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This new algorithm for reliability evaluation is a refinement of the state enumeration method. The set of enumerated states is different for different parts of the fault tree, in particular the number of enumerated states does not necessarily increase towards the top event. This method makes it feasible to treat some large fault trees analytically rather than by Monte Carlo simulation. A lot of research remains to be done, like programming and evaluating the algorithm, and finding intrinsic measures of difficulty for fault trees.