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On the Individuals Chart with Supplementary Runs Rules under Serial Dependence

Author

Listed:
  • Jungtaek Oh

    (Kyungpook National University
    Changwon National University)

  • Christian H. Weiß

    (Helmut Schmidt University)

Abstract

To improve the sensitivity of a Shewhart control chart, it is common among practitioners to use supplementary runs rules. The performance of such runs rules charts is studied in the presence of positive autocorrelation caused by a first-order discrete autoregressive process. This type of data-generating process allows to compute the chart’s run length properties exactly and efficiently, by utilizing the finite Markov chain embedding technique. Explicit formulae are derived for common types of runs rules. Afterwards, a detailed performance study about runs rules charts under serial dependence is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09760-2
    DOI: 10.1007/s11009-019-09760-2
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    References listed on IDEAS

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    3. 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.
    4. 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.
    5. 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.
    6. Demetrios Antzoulakos & Athanasios Rakitzis, 2010. "Runs rules schemes for monitoring process variability," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(7), pages 1231-1247.
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