Technical note: An improved range chart for normal and long‐tailed symmetrical distributions |
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| Authors: | Pandu Tadikamalla Mihai Banciu Dana Popescu |
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| Institution: | 1. Joseph M. Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, Pennsylvania;2. Stern School of Business, New York University, New York, New York |
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| 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 |
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| Keywords: | range control charts long‐tailed distributions normal distribution logistic distribution Laplace distribution Shewhart method statistical quality control |
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