On confidence intervals for failure probability estimates in Kriging-based reliability analysis

Abstract

Despite recent advancements in adaptive Kriging-based reliability analysis for complex limit states, estimation of the accuracy of extant techniques when the true failure probability is unknown remains an important challenge. The present study addresses this gap by developing analytical confidence intervals (CIs) for failure probability estimates. This is facilitated here by leveraging statistical properties of Poisson Binomial distribution for the expected number of failure points in the set of candidate design samples in adaptive Kriging as well as Lindeberg's condition for central limit theorem. Concerning computational demands involved in the computation of CIs, a simpler case where Kriging correlations are neglected is also derived. The performance of the proposed CIs is subsequently analyzed for five examples with different and varying complexities. Results indicate that the proposed CI with correlations considered offers the most accurate intervals. Additionally, whereas the CI estimated without Kriging correlation is not entirely satisfactory at early-stages of adaptive reliability analysis, it converges to accurate bounds at later stages.