Open Access
August, 1966 Some Properties of Statistical Reliability Functions
Siv Carlsson, Ulf Grenander
Ann. Math. Statist. 37(4): 826-836 (August, 1966). DOI: 10.1214/aoms/1177699363


Networks with independent components are considered. Assuming all components to have a probability $p$ of functioning we study the properties of the reliability function $R(p)$ that the network functions. In particular, we investigate networks of high order. It is shown that an arbitrary (randomized) network can be approximated by a pure one with an approximation error of the order $n^{-1}$. Bounds are obtained for the maximum difference quotient and derivative of the first and second order of $R(p)$. As a corollary we obtain an asymptotic result concerning the best possible approximation of a function of Lipschitz type by reliability functions.


Download Citation

Siv Carlsson. Ulf Grenander. "Some Properties of Statistical Reliability Functions." Ann. Math. Statist. 37 (4) 826 - 836, August, 1966.


Published: August, 1966
First available in Project Euclid: 27 April 2007

zbMATH: 0151.23806
MathSciNet: MR192623
Digital Object Identifier: 10.1214/aoms/1177699363

Rights: Copyright © 1966 Institute of Mathematical Statistics

Vol.37 • No. 4 • August, 1966
Back to Top