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Control Charts Based on the g-and-h Distribution

Author

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  • Nandini Das

    (SQC & OR Unit Indian Statistical Institute, 203 B T Road, Kolkata 700108, India.)

Abstract

Control charts are the most popular tool to detect the occurrence of an assignable cause in a production process. Traditional control charts are based on the approximation with the normal distribution. In many practical situation, however, assuming normality is not adequate. Under these situations, the use of traditional control chart may lead to erroneous decisions. For handling non-normal process distributions one may use non-parametric control charts, however these methods are rather inefficient. Another approach is to use a generalized distribution. In this work the univariate g-and-h distribution is used to approximate non-normal process distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:ecqcon:v:26:y:2011:i:1:p:3-14:n:1
    DOI: 10.1515/eqc.2011.001
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    References listed on IDEAS

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    1. Chao-Yu Chou & CHung-Ho Chen & Hui-Rong Liu, 2005. "Acceptance control charts for non-normal data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(1), pages 25-36.
    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. Zhenlin Yang & Min Xie, 2000. "Process monitoring of exponentially distributed characteristics through an optimal normalizing transformation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(8), pages 1051-1063.
    4. Layth C. Alwan & Harry V. Roberts, 1995. "The Problem of Misplaced Control Limits," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(3), pages 269-278, September.
    5. 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.
    6. Peter G. Moore, 1957. "Normality in Quality Control Charts," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 6(3), pages 171-179, November.
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