Bayesian updating model of failure probability function and its solution

When new observations are collected, the failure probability function (FPF) should be calibrated to match the new observations. However, there is a lack of FPF updating model and corresponding solution at present. Therefore, this paper devotes to the corresponding research. The main contribution of this paper includes two aspects. The first is constructing a Bayesian updating model of FPF, and the second is proposing two methods, i. e., combination sampling (CS) method and combination importance sampling (CIS) method, to solve the FPF updating model. In the constructed FPF updating model, the likelihood function, which approximately describes the probability of the observation error, is combined with the prior information to calibrate the prior FPF by Bayesian theory. And by sharing the sample information of the constructed CS density or the CIS density, the complete FPF can be updated through a single simulation run. Moreover, to enhance the efficiency of the CS and CIS, the adaptive Kriging model of performance function is nested in the CS and CIS methods. Five examples show that the two proposed methods need much less computational cost than the competitive methods under the similar accuracy of calibrating FPF, and the proposed CIS method is more efficient than the proposed CS method.