A mean extrapolation technique for high reliability analysis

A mean extrapolation method is proposed to estimate the high reliability with acceptable computational cost. In this method, the high reliability index is evaluated by extrapolating the obtained low reliability indexes due to the fact that the lower reliability indexes can be estimated with less samples. Eventually the computational cost for calculating the high reliability index is alleviated markedly. Two kinds of extrapolation models are presented on the asymptotic behavior of the failure probability with respect to the standard deviation of the random variables in the independent and identically distributed Gaussian space. The coefficients of all extrapolation models are calculated by the least-square fit method using the obtained lower reliability indexes. Then, the mean of all the extrapolation models is selected to calculate the high reliability index. The computational cost involved in the original extrapolation method is still not afforded due to the fact that several lower reliability indexes are required. In order to overcome this difficulty, a technique reusing the samples is also introduced. Several examples demonstrate the proposed method. The results show that no single extrapolation model is preferable. However, the mean extrapolation model is always stable and is very close to the exact result. Only tens of thousands of samples are required for obtaining a result with reasonable accuracy for high reliability index.