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On Distribution and Average Run Length of a Two-Stage Control Process

Author

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  • Hsing-Ming Chang

    (National Cheng Kung University)

  • James C. Fu

    (University of Manitoba)

Abstract

In this article a method, using finite Markov chains, to obtain the run-length properties of a two-stage control process is presented. The method furnishes the obtaining of the distribution of waiting time to signal that gives additional insight into the design and performance of a control chart when a warning zone is considered to feature a two-stage control process and when a departure from the null assumption can be clearly defined. An example is given for illustration when samples come from a normal population, though not necessary, with an outlined process inspection scheme. A second example is given to demonstrate the extension of our approach to modelling Markov dependent data observations.

Suggested Citation

  • Hsing-Ming Chang & James C. Fu, 2022. "On Distribution and Average Run Length of a Two-Stage Control Process," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2723-2742, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09935-4
    DOI: 10.1007/s11009-022-09935-4
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    References listed on IDEAS

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    1. Fu, James C. & Spiring, Fred A. & Xie, Hansheng, 2002. "On the average run lengths of quality control schemes using a Markov chain approach," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 369-380, February.
    2. C. Fu, James & Shmueli, Galit & Chang, Y. M., 2003. "A unified Markov chain approach for computing the run length distribution in control charts with simple or compound rules," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 457-466, December.
    3. Chang, Hsing-Ming & Chang, Yung-Ming & Fu, Winnie H.W. & Lee, Wan-Chen, 2018. "On limiting theorems for conditional causation probabilities of multiple-run-rules," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 151-156.
    4. Chan, L. Y. & Lai, C. D. & Xie, M. & Goh, T. N., 2003. "A two-stage decision procedure for monitoring processes with low fraction nonconforming," European Journal of Operational Research, Elsevier, vol. 150(2), pages 420-436, October.
    5. M. V. Koutras & S. Bersimis & P. E. Maravelakis, 2007. "Statistical Process Control using Shewhart Control Charts with Supplementary Runs Rules," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 207-224, June.
    6. Li, Hui & Liu, Liming, 2006. "Production control in a two-stage system," European Journal of Operational Research, Elsevier, vol. 174(2), pages 887-904, October.
    7. Koutras, Vasileios M. & Koutras, Markos V. & Yalcin, Femin, 2016. "A simple compound scan statistic useful for modeling insurance and risk management problems," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 202-209.
    8. Yung-Ming Chang & Tung-Lung Wu, 2011. "On Average Run Lengths of Control Charts for Autocorrelated Processes," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 419-431, June.
    9. Sotiris Bersimis & Markos V. Koutras & George K. Papadopoulos, 2014. "Waiting Time for an Almost Perfect Run and Applications in Statistical Process Control," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 207-222, March.
    10. Fu, James C. & Lou, W. Y., 1991. "On reliabilities of certain large linearly connected engineering systems," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 291-296, October.
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    Cited by:

    1. Xiaoyue Wang & Ru Ning & Xian Zhao, 2023. "Generalized mixed shock model for multi-component systems in the shock environment with a change point," Journal of Risk and Reliability, , vol. 237(4), pages 619-635, August.

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