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Estimation in Shewhart control charts: effects and corrections

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  • Willem Albers
  • Wilbert C.M. Kallenberg

Abstract

The influence of the estimation of parameters in Shewhart control charts is investigated. It is shown by simulation and asymptotics that (very) large sample sizes are needed to accurately determine control charts if estimators are plugged in. Correction terms are developed to get accurate control limits for common sample sizes in the in-control situation. Simulation and theory show that the new corrections work very well. The performance of the corrected control charts in the out-of-control situation is studied as well. It turns out that the correction terms do not disturb the behavior of the control charts in the out-of-control situation. On the contrary, for moderate sample sizes the corrected control charts remain powerful and therefore, the recommendation to take at least 300 observations can be reduced to 40 observations when corrected control charts are applied. Copyright Springer-Verlag 2004

Suggested Citation

  • Willem Albers & Wilbert C.M. Kallenberg, 2004. "Estimation in Shewhart control charts: effects and corrections," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(3), pages 207-234, June.
    • Handle: RePEc:spr:metrik:v:59:y:2004:i:3:p:207-234
    DOI: 10.1007/s001840300280
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    Citations

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    Cited by:

    1. Axel Gandy & Jan Terje Kvaløy, 2013. "Guaranteed Conditional Performance of Control Charts via Bootstrap Methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 647-668, December.
    2. Willem Albers & Wilbert Kallenberg, 2004. "Empirical Non-Parametric Control Charts: Estimation Effects and Corrections," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(3), pages 345-360.
    3. Rafajlowicz, Ewaryst & Pawlak, Mirosław & Steland, Ansgar, 2004. "Non-parametric vertical box control chart for monitoring the mean," Technical Reports 2004,52, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Willem Albers & Wilbert C.M. Kallenberg, 2006. "Alternative Shewhart-type charts for grouped observations," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 357-375.
    5. Nasir Abbas & Muhammad Riaz & Shabbir Ahmad & Muhammad Abid & Babar Zaman, 2020. "On the Efficient Monitoring of Multivariate Processes with Unknown Parameters," Mathematics, MDPI, vol. 8(5), pages 1-32, May.
    6. Pandu Tadikamalla & Mihai Banciu & Dana Popescu, 2008. "Technical note: An improved range chart for normal and long‐tailed symmetrical distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(1), pages 91-99, February.
    7. Ishaq Adeyanju Raji & Muhammad Hisyam Lee & Muhammad Riaz & Mu’azu Ramat Abujiya & Nasir Abbas, 2020. "Outliers Detection Models in Shewhart Control Charts; an Application in Photolithography: A Semiconductor Manufacturing Industry," Mathematics, MDPI, vol. 8(5), pages 1-17, May.
    8. 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.
    9. Frisén, Marianne & Andersson, Eva, 2008. "Semiparametric surveillance of outbreaks," Research Reports 2007:11, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.

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