Branch-and-bound algorithm for efficient reliability analysis of general coherent systems

Branch-and-bound algorithms, also known as bounding or decomposition algorithms, have been developed for reliability analysis of coherent systems. They can find a computationally efficient representation of a system failure or survival event, which can be re-used when the input probability distributions or reliabilities change, for example with time or when new data is available. Existing branch-and-bound algorithms can handle only a limited set of system performance functions, mostly network connectivity and maximum flow. Furthermore, they run redundant analyses on component vector states whose system state can be inferred from previous analysis results. We address these limitations by proposing the branch-and-bound for reliability analysis of general coherent systems (BRC) algorithm: an algorithm that automatically finds minimal representations of failure/survival events of general coherent systems. Computational efficiency is attained by dynamically inferring importance of component events from hitherto obtained results. We demonstrate advantages of the BRC method as a real-time risk management tool by application to the Eastern Massachusetts highway benchmark network.