Lifetime Distributions and their Approximation in Reliability of Serial/Parallel Networks

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,..., Y_M) and max(Y₁, Y₂,..., Y_M ), 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, Y_k, k = 1, 2, ..., being a sum of non-negative, i.i.d.r.v. in a Pascal distributed random number.