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Optimal designs of the double sampling X¯ chart with estimated parameters

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  • Khoo, Michael B.C.
  • Teoh, W.L.
  • Castagliola, Philippe
  • Lee, M.H.

Abstract

The double sampling (DS) X¯ chart detects small and moderate mean shifts quickly. Furthermore, this chart can reduce the sample size. The DS X¯ chart is usually investigated assuming that the process parameters are known. Nevertheless, the process parameters are usually unknown and are estimated from an in-control Phase-I dataset. This paper (i) evaluates the performances of the DS X¯ chart when process parameters are estimated by means of a new proposed theoretical method, (ii) shows that performances with estimated parameters are different from that with known parameters, and (iii) proposes three optimal design procedures: the first design minimizes the out-of-control average run length, the second design minimizes the in-control average sample size and the third design minimizes the average extra quadratic loss, by considering the number of Phase-I samples in these three designs. Additionally, for ease of implementation, this paper provides the new optimal parameters specially computed for the DS X¯ chart with estimated parameters, based on the number of Phase-I samples used in practice. These findings will lead to a more economically feasible process monitoring situation, especially when the process parameters are unknown.

Suggested Citation

  • Khoo, Michael B.C. & Teoh, W.L. & Castagliola, Philippe & Lee, M.H., 2013. "Optimal designs of the double sampling X¯ chart with estimated parameters," International Journal of Production Economics, Elsevier, vol. 144(1), pages 345-357.
    • Handle: RePEc:eee:proeco:v:144:y:2013:i:1:p:345-357
    DOI: 10.1016/j.ijpe.2013.02.022
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    References listed on IDEAS

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    4. Lee, Pei-Hsi & Torng, Chau-Chen & Liao, Li-Fang, 2012. "An economic design of combined double sampling and variable sampling interval X¯ control chart," International Journal of Production Economics, Elsevier, vol. 138(1), pages 102-106.
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    Cited by:

    1. Lim, S.L. & Khoo, Michael B.C. & Teoh, W.L. & Xie, M., 2015. "Optimal designs of the variable sample size and sampling interval X¯ chart when process parameters are estimated," International Journal of Production Economics, Elsevier, vol. 166(C), pages 20-35.
    2. Zhang, Min & Nie, Guohua & He, Zhen, 2014. "Performance of cumulative count of conforming chart of variable sampling intervals with estimated control limits," International Journal of Production Economics, Elsevier, vol. 150(C), pages 114-124.
    3. H.W. You & Michael B.C. Khoo & P. Castagliola & Liang Qu, 2016. "Optimal exponentially weighted moving average charts with estimated parameters based on median run length and expected median run length," International Journal of Production Research, Taylor & Francis Journals, vol. 54(17), pages 5073-5094, September.
    4. H. You & Michael Khoo & P. Castagliola & Yanjing Ou, 2015. "Side sensitive group runs $$\bar{{X}}$$ X ¯ chart with estimated process parameters," Computational Statistics, Springer, vol. 30(4), pages 1245-1278, December.

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