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Technical note: An improved range chart for normal and long‐tailed symmetrical distributions

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  • Pandu Tadikamalla
  • Mihai Banciu
  • Dana Popescu

Abstract

The distribution of the range of a sample, even in the case of a normal distribution, is not symmetric. Shewhart's control chart for range and other approximations for range from skewed distributions and long‐tailed (leptokurtic) symmetrical distributions assume the distribution of range as symmetric and provide 3 sigma control limits. We provide accurate approximations for the R‐chart control limits for the leptokurtic symmetrical distributions, using a range quantile approximation (RQA) method and illustrate the use of the RQA method with a numerical example. As special cases, we provide constants for the R‐chart for the normal, logistic, and Laplace distributions. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:55:y:2008:i:1:p:91-99
    DOI: 10.1002/nav.20265
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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.
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