Number of product terms in reliability formula of weighted-k-out-of-n system by SDP method

Abstract

A weighted version of the k -out-of-n system is considered. In the disjoint products version of reliability analysis of weighted-k -out-of-n systems, it is necessary to determine the order in which the weight of components is to be considered. The k -out-of-n :G(F) system consists of n components; each component has its own probability and positive integer weight such that the system is operational (failed) if and only if the total weight of some operational (failure) components is at least k. A method to compute the reliability formulas using SDP (Sum of Disjoint Products) method has been already published. The proposed method expresses the system reliability in fewer reliability formulas than those already published. The purpose of this paper is to point out that the number of product terms in the reliability formula of weighted-k -out-of-n system is influenced by the order of the minimal set of weighted components.