Note: Pairwise rearrangements in reliability structures

Abstract

Boland, Proschan, and Tong [2] used the notion of criticality of nodes in a coherent system to study the optimal component arrangement of reliability structures. They also provided a sufficient minimal cut (path) based criterion for verifying the criticality ordering of two nodes. We develop a necessary and sufficient condition for two nodes to be comparable and provide specific examples illustrating our result's applicability. As a corollary, certain optimal arrangement properties of well‐known systems are derived. © 1994 John Wiley & Sons, Inc.

An Overview of Various Importance Measures of Reliability System

“…Component and component are said to be permutation equivalent if and only if they are structurally symmetric and ( ) is said to be a permutation symmetric in and . Koutras et al (1994) proved the following properties for permutation importance and permutation equivalence.…”