The main objective of this paper is to quantify the effect of surrogate model uncertainty on reliability in addition to the aleatory randomness of the input variables, especially when Kriging surrogate model is utilized where the prediction uncertainty is modeled with a normal distribution. A novel approach is presented which requires only a single set of Monte Carlo Simulation (MCS) to precisely estimate the variance of reliability that is used as an uncertainty measure. It is found that the method only requires the bivariate cumulative distribution function, and the result shows that the uncertainty is well quantified without going through multiple numbers of MCS.
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