Jehan, M. and Nikolaidis, E., "Bootstrapping and Separable Monte Carlo Simulation Methods Tailored for Efficient Assessment of Probability of Failure of Structural Systems," SAE Int. J. Mater. Manf. 8(3):609-615, 2015, doi:10.4271/2015-01-0420.
There is randomness in both the applied loads and the strength of systems. Therefore, to account for the uncertainty, the safety of the system must be quantified using its reliability. Monte Carlo Simulation (MCS) is widely used for probabilistic analysis because of its robustness. However, the high computational cost limits the accuracy of MCS. Smarslok et al.  developed an improved sampling technique for reliability assessment called Separable Monte Carlo (SMC) that can significantly increase the accuracy of estimation without increasing the cost of sampling. However, this method was applied to time-invariant problems involving two random variables. This paper extends SMC to problems with multiple random variables and develops a novel method for estimation of the standard deviation of the probability of failure of a structure. The method is demonstrated and validated on reliability assessment of an offshore wind turbine under turbulent wind loads. The results show the method can reduce the computational cost by two orders of magnitude compared to standard MCS for failure probabilities as low as 10−4.