Lifetime distributions and their approximation in reliability of serial/parallel networks

Abstract

In this paper we present limit theorems for lifetime distributions connected with network's reliability as distributions of random variables(r.v.) min(Y1,Y2,...,YM) and max(Y1,Y2,...,YM), where Y1,Y2,..., are independent, identically distributed random variables (i.i.d.r.v.), M being Power Series Distributed (PSD) r.v. independent of them and, at the same time, Yk , k = 1; 2; :::; being a sum of non-negative, i.i.d.r.v. in a Pascal distributed random number.