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Kurtosis correction method for X̄ and R control charts for long‐tailed symmetrical distributions

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  • Pandu R. Tadikamalla
  • Dana G. Popescu

Abstract

This paper proposes a kurtosis correction (KC) method for constructing the X̄ and R control charts for symmetrical long‐tailed (leptokurtic) distributions. The control charts are similar to the Shewhart control charts and are very easy to use. The control limits are derived based on the degree of kurtosis estimated from the actual (subgroup) data. It is assumed that the underlying quality characteristic is symmetrically distributed and no other distributional and/or parameter assumptions are made. The control chart constants are tabulated and the performance of these charts is compared with that of the Shewhart control charts. For the case of the logistic distribution, the exact control limits are derived and are compared with the KC method and the Shewhart method. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Suggested Citation

  • Pandu R. Tadikamalla & Dana G. Popescu, 2007. "Kurtosis correction method for X̄ and R control charts for long‐tailed symmetrical distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 371-383, June.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:4:p:371-383
    DOI: 10.1002/nav.20211
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    References listed on IDEAS

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    1. Lai K. Chan & Heng J. Cui, 2003. "Skewness correction X̄ and R charts for skewed distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 555-573, September.
    2. E. George & G. Mudholkar, 1983. "On the convolution of logistic random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 30(1), pages 1-13, December.
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    Cited by:

    1. Guoyi Zhang, 2014. "Improved R and s control charts for monitoring the process variance," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1260-1273, June.

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