Abstract
In this note a new method of comparing component structural importance is introduced and compared to other existing ones. Especially, relationships of the new comparison method to the H-importance due to Hwang (2001,2005), the criticality ordering due to Boland et al. (1989) and Birnbaum importance are obtained. Illustrative examples are given.
Highlights
Consider a binary coherent system (C, φ) composed of n independent components, where C = {1, 2, . . . , n} denotes the index set of the n components, and φ, a mapping from {0, 1}n to {0, 1}, denotes the structure function of the system
Various measures of component importance for binary coherent systems have been introduced in the literature
In the absence of information about component reliabilities, the Birnbaum structural importance measure provides a fair comparison of relative importance among system components
Summary
Various measures (orderings) of component importance for binary coherent systems have been introduced in the literature. In the absence of information about component reliabilities, the Birnbaum structural importance measure provides a fair comparison of relative importance among system components. Butler (1979) developed an alternative structural ordering, namely the cut-importance ordering, and obtained a relationship between the cut-importance and the Birnbaum reliability importance measure for high values of p.
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