Controlling Bivariate Categorical Processes using Scan Rules

  • Sotirios Bersimis
  • Athanasios Sachlas
  • Philippe Castagliola
Article

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.

Keywords

Multi-attribute processes Markov chain embeddable random variables Multivariate statistical process control Waiting time distributions 

Mathematics Subject Classification

60E05 60J10 

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References

  1. Antzoulakos DL, Rakitzis AC (2010) Runs rules schemes for monitoring process variability. J Appl Stat 37(7):1231–1247MathSciNetCrossRefGoogle Scholar
  2. Balakrishnan N, Koutras MV (2009) Runs and Scans with Applications. Wiley, New YorkMATHGoogle Scholar
  3. Balakrishnan N, Bersimis S, Koutras MV (2009) Run and frequency quota rules in process monitoring and acceptance sampling. J Qual Technol 41(1):66–81Google Scholar
  4. Chakraborti S, Eryilmaz S (2007) A nonparametric shewhart-type signed-rank control chart based on runs. Communications in Statistics - Theory and Methods, vol 36Google Scholar
  5. Champ CW, Woodall WH (1987) Exact results for shewhart control charts with supplementary runs rules. Technometrics 29(4):393–399CrossRefMATHGoogle Scholar
  6. Cook RJ (1994) Interim monitoring of bivariate responses using repeated confidence intervals. Control Clin Trials 15(3):187–200CrossRefGoogle Scholar
  7. Cook RJ (1996) Coupled error spending functions for bivariate sequential tests. Biometrics 52(2):442–450CrossRefMATHGoogle Scholar
  8. Cook RJ, Farewell VT (1995) Guidelines for monitoring efficacy and toxicity in clinical trials. Biometrics 50(4):1146–1152MathSciNetCrossRefMATHGoogle Scholar
  9. Costa AFB, de Magalhães MS, Epprecht EK (2009) Mnitoring the process mean and variance using a synthetic control chart with two-stage testing. Int J Prod Res 18:5067–5086CrossRefMATHGoogle Scholar
  10. de Leval MR, François K, Bull C, Brawn W, Spiegelhalter D (1994) Analysis of a cluster of surgical failures. application to a series of neonatal arterial switch operations. J Thorac Cardiovasc Surg 107(3):914–924Google Scholar
  11. Jakobson T, Karjagin J, Vipp L, Padar M, Parik AH, Starkopf L, Kern H, Tammik O, Starkopf J (2014) Postoperative complications and mortality after major gastrointestinal surgery. Medicina 50(2):111–117CrossRefGoogle Scholar
  12. Koutras MV, Bersimis S, Maravelakis PE (2006) Improving the performance of the chi-square control chart via runs rules. Methodol Comput Appl Probab 8(3):409–426MathSciNetCrossRefMATHGoogle Scholar
  13. Koutras MV, Bersimis S, Maravelakis PE (2007) Statistical process control using shewhart control charts with supplementary runs rules. Methodol Comput Appl Probab 9(2):207–224MathSciNetCrossRefMATHGoogle Scholar
  14. Koutras MV, Maravelakis PE, Bersimis S (2008) Techniques for controlling bivariate grouped observations. J Multivar Anal 99(7):1474–1480MathSciNetCrossRefMATHGoogle Scholar
  15. Li J, Tsung F, Zou C (2014) Multivariate binomial/multinomial control chart. IIE Trans 46(5):526–542CrossRefGoogle Scholar
  16. Maleki MR, Amiri A (2015) Simultaneous monitoring of multivariate-attribute process mean and variability using artificial neural networks. J Quality Eng Prod Optim 1(1):43–54Google Scholar
  17. Montgomery DC (2005) Introduction to Statistical Quality Control. Wiley, New YorkMATHGoogle Scholar
  18. Rakitzis AC, Antzoulakos DL (2011) Chi-square control charts with runs rules. Methodol Comput Appl Probab 13(4):657–669MathSciNetCrossRefMATHGoogle Scholar
  19. Roche JJ, Wenn RT, Sahota O, Moran CG (2005) Effect of comorbidities and postoperative complications on mortality after hip fracture in elderly people: prospective observational cohort study. Br Med J 331(7529):1374CrossRefGoogle Scholar
  20. Schatz R, Egger S, Platzer A (2011) Poor, good enough or even better? bridging the gap between acceptability and qoe of mobile broadband data services. In: Proceedings of the 2011 IEEE International Conference on Communications, pages 1–6, KyotoGoogle Scholar
  21. Steiner SH, Cook RJ, Farewell VT (1999) Monitoring paired binary surgical outcomes using cumulative sum charts. Stat Med 18(1):69–86CrossRefGoogle Scholar
  22. Story DA (2013) Postoperative complications in australia and new zealand (the reason study). Perio Med 2:16CrossRefGoogle Scholar
  23. Topalidou E, Psarakis S (2009) Review of multinomial and multi-attribute quality control charts. Qual Reliab Eng Int 25(7):773–804CrossRefGoogle Scholar
  24. Woodall WH (1997) Control charting based on attribute data: Bibliography and review. J Qual Technol 29(2):172–183Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Sotirios Bersimis
    • 1
  • Athanasios Sachlas
    • 1
  • Philippe Castagliola
    • 2
  1. 1.Department of Statistics & Insurance ScienceUniversity of PiraeusPiraeusGreece
  2. 2.LUNAM Université, Université de Nantes & IRCCyN UMR CNRS 6597CarquefouFrance

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