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Mean time to failure (MTTF) is an important reliability measure. Previous research is mainly concerned with the MTTF computation of coherent systems. In this paper, we derive equations to calculate the steady-state MTTF for noncoherent systems. Based on the equations, we extend the BDD by adding an intersection edge in each BDD node to efficiently store additional information for MTTF computation of noncoherent systems. A recursive algorithm is developed for MTTF computation using the extended BDD. To accelerate building the extended BDD, a method is proposed to avoid calculating the intersection edge for some nodes by keeping node monotonicity during the BDD construction. We show the efficiency of our algorithm by applying it to some example fault trees, real-life applications, and large fault tree benchmarks.