Technical note: An improved range chart for normal and long‐tailed symmetrical distributions
Technical note: An improved range chart for normal and long‐tailed symmetrical distributions
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DOI：
10.1002/nav.20265
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发表时间：
2008-02
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影响因子：
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通讯作者：
P. Tadikamalla;Mihai Banciu;Dana G. Popescu
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文献类型：
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作者：
P. Tadikamalla;Mihai Banciu;Dana G. Popescu
样本的极差分布，即使是正态分布，也是不对称的。Shewhart的极差控制图和来自偏态分布和长尾（尖峰）对称分布的极差的其他近似值假设极差分布是对称的，并提供3 sigma控制限。我们使用范围分位数近似（RQA）方法为尖峰对称分布的R图控制限提供了精确的近似值，并通过一个数值例子说明了RQA方法的使用。作为特殊情况，我们为正态分布、Logistic分布和拉普拉斯分布的R图提供常数。© 2007 Wiley Periodicals，Inc.海军研究后勤，2008年
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