Reliability assessment and updating of complex systems by LP

Complex systems are characterized by large numbers of components and by statistical dependence between the component states. In this paper, a system decomposition approach is described, which, together with a linear programming formulation, allows determination of bounds on the reliability of complex systems with manageable computational effort. The approach also facilitates multi-scale modeling and analysis of a system, whereby varying degrees of detail can be considered in the decomposed system. The paper also describes a method for computing bounds on conditional probabilities by use of linear programming, which can be used to update the system reliability for any given event. Applications to a power network demonstrate the methodology.