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Economic and economic statistical designs of the synthetic X¯ chart using loss functions

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  • Yeong, Wai Chung
  • Khoo, Michael B.C.
  • Lee, Ming Ha
  • Rahim, M.A.

Abstract

This paper proposes the economic and economic statistical designs of the synthetic X¯ chart. In the economic design, the optimal chart parameters that minimize the expected cost function are obtained, while in the economic statistical design, the optimal chart parameters are obtained by minimizing the expected cost function, subject to constraints on the in-control average run length (ARL0) and the out-of-control average run length (ARL1). A small increase in cost is incurred when the statistical constraints are added to the economic design, however, a significant improvement in statistical performance is attained. The sensitivity of the optimal cost and the chart parameters for different loss functions and input parameters is investigated. The effects of misspecification of the type of the loss function, and the Taguchi loss coefficient, as well as the risk aversion coefficient of the loss function, are also investigated. In addition, effects of the process capability index are studied. Based on numerical studies, comparisons are made between the synthetic X¯, Shewhart X¯, and EWMA charts.

Suggested Citation

  • Yeong, Wai Chung & Khoo, Michael B.C. & Lee, Ming Ha & Rahim, M.A., 2013. "Economic and economic statistical designs of the synthetic X¯ chart using loss functions," European Journal of Operational Research, Elsevier, vol. 228(3), pages 571-581.
    • Handle: RePEc:eee:ejores:v:228:y:2013:i:3:p:571-581
    DOI: 10.1016/j.ejor.2013.02.021
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    References listed on IDEAS

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    6. Lee, Pei-Hsi, 2013. "Joint statistical design of X¯ and s charts with combined double sampling and variable sampling interval," European Journal of Operational Research, Elsevier, vol. 225(2), pages 285-297.
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    Cited by:

    1. Song, Zhi & Mukherjee, Amitava & Liu, Yanchun & Zhang, Jiujun, 2019. "Optimizing joint location-scale monitoring – An adaptive distribution-free approach with minimal loss of information," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1019-1036.
    2. Amir Ahmadi-Javid & Mohsen Ebadi, 2017. "Economic Design of Memory-Type Control Charts: The Fallacy of the Formula Proposed by Lorenzen and Vance (1986)," Papers 1708.06160, arXiv.org.
    3. Lei Yong Lee & Michael Boon Chong Khoo & Sin Yin Teh & Ming Ha Lee, 2015. "A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-18, May.
    4. Reza Pourtaheri, 2022. "Economic Statistical Design for Three-level Control Charts with Variable Sample Size," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 130-145, May.
    5. Yin, Hui & Zhang, Guojun & Zhu, Haiping & Deng, Yuhao & He, Fei, 2015. "An integrated model of statistical process control and maintenance based on the delayed monitoring," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 323-333.
    6. M. Abolmohammadi & A. Seif & M. H. Behzadi & M. B. Moghadam, 2021. "Economic statistical design of adaptive $$\bar{X}$$ X ¯ control charts based on quality loss functions," Operational Research, Springer, vol. 21(2), pages 1041-1080, June.
    7. CHEN, Piao & YE, Zhi-Sheng, 2018. "A systematic look at the gamma process capability indices," European Journal of Operational Research, Elsevier, vol. 265(2), pages 589-597.

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