomcor/2022/v29i27874

Downloads

Download data is not yet available.

References

Gupta PK, Hira DS. Operation research (Rev. ed.). New Delhi, India: S. Chand & Company Ltd; 2014.

Alford PL, Beatty RH. Principles of industrial management (Rev. ed.). New York: Ronald Press Company;1951.

Jackson JE. A user’s guide to principal components. John Wiley & Sons, Inc; 1991.

Montgomery CD. Introduction to statistical quality control (6th ed.). United States of America: John Wiley &sons, Inc;2009.

Mason RL, Tracy ND, Young CH. Decomposition of for multivariate control chart interpretation. Journal of Quality Technology.1995;27(2):99-108.

Doganaksoy N, Faltin FW, Tucker WT. Identification of out of control quality characteristics in a multivariate manufacturing environment. Communications in Statistics – Theory and Methods. 1991;20(9):2775-2790.

Alt FB. Multivariate quality control. In S. Kotz et al. (Eds.), Encyclopedia of statistical sciences. New York: John Wiley;1985.

Roy J. Step-down procedure in multivariate analysis. Ann. Math. Statist. 1985;29:1177-1187.

Hawkins DM. Multivariate quality control based on regression–adjusted variables. Technometrics. 1991;33(1):67-75.

Mason RL, Chou Y, Young JC. Applying Hotelling’s statistic to batch processes. Journal of Quality Technology. 2001;33(4):466-479.

Parra MG, Loaiza PR. Application of the multivariate control chart and the Mason-Tracy-Young decomposition procedure to the study of the consistency of impurity profiles of drug substances. Quality Engineering. 2003;16(1):127-142.

Sharaf El-Din MA, Rasheed HI, El-khabeery. Statistical process control charts applied to steelmaking quality improvement. Quality Technology and Quantitative management. 2006;3(4):473-491.

Das N, Prakash V. Interpreting the out-of-control signal in multivariate control chart- a comparative study. Int J Adv Manuf Technol. 2008;37:966-979.

Murphy BJ. Selecting out of control variable with the multivariate quality control procedure. The Statistician. 1987;36:571-583.

Waterhouse M, Smith I, Assareh H, Mengersen K. Implementation of multivariate control charts in a clinical setting. International Journal for Quality in Health Care. 2010;22(5):408-414.

Xi C, Fenggong G, Yaoguang H, YanYan. Multivariate quality control of plastic products based on principal component analysis. National High Technology Research and Development Program of China. 2010;552-557.

Onwuka GI. Hotellings T-square and principal component analysis approaches to quality control sustainability. International Journal of Computational Engineering Research. 2012;8(2):211-217.

Rao OR, Subbaiah VK, Rao NK, Rao ST. Application of multivariate control chart for improvement in quality of hot metal. International Journal of Quality Research.2013;7(4):623-640.

Mason RL, Young JC. Multivariate statistical process control with industrial applications. American Statistical Association and the Society for Industrial and Applied Mathematics;2002.