Relationships of Fussell–Vesely and Birnbaum importance to structural importance in coherent systems

The notion of node criticality was introduced by Boland, Proschan and Tong to study the problem of optimal rearrangement of components in binary coherent systems. In this paper, we use this notion to study the importance of system components. We derive various relationships between the node criticality and the component importance measures due to Birnbaum, Fussell and Vesely, respectively. Some previous results due to Boland and Proschan, and Meng have been improved.