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The principles of fault simulation and fault grading are introduced by a general description of the problem. Based upon the well-known concept of restricting fault simulation to the fanout stems and of combining it with a backward traversal inside the fanout-free regions of the circuit, proposals are presented to further accelerate fault simulation and fault grading. These proposals aim at parallel processing of patterns at all stages of the calculation procedure, at reducing the number of fanout stems for which a fault simulation has to be carried out, and at taking advantage of structural characteristics of the circuit. An experiment with a set of benchmark circuits demonstrates the efficiency of the proposed approaches.