Hierarchical analysis of fault trees with dependencies, using decomposition

Analytical methods for fault tree analysis involves the determination of the minimum cut sets, whose number grows extremely quickly with the number of events. This problem can be solved by utilizing the methods of decomposition and aggregation. That is, dividing the system into smaller subsystems, solving the subsystems separately, and then synthesizing these results to produce the larger systems' solution. In this paper, we demonstrate a decomposition scheme where independent subtrees of a fault tree are detected and solved hierarchically, a subtree is replaced by a single event in the parent tree whose probability of occurrence represents the probability of the occurrence of the subtree. The decomposition and hierarchical solution can be more useful in case of fault trees with dependencies. Instead of solving the whole system as a Markov model only the appropriate subsystem needs to be analyzed as a Markov model.