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The traditional static fault trees with AND, OR and voting gates cannot capture the dynamic behavior of system failure mechanisms such as sequence-dependent events, spares and dynamic redundancy management and priorities of failure events. Therefore, researchers introduced dynamic gates into fault trees to capture these sequence-dependent failure mechanisms. Dynamic fault trees are generally solved using automatic conversion to Markov models; however, this process generates a huge state space even for moderately sized problems. In this paper, the authors propose a new method to analyze dynamic fault trees. In most cases, the proposed method solves the fault trees without converting them to Markov models. They use the best methods that are applicable for static fault tree analysis in solving dynamic fault trees. The method is straightforward for modular fault trees; and for the general case, they use conditional probabilities to solve the problem. In this paper, the authors concentrate only on the exact methods. The proposed methodology solves the dynamic fault tree quickly and accurately.