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A Class of Enhanced Nonparametric Control Schemes Based on Order Statistics and Runs

Author

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  • Nikolaos I. Panayiotou

    (Department of Computer Science & Biomedical Informatics, University of Thessaly, 38221 Volos, Greece)

  • Ioannis S. Triantafyllou

    (Department of Statistics and Insurance Science, University of Piraeus, 18534 Pireas, Greece
    Department of Management Studies, Graphic Era Deemed to be University, Dehradun 248002, India)

Abstract

In this article, we establish a new class of nonparametric Shewhart-type control charts based on order statistics with signaling runs-type rules. The proposed charts offer to the practitioner the opportunity to reach, as close as possible, a pre-specified level of performance by determining appropriately their design parameters. Special monitoring schemes, already established in the literature, are ascertained to be members of the proposed class. In addition, several new nonparametric control charts that belong to the family are introduced and studied in some detail. Exact formulae for the variance of the run length distribution and the average run length (ARL) for the proposed monitoring schemes are also derived. A numerical investigation is carried out and demonstrates that the proposed schemes acquire competitive performance in detecting the shift of the underlying distribution. Although the large number of design parameters is quite hard to handle, the numerical results presented throughout the lines of the present manuscript provide practical guidance for the implementation of the proposed charts.

Suggested Citation

  • Nikolaos I. Panayiotou & Ioannis S. Triantafyllou, 2023. "A Class of Enhanced Nonparametric Control Schemes Based on Order Statistics and Runs," Stats, MDPI, vol. 6(1), pages 1-14, February.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:1:p:17-292:d:1061180
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    References listed on IDEAS

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    1. Jean-Claude Malela-Majika & Sandile C. Shongwe & Philippe Castagliola, 2022. "One-sided precedence monitoring schemes for unknown shift sizes using generalized 2-of-(h+1) and w-of-w improved runs-rules," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(9), pages 2803-2837, March.
    2. Ioannis S. Triantafyllou & Nikolaos I. Panayiotou, 2020. "Distribution-free monitoring schemes based on order statistics: a general approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(12), pages 2230-2257, September.
    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, Elsevier, vol. 53(4), pages 1054-1065, February.
    4. S. Chakraborti & P. van der Laan & M. A. van de Wiel, 2004. "A class of distribution‐free control charts," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(3), pages 443-462, August.
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