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April, 1965 Bounds on Integrals with Applications to Reliability Problems
Richard E. Barlow
Ann. Math. Statist. 36(2): 565-574 (April, 1965). DOI: 10.1214/aoms/1177700168

Abstract

Certain statistical problems in life testing and reliability lead to the consideration of minimizing and maximizing certain integrals of the form $\int^\infty_0 \phi(x, \bar F(x)) dx,\quad\bar F(x) = 1 - F(x)$, under the assumption that the distribution function $F$ has increasing hazard rate and that one or two moments are given. The minimizing (maximizing) distributions for the special cases considered are members of the extremal class considered by A. Marshall and the author [2]. Bounds on the expected values of the minimum and maximum order statistics as well as the operating characteristics of replacement policies based on age are obtained under these assumptions.

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Richard E. Barlow. "Bounds on Integrals with Applications to Reliability Problems." Ann. Math. Statist. 36 (2) 565 - 574, April, 1965. https://doi.org/10.1214/aoms/1177700168

Information

Published: April, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0134.15201
MathSciNet: MR173344
Digital Object Identifier: 10.1214/aoms/1177700168

Rights: Copyright © 1965 Institute of Mathematical Statistics

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Vol.36 • No. 2 • April, 1965
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