Efficient Bayesian network modeling of systems

The Bayesian network (BN) is a convenient tool for probabilistic modeling of system performance, particularly when it is of interest to update the reliability of the system or its components in light of observed information. In this paper, BN structures for modeling the performance of systems that are defined in terms of their minimum link or cut sets are investigated. Standard BN structures that define the system node as a child of its constituent components or its minimum link/cut sets lead to converging structures, which are computationally disadvantageous and could severely hamper application of the BN to real systems. A systematic approach to defining an alternative formulation is developed that creates chain-like BN structures that are orders of magnitude more efficient, particularly in terms of computational memory demand. The formulation uses an integer optimization algorithm to identify the most efficient BN structure. Example applications demonstrate the proposed methodology and quantify the gained computational advantage.