Evaluation of a dynamic reliability problem based on order of component failure

A dynamic reliability problem is considered where system components are operating in time. A general framework for analyzing the relationship of prior information and variance of a Monte Carlo estimator is developed. The variance of an estimator based on less prior information is less than that of an estimator based on more prior information. The first application derives a sequential destruction method as a special case in this general framework. The method uses the order of component failure as prior information instead of the time to failure of components. The second application shows that the use of less prior information than the order of component failure can circumvent difficulties faced by a state transition method. A numerical example is presented