Reliability importance measures of the components in a system based on semivalues and probabilistic values

The main contribution of this paper consists in providing different ways to value importance measures for components in a given reliability system or in an electronic circuit. The main tool used is a certain type of semivalues and probabilistic values. One of the results given here extends the indices given by Birnbaum and Barlow & Proschan, which respectively coincide with the Banzhaf and the Shapley and Shubik indices so well-known in game theory.