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Joint Economically Optimal Design of X\bar and R Control Charts

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  • Erwin M. Saniga

    (University of Delaware)

Abstract

In this paper, we develop an expected cost model for a process whose mean is controlled by an X\bar chart and whose variance is controlled by an R chart. The expected cost comprises the fixed and variable costs of sampling, the cost of investigating and correcting the process when at least one control chart indicates that the process parameters have shifted, and the cost of producing defective units. We use a search procedure to determine the sample size, interval between samples and control limits for both charts that minimize the expected cost. Optimal solutions to numerical examples are presented. A sensitivity analysis of the model is performed. In addition, we find the optimal interval between samples and the expected cost for several examples with large shifts in the mean and variance where Shewhart's heuristic design is used in place of the optimal design. Comparison of the expected cost of the optimal design to the expected cost of Shewhart's design shows an increase in expected cost of only 0.4 to 8.2 percent for the latter design. But other situations are discussed and examples presented which indicate that the optimal design is preferred.

Suggested Citation

  • Erwin M. Saniga, 1977. "Joint Economically Optimal Design of X\bar and R Control Charts," Management Science, INFORMS, vol. 24(4), pages 420-431, December.
    • Handle: RePEc:inm:ormnsc:v:24:y:1977:i:4:p:420-431
    DOI: 10.1287/mnsc.24.4.420
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    Cited by:

    1. Yang, Yit-Ming & Su, Chia-Yi & Pearn, W.L., 2010. "Economic design of x¯-control charts for continuous flow process with multiple assignable causes," International Journal of Production Economics, Elsevier, vol. 128(1), pages 110-117, November.
    2. Chen, Yun-Shiow & Yang, Yit-Ming, 2002. "Economic design of -control charts with Weibull in-control times when there are multiple assignable causes," International Journal of Production Economics, Elsevier, vol. 77(1), pages 17-23, May.
    3. Turnes Osiris & Lee Ho Linda & Imaña Christian Rainier, 2002. "Comparison of Semi-Economic and -R Control Charts for Non-Ageing and Ageing Process," Stochastics and Quality Control, De Gruyter, vol. 17(1), pages 99-112, January.
    4. Chung-Ming Yang, 1999. "Economic Process Management and Its Application on Bank Industry," Quality & Quantity: International Journal of Methodology, Springer, vol. 33(4), pages 381-394, November.
    5. De Magalhaes, Maysa S. & Moura Neto, Francisco D., 2005. "Joint economic model for totally adaptive and R charts," European Journal of Operational Research, Elsevier, vol. 161(1), pages 148-161, February.
    6. Emre Berk & Ayhan Özgür Toy, 2009. "Quality control chart design under Jidoka," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(5), pages 465-477, August.
    7. Chen, Yun-Shiow & Yang, Yit-Ming, 2002. "An extension of Banerjee and Rahim's model for economic design of moving average control chart for a continuous flow process," European Journal of Operational Research, Elsevier, vol. 143(3), pages 600-610, December.
    8. Ho, Linda Lee & Trindade, Anderson Laécio Galindo, 2009. "Economic design of an X chart for short-run production," International Journal of Production Economics, Elsevier, vol. 120(2), pages 613-624, August.

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