Joint reliability-importance of two edges in an undirected network

Joint reliability importance (JRI) of two edges in an undirected network is introduced. Concepts of joint failure importance (JFI) and marginal failure importance (MFI), duals of JRI and marginal reliability importance (MRI), are also introduced. The JRI of two edges in an undirected network is represented by the MRI of each edge in subnetworks. Relationships between JRI and MRI, JRI and JFI, and JFI and MFI are presented. From these relationships, it is shown that the JRI is an appropriate quantitative measure of the interactions of two edges in a network, with respect to source-to-terminal reliability. It can also show that the sign of the JRI of two edges can be determined without computing the JRI of these two edges in some special cases