Calculation of Critical Importance for Multi-State Components

The application of the critical importance introduced by Birnbaum is restricted to 2-state components. Other authors have proposed importance measures and importance rankings for multi-state components in coherent systems. This paper introduces a sensitivity formula for multi-state components that applies to non-coherent systems as well and which reduces to the Birnbaum importance when applied to 2-state components. The event importances required in this formula can be obtained by the algorithm given. Since this algorithm is based on the inclusion-exclusion principle it is possible to combine the calculations of event importances, top probability, and top frequency in one computer program. one computer program.