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A class of distribution‐free control charts

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  • S. Chakraborti
  • P. van der Laan
  • M. A. van de Wiel

Abstract

Summary. A class of Shewhart‐type distribution‐free control charts is considered. A key advantage of these charts is that the in‐control run length distribution is the same for all continuous process distributions. Exact expressions for the run length distribution and the average run length (ARL) are derived and properties of the charts are studied via evaluations of the run length distribution probabilities and the ARL. Tables are provided for implementation for some typical ARL values and false alarm rates. The charts proposed are preferable from a robustness point of view, have attractive ARL properties and would be particularly useful in situations where one uses a classical Shewhart X‐chart. A numerical illustration is given.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:53:y:2004:i:3:p:443-462
    DOI: 10.1111/j.1467-9876.2004.0d489.x
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    Cited by:

    1. 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.
    2. EryIlmaz, Serkan, 2008. "Distribution of runs in a sequence of exchangeable multi-state trials," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1505-1513, September.
    3. M. A. Graham & S. W. Human & S. Chakraborti, 2010. "A Phase I nonparametric Shewhart-type control chart based on the median," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(11), pages 1795-1813.
    4. Nandini Das, 2011. "Control Charts Based on the g-and-h Distribution," Stochastics and Quality Control, De Gruyter, vol. 26(1), pages 3-14, January.
    5. Willem Albers & Wilbert C. M. Kallenberg, 2009. "Normal control charts with nonparametric safeguard," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(1), pages 63-81, February.
    6. Lianjie Shu & Jinyu Fan, 2018. "A distribution‐free control chart for monitoring high‐dimensional processes based on interpoint distances," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 317-330, June.
    7. Koutras, M.V. & Sofikitou, E.M., 2017. "A new bivariate semiparametric control chart based on order statistics and concomitants," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 340-347.
    8. 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.
    9. Bairamov, Ismihan & EryIlmaz, Serkan, 2009. "Waiting times of exceedances in random threshold models," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 676-683, March.
    10. Sotiris Bersimis & Kostas Triantafyllopoulos, 2020. "Dynamic Non-parametric Monitoring of Air-Pollution," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1457-1479, December.
    11. Willem Albers & Wilbert Kallenberg, 2009. "CUMIN charts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 111-130, June.
    12. Graham, M.A. & Mukherjee, A. & Chakraborti, S., 2012. "Distribution-free exponentially weighted moving average control charts for monitoring unknown location," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2539-2561.
    13. Saber Ali & Zameer Abbas & Hafiz Zafar Nazir & Muhammad Riaz & Xingfa Zhang & Yuan Li, 2020. "On Designing Non-Parametric EWMA Sign Chart under Ranked Set Sampling Scheme with Application to Industrial Process," Mathematics, MDPI, vol. 8(9), pages 1-20, September.

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