Extensions of A simple model :with applications in reliability, extinction of specizs, inventory depletion and URN sampling

Abstract

This paper is devoted to the study of che following tsodel:A series-parallel system consists of (k + 1) subsystem C0C1 ,…,Ck, , also called cut sets. Cut sec C1 has ni. com­ponents arranged in parallel, i = 0,1,…,k. Jo two cut sets have a component in comeon. This model was introduced and studied by El-Heweihi, Proschan, and Sethuraiaan (1978) under the assumption that component lifelengths are continuous, indepdent, and identically distributed random variables. They obtained several equivalent expressions for the probability that a specified cut set C0, say, fails first. These expressions aere then used to derive qualitative properties of this probability, such as monotonicity, Schur-concavity, etc. In this paper we obtain extensions of these results, tinder -he same assumptions ve study the probability that a. specified cut set C0say, fails in the rth place, r = l,2,…,k. This probability Is shown to retain most of the interesting qualitative features enjoyed in the special case r = 1. We then assure* th...