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Distribution-Free Methods for Statistical Process Monitoring and Control pp 219–241Cite as

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

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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.

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References

  • Balakrishnan, N., & Koutras, M. V. (2002). Runs and scans with applications. New York: Wiley.

    Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Chakraborti, S., & Graham, M. (2019). Nonparametric statistical process control. USA: Wiley.

    Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Derman, C., & Ross, S. M. (1997). Statistical aspects of quality control. San Diego: Academic Press.

    MATH  Google Scholar 

  • 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.

    Book  Google Scholar 

  • George, E. O., & Bowman, D. (1995). A full likelihood procedure for analyzing exchangeable binary data. Biometrics, 51, 512–523.

    Article  MathSciNet  Google Scholar 

  • Klein, M. (2000). Two alternatives to the Shewhart \(\bar{X}\) control chart. Journal of Quality Technology, 32, 427–431.

    Google Scholar 

  • Kingman, J. F. C. (1978). Uses of exchangeability. Annals of Probability, 6, 183–197.

    Article  MathSciNet  Google Scholar 

  • Koutras, M. V., & Triantafyllou, I. S. (2018). A general class of nonparametric control charts. Quality and Reliability Engineering International, 34, 427–435.

    Google Scholar 

  • Lehmann, E. L. (1953). The power of rank tests. Annals of Mathematical Statistics, 24, 23–43.

    Article  MathSciNet  Google Scholar 

  • Montgomery, D. C. (2009). Introduction to statistical quality control (6th ed.). New York: Wiley.

    MATH  Google Scholar 

  • Qiu, P. (2014). Introduction to statistical process control. New York: CRC Press, Taylor & Francis Group.

    Google Scholar 

  • Qiu, P. (2018). Some perspectives on nonparametric statistical process control. Journal of Quality Technology, 50, 49–65.

    Article  Google Scholar 

  • Qiu, P. (2019). Some recent studies in statistical process control. In Statistical quality technologies, pp. 3–19.

    Google Scholar 

  • Shewhart, W. A. (1926). Quality control charts. Bell System Technical Journal, 2, 593–603.

    Article  Google Scholar 

  • Triantafyllou, I. S. (2018). Nonparametric control charts based on order statistics. Communication in Statistics: Simulation and Computation, 47, 2684–2702.

    Article  MathSciNet  Google Scholar 

  • Triantafyllou, I. S. (2019a). A new distribution-free control scheme based on order statistics, Journal of Nonparametric Statistics, 31, 1–30.

    Google Scholar 

  • 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.

  • Woodall, W. H. (2000). Controversies and contradictions in statistical process control. Journal of Quality Technology, 32, 341–350.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science & Biomedical Informatics, University of Thessaly, Volos, Greece

    Ioannis S. Triantafyllou & Nikolaos I. Panayiotou

Authors
  1. Ioannis S. Triantafyllou
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  2. Nikolaos I. Panayiotou
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Corresponding author

Correspondence to Ioannis S. Triantafyllou .

Editor information

Editors and Affiliations

  1. Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece

    Markos V. Koutras

  2. Department of Computer Science and Biomedical Informatics, University of Thessaly, Volos, Greece

    Ioannis S. Triantafyllou

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Triantafyllou, I.S., Panayiotou, N.I. (2020). Distribution-Free Phase II Control Charts Based on Order Statistics with Runs-Rules. In: Koutras, M., Triantafyllou, I. (eds) Distribution-Free Methods for Statistical Process Monitoring and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-25081-2_7

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  • DOI: https://doi.org/10.1007/978-3-030-25081-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25080-5

  • Online ISBN: 978-3-030-25081-2

  • eBook Packages: EngineeringEngineering (R0)

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