A performance index for semicoherent structures

The index introduced here provides a normalized measure of the effectiveness of any semicoherent structure. We study the mathematical properties of the index and derive different axiomatic characterizations for it. Moreover, close relationships are shown to reliability functions and also to the Birnbaum structural importance measure—for which twice the performance index plays the role of potential function—that give rise to computational procedures. Some numerical examples illustrate the application of the index.