Design Under Uncertainty Using Monte Carlo Simulation and Probabilistic Sufficiency Factor

Monte Carlo simulation is commonly employed to evaluate system probability of failure for problems with multiple failure modes in design under uncertainty. The probability calculated from Monte Carlo simulation has random errors due to limited sample size, which create numerical noise in the dependence of the probability on design variables. This in turn may lead the design to spurious optimum. A probabilistic sufficiency factor (PSF) approach is proposed that combines safety factor and probability of failure. The PSF represents a factor of safety relative to a target probability of failure, and it can be calculated from the results of Monte Carlo simulation (MCS) with little extra computation. The paper presents the use of PSF with a design response surface (DRS), which fits it as function of design variables, filtering out the noise in the results of MCS. It is shown that the DRS for the PSF is more accurate than DRS for probability of failure or for safety index. The PSF also provides more information than probability of failure or safety index for the optimization procedure in regions of low probability of failure. Therefore, the convergence of reliability-based optimization is accelerated. The PSF gives a measure of safety that can be used more readily than probability of failure or safety index by designers to estimate the required weight increase to reach a target safety level. To reduce the computational cost of reliability-based design optimization, a variable-fidelity technique and deterministic optimization were combined with probabilistic sufficiency factor approach. Example problems were studied here to demonstrate the methodology.