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Control Chart Constants for Largest and Smallest in Sampling from a Normal Distribution Using the Generalized Burr Distribution

John A. Austin, Jr.
Technometrics
Vol. 15, No. 4 (Nov., 1973), pp. 931-933
DOI: 10.2307/1267403
Stable URL: http://www.jstor.org/stable/1267403
Page Count: 3
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Control Chart Constants for Largest and Smallest in Sampling from a Normal Distribution Using the Generalized Burr Distribution
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Abstract

This paper represents a first detailed study of the application of a generalized probability distribution, the Burr distribution, to control charts for the maximum and minimum value in a sample of size n. The Burr distribution is a two parameter probability distribution with cumulative distribution function represented by $FX(x)=\left\{ \matrix\format\c\kern.8em&\c\\ 1-\frac{1}{(1+x^{c})^{k}} & x\geq \mathit{0} \\ \mathit{0} & x<\mathit{0} \endmatrix \right.\quad c,k\geq 1$ This paper illustrates the application of the Burr distribution to control charts for the maximum and minimum value in sampling from a normal distribution and compares results with those previously derived using the standard normal distribution.

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