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Tadikamalla, Pandu, Banciu, Mihai, and Popescu, Dana. An Improved Range Chart for Long Tailed Symmetrical Distributions. Naval Research Logistics, 55(1), pp. 91-99, 2008.

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.

Keywords: range control charts, long-tailed distributions, normal distribution, logistic distribution, Laplace distribution, Shewhart method, statistical quality control


Posted by Mihai Banciu


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