Note: Pairwise rearrangements in reliability structures

Boland, Proschan, and Tong 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. The authors develop a necessary and sufficient condition for two nodes to be comparable and provide specific examples illustrating the present result’s applicability. As a corollary, certain optimal arrangement properties of well-known systems are derived.