Improving accuracy of failure probability estimates with separable Monte Carlo

Separable Monte Carlo (SMC) is an efficient simulation-based technique that exploits statistical independence of limit state random variables for improved accuracy of reliability calculations. This paper derives accuracy estimates for probabilities of failure for the case where the limit state can be written as capacity minus response. Estimates for traditional Monte Carlo and conditional expectation methods are reviewed for comparison. It is shown that accuracy of SMC can be estimated from the samples used to calculate the probability. Separating the sampling of response and capacity allows flexible sample sizes, permitting low samples of the more expensive component (usually the response). This motivates the beneficial reallocation of uncertainty by reformulating the limit state. An example of bending in a composite plate is used to compare the Monte Carlo methods, demonstrate the accuracy of variance estimates, and show that reformulating the limit state improves the accuracy of the failure probability estimate.