For probabilistic designs or assessments to be acceptable, they must have the statistically robust confidence intervals provided by sampling methods. However, sample-based analyses require the number of function evaluations to be so great as to be impractical for many complex engineering applications. Efficient sampling methods allow probabilistic analysis on more applications than basic methods, although they still require a significant computational budget. This paper reviews a series of tools that aim to reduce variance in individual failure rate estimates which would reduce the confidence interval for the same number of evaluations. Several methods share a common goal, lowering the sample discrepancy within the sample space, that will create near optimal low-discrepancy sample sets. The optimization approaches include evolutionary algorithms, piecewise optimization, and centroidal Voronoi tessellation. The results of the optimization procedures show a much lower discrepancy than previous methods.

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