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The recent literature showed that, in many cases, ordered binary decision diagram (OBDD)-based algorithms are more efficient in reliability evaluation compared to other methods such as the inclusion-exclusion (I-E) method and the sum of disjoint products (SDP) method. We present algorithms based on OBDD to compute system failure frequencies and reliability importance measures. Methods are presented to calculate both steady-state and time-specific frequencies of system-failure as well as system-success. The reliability importance measures include the Birnbaum importance, the criticality importance, and other indices for the risk evaluation of a system. In addition, we propose an efficient approach based on OBDD to evaluate the reliability of a nonrepairable system and the availability of a repairable system with imperfect fault-coverage mechanisms. The powerful capability of OBDD for reliability evaluation is fully exploited. Further, we extend all of the proposed algorithms to analyze systems with imperfect fault-coverage.