Small failure probability: principles, progress and perspectives

Design of structural and multidisciplinary systems under uncertainties requires estimation of their reliability or equivalently the probability of failure under the given operating conditions. Various high technology systems including aircraft and nuclear power plants are designed for very small probabilities of failure, and estimation of these small probabilities is computationally challenging. Even though substantial number of approaches have been proposed to reduce the computational burden, there is no established guideline to decide which approach is the best choice for a given problem. This paper provides a review of the approaches developed for small probability estimation of structural or multidisciplinary systems and enlists the criterion/metrics to choose the preferred approach amongst the existing ones, for a given problem. First, the existing approaches are categorized into the sampling-based, the surrogate-based, and statistics of extremes based approaches. Next, the small probability estimation methods developed for time-independent systems and the ones tailored for time-dependent systems are discussed, respectively. Then, some real-life engineering applications in structural and multidisciplinary design studies are summarized. Finally, concluding remarks are provided, and areas for future research are suggested.