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Circumstances favoring the use of Monte Carlo methods for evaluating the reliability of large systems are discussed. A new method, that of Sequential Destruction (SD) is introduced. The SD method requires no preparatory topological analysis of the system, and remains viable when element failure probabilities are small. It applies to a variety of reliability measures and does not require element failures to be s-independent. The method can be used to improve the performance of selective sampling techniques. Substantial variance reductions, as well as computational savings, are demonstrated using a sample system with more than 100 elements.