Uncertainty propagation in complex engineering systems by advanced Monte Carlo methods

This paper presents a recently developed advanced Monte Carlo method called 'Subset Simulation' for efficient stochastic analysis of complex engineering systems. The method investigates rare failure scenarios by efficiently generating 'conditional samples' that populate progressively towards the rare failure region. In addition to reliability analysis and performance margin estimation, the conditional samples also provide information for sensitivity and data-mining purposes. Subset Simulation is based on a simple but important observation that a small failure probability can be expressed as a product of large conditional failure probabilities of some intermediate failure events. This perspective makes use of the defining properties of conditional probabilities, and so is valid for all applications. The method is illustrated with applications in structural and aerospace engineering. Recent and future development of the method will also be discussed.