Subset simulation with markov chain Monte Carlo: a review

Abstract

Knowledge of probability of failure of a system is crucial for any engineer. Reliability, defined as the complement of probability of failure, can be estimated using both analytical and simulation techniques, both of which have their advantages and drawbacks. Simulation based methods are often preferred owing to their simplicity of implementation. The most robust simulation technique is the brute force Monte Carlo Simulation method. A very significant drawback of this technique is its inefficiency in dealing with events with very low failure probabilities. This is due to the large computational effort required to obtain a low variance of the estimate. In this context, several variance reduction techniques (Importance Sampling, Line sampling etc.) have been developed to solve increasingly complex reliability problems without significantly reducing the robustness and simplicity of brute force MCS. Subset Simulation is one such recently developed method which tackles problems in high dimensions with low failure probability estimates. This paper describes and analyzes Subset Simulation as a method for simulation-based reliability analysis. Example problems have been solved to demonstrate its advantages and drawbacks with respect to more classical methods.