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Economic Design of Control Charts with Different Control Limits for Different Assignable Causes

Author

Listed:
  • George Tagaras

    (Department of Decision Sciences, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Hau L. Lee

    (Department of Industrial Engineering and Engineering Management, Stanford University, Stanford, California 94305)

Abstract

The use of multiple control limits and multiple corresponding levels of response for processes is an effective way for statistical process control when different assignable causes exist which lead to different out-of-control states of the processes, and different restoration procedures. This paper examines the optimal economic design of such process control charts. The exact mathematical model is developed and the expected cost per time unit function is derived. The costs associated with the statistical process control are minimized by means of an optimization procedure involving a quasi-Newton method and a Fibonacci lattice search. Sensitivity analysis performed on a large number of numerical examples reveals key relationships between model parameters. A comparison between the proposed control chart and an approximate matched single-cause chart shows that the former can be a significant improvement over the latter. Several model extensions and managerial implications are also discussed.

Suggested Citation

  • George Tagaras & Hau L. Lee, 1988. "Economic Design of Control Charts with Different Control Limits for Different Assignable Causes," Management Science, INFORMS, vol. 34(11), pages 1347-1366, November.
    • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:11:p:1347-1366
    DOI: 10.1287/mnsc.34.11.1347
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    Citations

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    Cited by:

    1. Timothy S. Vaughan, 1999. "The effect of process adjustment error on X̄ chart design," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 597-612, September.
    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. Jerry Dechert & Kenneth Case, 1999. "An economic model for clinical quality control," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(5), pages 553-562.
    4. 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.
    5. George Tagaras, 1989. "Power approximations in the economic design of control charts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 639-654, October.
    6. George Tagars & Hau L. Lee, 1989. "Approximate semieconomic design of control charts with multiple control limtis," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(3), pages 337-353, June.
    7. Chen, Huifen & Cheng, Yuyen, 2007. "Non-normality effects on the economic-statistical design of charts with Weibull in-control time," European Journal of Operational Research, Elsevier, vol. 176(2), pages 986-998, January.

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