Examples of Monte Carlo methods in reliability estimation based on reduction of prior information

Following the proposal of Tanaka, Kumamoto and Inoue (1989), Monte Carlo methods are constructed based on less prior information, and yield estimators with smaller standard deviation. The first application derives a variant of the sequential destruction method. The second application obtains the traditional importance sampling Monte Carlo method for static reliability problems, starting with a dynamic reliability problem; a class of systems is given, where standard-deviation reduction can be guaranteed before any Monte Carlo trials