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

✍ Scribed by Pandu Tadikamalla; Mihai Banciu; Dana Popescu

• Book ID: 102544116
• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 182 KB
• Volume: 55
• Category: Article
• ISSN: 0894-069X
• DOI: 10.1002/nav.20265

✦ Synopsis

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