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A Combinatorial Approach for Component Importance

Abstract A number of structural importance measures like Birnbaum importance, Barlow–Proschan importance etc., are used for studying component importance in a system. A unified approach for calculating component importance in a system was introduced by Seth and Ramamurthy. It is based on the concept of structural matrix which needs to be determined from the simple form of a structure function of a system. In this article, we present a combinatorial expression for the elements of the structural matrix. Other related results and applications of this approach to different systems are considered. Results of this article is also applicable to the problem of finding power of a player in game theory.