The paper presents an efficient method for time-dependent reliability analysis. Probabilistic modeling is used to quantify uncertainties and additional information is incorporated using Bayes theorem to perform various updating and reduce inference uncertainty. To improve the computational efficiency, Laplace approximation and inverse reliability methods are proposed to evaluate the Bayesian posterior distributions and reliability responses, respectively. A numerical example and and fatigue reliability application are presented to demonstrate the overall methodology. The efficiency and effectiveness of the proposed method is compared with traditional simulation-based method.
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