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Statistical Process Control using Shewhart Control Charts with Supplementary Runs Rules

Author

Listed:
  • M. V. Koutras

    (University of Piraeus)

  • S. Bersimis

    (University of Piraeus)

  • P. E. Maravelakis

    (University of Piraeus)

Abstract

The aim of this paper is to present the basic principles and recent advances in the area of statistical process control charting with the aid of runs rules. More specifically, we review the well known Shewhart type control charts supplemented with additional rules based on the theory of runs and scans. The motivation for this article stems from the fact that during the last decades, the performance improvement of the Shewhart charts by exploiting runs rules has attracted continuous research interest. Furthermore, we briefly discuss the Markov chain approach which is the most popular technique for studying the run length distribution of run based control charts.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:2:d:10.1007_s11009-007-9016-8
    DOI: 10.1007/s11009-007-9016-8
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    References listed on IDEAS

    as
    1. Markos V. Koutras & Sotirios Bersimis & Demetrios L. Antzoulakos, 2006. "Improving the Performance of the Chi-square Control Chart via Runs Rules," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 409-426, September.
    2. 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.
    3. 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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    Citations

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    Cited by:

    1. 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.
    2. 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.
    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. Sánchez, Ismael, 2015. "Adaptive EWMA Control Charts with a Time Varying Smoothing Parameter," DES - Working Papers. Statistics and Econometrics. WS ws1507, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Sotirios Bersimis & Athanasios Sachlas & Philippe Castagliola, 2017. "Controlling Bivariate Categorical Processes using Scan Rules," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1135-1149, December.
    6. Sotiris Bersimis & Kostas Triantafyllopoulos, 2020. "Dynamic Non-parametric Monitoring of Air-Pollution," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1457-1479, December.
    7. Serkan Eryilmaz, 2018. "Stochastic Ordering Among Success Runs Statistics in a Sequence of Exchangeable Binary Trials," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 563-573, June.
    8. Sotirios Bersimis & Athanasios Sachlas & Ross Sparks, 2017. "Performance Monitoring and Competence Assessment in Health Services," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1169-1190, December.
    9. F. Jamaluddin* & H. H. Ali & S. S. Syed Yahaya & Z. Zain, 2018. "The Performance of Robust Multivariate Ewma Control Charts," The Journal of Social Sciences Research, Academic Research Publishing Group, pages 52-58:6.
    10. Athanasios C. Rakitzis & Demetrios L. Antzoulakos, 2011. "Chi-square Control Charts with Runs Rules," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 657-669, December.
    11. 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.
    12. Tung-Lung Wu, 2020. "Conditional waiting time distributions of runs and patterns and their applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 531-543, April.
    13. Athanasios Rakitzis & Demetrios Antzoulakos, 2015. "Start-up demonstration tests with three-level classification," Statistical Papers, Springer, vol. 56(1), pages 1-21, February.
    14. 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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