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Non-parametric vertical box control chart for monitoring the mean

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  • Rafajlowicz, Ewaryst
  • Pawlak, Mirosław
  • Steland, Ansgar

Abstract

A new class of non-parametric control charts for de- tecting the change in the process mean is examined. The method, called a Vertical Box Control Chart (V-Box Chart), offers a simple and quick detection of the mean change in an observed process. No parametric assumption on the distribution function of the pro- cess is required. Furthermore, the V-Box Chart outperforms the classical Shewhart control chart by lowering the probability of de- tection of the out-of-control situation with the zero delay. The- oretical bounds on in-control and out-of-control behaviors of the V-Box Chart are worked out. The developed theory is supported by simulation examples.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:sfb475:200452
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    References listed on IDEAS

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    1. 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.
    2. Prewitt K.A., 2003. "A Distribution-Free Theory of Nonparametric Regression. Laszlo Gyorfi, Michael Kohler, Adam Krzyzak, and Harro Walk," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1084-1084, January.
    3. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 781-796, December.
    4. Margavio, Thomas M. & Conerly, Michael D. & Woodall, William H. & Drake, Laurel G., 1995. "Alarm rates for quality control charts," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 219-224, August.
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