Equivalence of new-direct and new-indirect Monte Carlo methods

It is well known that the reliability analysis of complex systems, such as nuclear power plants, may require Monte Carlo simulation, [1] a method which allows detailed modeling and more realistic component and system representation. Quite often, Monte Carlo must be associated with variance reduction techniques, due to the rareness of the failure events. In these cases, in order to define and compute correctly the weights, a clear definition of the system failure probability is required. Starting from a rigorous definition, a new form of the direct Monte Carlo has been derived, [2] and the procedure is briefly presented. Then, using the insights of this formulation, a new form of the indirect Monte Carlo method is presented, and the equivalence between the two approaches is demonstrated. The comparison with the traditional direct and indirect approaches is presented. It shows that the new ones consider a history as a set of sequences, while the previous as a single sequence: consequently, the results are the same but the efficiency is enhanced with the new approaches.