Extracting rare failure events in composite system reliability evaluation via subset simulation

This paper proposes an efficient method for evaluating composite system reliability via subset simulation. The central idea is that a small failure probability can be expressed as a product of larger conditional probabilities, thereby turning the problem of simulating a rare failure event into several conditional simulations of more frequent intermediate failure events. In existing methods, system states are simply assessed in a binary secure/failure manner. To fit into the context of subset simulation, the adequacy of system states is parametrized with a metric based on linear programming, thus allowing for an adaptive choice of intermediate failure events. Samples conditional on these events are generated by Markov chain Monte Carlo simulation. The proposed method requires no prior information before simulation. Different models for renewable energy sources can also be accommodated. Numerical tests show that this method is significantly more efficient than standard Monte Carlo simulation, especially for simulating rare failure events.