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Chi-square Control Charts with Runs Rules

Author

Listed:
  • Athanasios C. Rakitzis

    (University of Piraeus)

  • Demetrios L. Antzoulakos

    (University of Piraeus)

Abstract

The Hotelling’s χ2 control chart is one of the most widely used multivariate charting procedures for monitoring the vector of means of several quality characteristics. As a Shewhart-type control chart, it incorporates information pertaining to most recently inspected sample and subsequently it is relatively insensitive in quickly detecting small magnitude shifts in the process mean vector. A popular solution suggested to overcome this handicap was the use of runs and scans rules as criteria to declare a process out-of-control. During the last years, the examination of Hotelling’s χ2 control charts supplemented with various runs rules has attracted continuous research interest. In the present article we study the performance of the Hotelling’s χ2 control chart supplemented with a r-out-of-m runs rule. The new control chart demonstrates an improved performance over other competitive runs rules based control charts.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:4:d:10.1007_s11009-010-9178-7
    DOI: 10.1007/s11009-010-9178-7
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    References listed on IDEAS

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    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. 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.
    3. Bersimis, Sotiris & Psarakis, Stelios & Panaretos, John, 2006. "Multivariate Statistical Process Control Charts: An Overview," MPRA Paper 6399, University Library of Munich, Germany.
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    Cited by:

    1. Spiros D. Dafnis & Frosso S. Makri, 2022. "Weak runs in sequences of binary trials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 573-603, July.
    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. 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.
    4. Athanasios Rakitzis & Demetrios Antzoulakos, 2015. "Start-up demonstration tests with three-level classification," Statistical Papers, Springer, vol. 56(1), pages 1-21, February.

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