New version of SDP method for weighted weighted–k –out out–of of–n sy system

Yoichi Higashiyama and Ventsi Rumchev


In this paper, a binary 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 . Four methods to compute the reliability formula of the weighted system have been already proposed. The proposed methods express the system reliability in fewer reliability formulas than those already published. The purpose of this paper is to point out the relation of the order of weighted components. Wu & Chen method and old version of Higashiyama methods (modified Wu & Chen method and old version of SDP method) have got the best results (smallest reliability formula) under the ascending order of weighted components, but new version of SDP method gets the best result under the descending order of weighted components.

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