Technical Note: An Improved Range Chart for Normal and Long-tailed Symmetrical Distributions

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. The authors 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.