Premium
Technical note: An improved range chart for normal and long‐tailed symmetrical distributions
Author(s) -
Tadikamalla Pandu,
Banciu Mihai,
Popescu Dana
Publication year - 2008
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.20265
Subject(s) - kurtosis , range (aeronautics) , mathematics , control chart , chart , statistics , normal distribution , quantile , heavy tailed distribution , distribution (mathematics) , probability distribution , computer science , mathematical analysis , materials science , process (computing) , composite material , operating system
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