Multiple tail models including inverse measures for structural design under uncertainties

Sampling-based reliability estimation with expensive computer models may be computationally prohibitive due to a large number of required simulations. One way to alleviate the computational expense is to extrapolate reliability estimates from observed levels to unobserved levels. Classical tail modeling techniques provide a class of models to enable this extrapolation using asymptotic theory by approximating the tail region of the cumulative distribution function (CDF). This work proposes three alternate tail extrapolation techniques including inverse measures that can complement classical tail modeling. The proposed approach, multiple tail models, applies the two classical and three alternate extrapolation techniques simultaneously to estimate inverse measures at the extrapolation regions and use the median as the best estimate. It is observed that the range of the five estimates can be used as a good approximation of the error associated with the median estimate. Accuracy and computational efficiency are competing factors in selecting sample size. Yet, as our numerical studies reveal, the accuracy lost to the reduction of computational power is very small in the proposed method. The method is demonstrated on standard statistical distributions and complex engineering examples.