Subset simulation

Subset simulation^[1] is a method used in reliability engineering to compute small (i.e., rare event) failure probabilities encountered in engineering systems. The basic idea is to express a small failure probability as a product of larger conditional probabilities by introducing intermediate failure events. This conceptually converts the original rare-event problem into a series of frequent-event problems that are easier to solve. In the actual implementation, samples conditional on intermediate failure events are adaptively generated to gradually populate from the frequent to rare event region. These 'conditional samples' provide information for estimating the complementary cumulative distribution function (CCDF) of the quantity of interest (that governs failure), covering the high as well as the low probability regions. They can also be used for investigating the cause and consequence of failure events. The generation of conditional samples is not trivial but can be performed efficiently using Markov chain Monte Carlo (MCMC).

Subset simulation takes the relationship between the (input) random variables and the (output) response quantity of interest as a 'black box'. This can be attractive for complex systems where it is difficult to use other variance reduction or rare-event sampling techniques that require prior information about the system behaviour. For problems where it is possible to incorporate prior information into the reliability algorithm, it is often more efficient to use other variance reduction techniques such as importance sampling. It has been shown that subset simulation is more efficient than traditional Monte Carlo simulation, but less efficient than line sampling, when applied to a fracture mechanics test problem.^[2]