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Controlling Bivariate Categorical Processes using Scan Rules

Author

Listed:
  • Sotirios Bersimis

    (University of Piraeus)

  • Athanasios Sachlas

    (University of Piraeus)

  • Philippe Castagliola

    (LUNAM Université, Université de Nantes & IRCCyN UMR CNRS 6597)

Abstract

In this paper, we introduce a methodology for efficiently monitoring a health process that classify the intervention outcome, in two dependent characteristics, as “absolutely successful”, “with minor but acceptable complications” and “unsuccessful due to severe complications”. The monitoring procedure is based on appropriate 2-dimensional scan rules. The run length distribution is acquired by studying the waiting time distribution for the first occurrence of a 2-dimensional scan in a bivariate sequence of trinomial trials. The waiting time distribution is derived through a Markov chain embedding technique. The proposed procedure is applied on two simulated cases while it is tested against a competing method showing an excellent performance.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:4:d:10.1007_s11009-016-9508-5
    DOI: 10.1007/s11009-016-9508-5
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    References listed on IDEAS

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    1. Koutras, M.V. & Maravelakis, P.E. & Bersimis, S., 2008. "Techniques for controlling bivariate grouped observations," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1474-1488, August.
    2. 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.
    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. 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.
    5. 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.
    6. Jian Li & Fugee Tsung & Changliang Zou, 2014. "Multivariate binomial/multinomial control chart," IISE Transactions, Taylor & Francis Journals, vol. 46(5), pages 526-542.
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