Link interaction for K-terminal network cascading failures subject to saturating branching process

When improving a multi-component system reliability, we often replaced or maintained a component while ignoring the reliability of another component due to the budget cost constraint. Thus, the interaction effects regarding system reliability between two components should be analyzed. However, conventional research efforts concerning component interactions have two gaps: (i) they are unsuitable for systems with complex structures, such as K-terminal network (for short network), only pertaining to multi-component systems with simple structures; and (ii) they fail to consider component interactions in the context of cascading failure. To fill these gaps, this paper analyzes the effects of link interactions regarding network reliability in the context of link cascading failures. Under this context, we characterize the total number of link failures by a saturating branching process, based on which a network reliability model is established. According to the reliability model, we introduce the joint reliability importance (JRI) measure of two links to analyze link interactions. To evaluate the JRI, we derive several equations and construct a numerical algorithm from the theoretical and numerical standpoints, respectively. Theoretically, we find the conditions under which the scale and sign of the JRI is decided, so that the extent and type of interactions for two links can be analyzed. Numerically, an experiment is conducted to demonstrate how to apply JRI to evaluate link interactions in the circumstance of link cascading failures, which further confirms the theoretical analysis.