Bayesian updating of conditional failure probability using method of moments

Bayesian updating reduces epistemic uncertainty for more reliable predictions, but characterizing the distribution of conditional failure probability with measurement data is complex. This study proposes an efficient and accurate method to fully describe the probabilistic characteristics of the updated conditional failure probability. It formulates the first three raw moments of the updated conditional reliability index and uses weighted sparse grid numerical integration to evaluate these moments. A shifted lognormal distribution is then used to approximate the probability density function of the updated conditional reliability index, allowing for the determination of the mean, quantiles, and distribution of the updated conditional failure probability with information reuse. An illustrative example was conducted to demonstrate the method's performance, with results compared against benchmarks from MCMC combined with MCS.