Birnbaum joint importance measures for three components of a repairable multistate systems

Abstract

In this paper new measures of joint importance of two and three components for repairable multistate systems based on the classical Birnbaum measure, are proposed. By considering repairable system, first joint relevancy conditions of two and three components are given. Then probabilities of each of the relevancy are measured. The proposed method is applied on a data set. An illustrative example is given. As in the Birnbaum measure, the proposed measures are generic since they depend on the probabilistic properties of the components and the system structure. These measures are useful when consider repairable system.