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Economic Design of T 2 Control Charts to Maintain Current Control of a Process

Author

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  • Douglas C. Montgomery

    (Georgia Institute of Technology)

  • Phillip J. Klatt

    (Georgia Institute of Technology)

Abstract

An approximate cost model for a quality control procedure for two or more related variables is investigated. A method is presented to determine the optimal sample size, interval between samples, and critical region parameter for the Hotelling T 2 control chart. This model is a multivariate analog of several well-known models for the univariate X\bar -chart. It is assumed that only one assignable cause of variation exists and the time between occurrences is exponentially distributed. Numerical results are provided in a particular bivariate case for several values of the cost coefficients. The behavior of the model to variation of the model parameters is discussed.

Suggested Citation

  • Douglas C. Montgomery & Phillip J. Klatt, 1972. "Economic Design of T 2 Control Charts to Maintain Current Control of a Process," Management Science, INFORMS, vol. 19(1), pages 76-89, September.
    • Handle: RePEc:inm:ormnsc:v:19:y:1972:i:1:p:76-89
    DOI: 10.1287/mnsc.19.1.76
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    Cited by:

    1. W. Chiu, 1976. "On the estimation of data parameters for economic optimum 135-1135-1135-1-Charts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 23(1), pages 135-147, December.
    2. Liang Liu & Cong Feng & Hongwei Zhang & Xuehua Zhang, 2015. "Game Analysis and Simulation of the River Basin Sustainable Development Strategy Integrating Water Emission Trading," Sustainability, MDPI, vol. 7(5), pages 1-21, April.
    3. Wu, Jianmou & Makis, Viliam, 2008. "Economic and economic-statistical design of a chi-square chart for CBM," European Journal of Operational Research, Elsevier, vol. 188(2), pages 516-529, July.
    4. Yang, S.F. & Rahim, M.A., 2005. "Economic statistical process control for multivariate quality characteristics under Weibull shock model," International Journal of Production Economics, Elsevier, vol. 98(2), pages 215-226, November.
    5. Asghar Seif & Alireza Faraz & C�dric Heuchenne & Erwin Saniga & M. B. Moghadam, 2011. "A modified economic-statistical design of the T-super-2 control chart with variable sample sizes and control limits," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2459-2469, January.
    6. Y-K Chen, 2007. "Economic design of an adaptive T 2 control chart," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(3), pages 337-345, March.
    7. Xiao, Xiao & Jiang, Wei & Luo, Jianwen, 2019. "Combining process and product information for quality improvement," International Journal of Production Economics, Elsevier, vol. 207(C), pages 130-143.
    8. Jolayemi, Joel K., 1995. "A power function model for determining sample sizes for the operations of multivariate control charts," Computational Statistics & Data Analysis, Elsevier, vol. 20(6), pages 633-641, December.
    9. Yan-Kwang Chen, 2009. "Economic design of T 2 control charts with the VSSI sampling scheme," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(1), pages 109-122, January.

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