Birnbaum's measure of component importance for noncoherent systems

Importance analysis of noncoherent systems is limited, and is generally inaccurate because all measures of importance that have been developed are strictly for coherent analysis. This paper considers the probabilistic measure of component importance developed by Birnbaum (1969). An extension of this measure is proposed which enables noncoherent importance analysis. As a result of the proposed extension the average number of system failures in a given interval for noncoherent systems can be calculated more efficiently. Furthermore, because Birnbaum's measure of component importance is central to many other measures of importance; its extension should make the derivation of other measures possible.