Structural importance of components

The authors study the problem of structural importance of components in the system. Measures of importance or component ranking considered are: Birnbaum structural importance, Barlow-Proschan structural importance measure and Butler cut importance ranking. We introduce the concept of a structural matrix and use it to present a new and unified approach for calculating these measures. Structural importance of components in the dual system is also studied by defining the transformation matrix. We also give the properties of the transformation matrix. Results of this paper are applicable to simple games.