Some Properties of Statistical Reliability Functions

Abstract

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.