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Distribution-Free Phase II Control Charts Based on Order Statistics with Runs-Rules

  • Ioannis S. TriantafyllouEmail author
  • Nikolaos I. Panayiotou
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Abstract

In this article, we introduce two nonparametric Shewhart-type control charts based on order statistics with signaling runs-type rules. The proposed monitoring schemes enhance the control charts established by Triantafyllou (2018). Exact formulae for the alarm rate, the variance of the run length distribution and the average run length (ARL) for both charts are all derived. Tables are provided for the implementation of the proposed schemes for some typical ARL-values. In addition, several numerical comparisons against competitive nonparametric control charts reveal that the new monitoring schemes, under different out-of-control situations, are quite efficient in detecting the shift of the underlying distribution.

Keywords

Average run length Distribution-free control charts Lehmann alternatives Nonparametric methods Runs-type rules Statistical process control 

References

  1. Balakrishnan, N., & Koutras, M. V. (2002). Runs and scans with applications. New York: Wiley.Google Scholar
  2. Balakrishnan, N., Triantafyllou, I. S., & Koutras, M. V. (2010). A distribution-free control chart based on order statistics. Communication in Statistics: Theory & Methods, 39, 3652–3677.MathSciNetCrossRefGoogle Scholar
  3. Chakraborti, S., Eryilmaz, S., & Human, S. W. (2009). A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules. Computational Statistics & Data Analysis, 53, 1054–1065.MathSciNetCrossRefGoogle Scholar
  4. Chakraborti, S., & Graham, M. (2019). Nonparametric statistical process control. USA: Wiley.Google Scholar
  5. Chakraborti, S., van der Laan, P., & van der Wiel, M. A. (2004). A class of distribution-free control charts. Journal of the Royal Statistical Society, Series C-Applied Statistics, 53, 443–462.MathSciNetCrossRefGoogle Scholar
  6. Derman, C., & Ross, S. M. (1997). Statistical aspects of quality control. San Diego: Academic Press.zbMATHGoogle Scholar
  7. Fu, J. C., & Lou, W. Y. W. (2003). Distribution theory of runs and patterns and its applications: A finite Markov chain imbedding approach. Singapore: World Scientific Publishing.CrossRefGoogle Scholar
  8. George, E. O., & Bowman, D. (1995). A full likelihood procedure for analyzing exchangeable binary data. Biometrics, 51, 512–523.MathSciNetCrossRefGoogle Scholar
  9. Klein, M. (2000). Two alternatives to the Shewhart \(\bar{X}\) control chart. Journal of Quality Technology, 32, 427–431.Google Scholar
  10. Kingman, J. F. C. (1978). Uses of exchangeability. Annals of Probability, 6, 183–197.MathSciNetCrossRefGoogle Scholar
  11. Koutras, M. V., & Triantafyllou, I. S. (2018). A general class of nonparametric control charts. Quality and Reliability Engineering International, 34, 427–435.Google Scholar
  12. Lehmann, E. L. (1953). The power of rank tests. Annals of Mathematical Statistics, 24, 23–43.MathSciNetCrossRefGoogle Scholar
  13. Montgomery, D. C. (2009). Introduction to statistical quality control (6th ed.). New York: Wiley.zbMATHGoogle Scholar
  14. Qiu, P. (2014). Introduction to statistical process control. New York: CRC Press, Taylor & Francis Group.Google Scholar
  15. Qiu, P. (2018). Some perspectives on nonparametric statistical process control. Journal of Quality Technology, 50, 49–65.CrossRefGoogle Scholar
  16. Qiu, P. (2019). Some recent studies in statistical process control. In Statistical quality technologies, pp. 3–19.Google Scholar
  17. Shewhart, W. A. (1926). Quality control charts. Bell System Technical Journal, 2, 593–603.CrossRefGoogle Scholar
  18. Triantafyllou, I. S. (2018). Nonparametric control charts based on order statistics. Communication in Statistics: Simulation and Computation, 47, 2684–2702.MathSciNetCrossRefGoogle Scholar
  19. Triantafyllou, I. S. (2019a). A new distribution-free control scheme based on order statistics, Journal of Nonparametric Statistics, 31, 1–30.Google Scholar
  20. Triantafyllou, I. S. (2019b). Wilcoxon-type rank-sum control charts based on progressively censored reference data, Communication in Statistics: Theory and Methods.  https://doi.org/10.1080/03610926.2019.1634816.
  21. Woodall, W. H. (2000). Controversies and contradictions in statistical process control. Journal of Quality Technology, 32, 341–350.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Ioannis S. Triantafyllou
    • 1
    Email author
  • Nikolaos I. Panayiotou
    • 1
  1. 1.Department of Computer Science & Biomedical InformaticsUniversity of ThessalyVolosGreece

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