Some limits theorems for lifetime’s distributions and their applications in Network’s Reliability

Abstract

In this paper it was presented limits theorems for lifetime distributions as a limits of distributions of random variables min(X1,X2,..., Xn) and max(X1,X2,..., Xn), where X1,X2,..., Xn are independent identically distributed random variables such that Xk = Xk1 + Xk2 + ...XkN , Xk1, Xk2, ..., XkN are nonnegative independent identically distributed random variables and N is a Pascal distributed random variable independent of random variables Xk1, Xk2, ... . We connect this results with some mathematical models in Network’s Reliability and show their effectiveness to approximate and simplify research of reliability characteristics of different types of Networks.