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On Average Run Lengths of Control Charts for Autocorrelated Processes

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  • Yung-Ming Chang

    (National Taitung University)

  • Tung-Lung Wu

    (National University of Kaohsiung)

Abstract

It is well known that statistical control charts such as Shewhart, CUSUM and EWMA charts have widespread applications in improving the quality for manufacturing and service systems. The average run length is a traditional measurement of a control chart’s performance. Usually, finding the run length distribution and the average run length is a difficult and tedious task. In this article, we develop a general and unified approach based on the use of discretization and the finite Markov chain imbedding technique to investigate the run length properties for various control charts when the process observations are autocorrelated. Numerical results are presented for illustrative purposes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:2:d:10.1007_s11009-009-9160-4
    DOI: 10.1007/s11009-009-9160-4
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Jingwen Lu & He Yi & Xiang Li & Narayanaswamy Balakrishnan, 2023. "Joint Reliability of Two Consecutive-(1, l) or (2, k)-out-of-(2, n): F Type Systems and Its Application in Smart Street Light Deployment," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    2. Yu-Fei Hsieh & Tung-Lung Wu, 2013. "Recursive equations in finite Markov chain imbedding," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 513-527, June.
    3. Yin, Juan & Cui, Lirong & Balakrishnan, Narayanaswamy, 2022. "Reliability of consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    4. Jungtaek Oh & Christian H. Weiß, 2020. "On the Individuals Chart with Supplementary Runs Rules under Serial Dependence," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1257-1273, September.
    5. Tung-Lung Wu, 2013. "On Finite Markov Chain Imbedding and Its Applications," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 453-465, June.
    6. Lin, Cong & Zeng, Zhaoyang & Zhou, Yan & Xu, Ming & Ren, Zhanyong, 2019. "A lower bound of reliability calculating method for lattice system with non-homogeneous components," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 36-46.
    7. 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.

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