An efficient method for estimating conditional failure probabilities

Conditional reliability measures provide a more detailed description of the performance of a system, being representative of different initial configurations. Commonly, since the failure region is characterized by a small probability of occurrence, advanced sampling techniques are required to reduce the computational effort of a simulation based approach. These techniques if on one hand decrease the number of samples needed to identify the failure domain, on the other hand do not generally allow a direct estimation of the conditional failure probability for different given inputs. This study aims at providing an efficient and simple methodology to evaluate the conditional failure probability in the case of a static reliability analysis. In particular, under the assumption of probability density functions (PDFs) with a finite support, the failure region mapping process is carried out using surrogate PDFs associated with Sobol’ sequences in order to reduce as much as possible the model evaluations. Finally, the integration of the failure region in the standard normal space employs probabilistic weights instead of a classic indicator function to account for the uncertainty associated with the failure region definition. The approach is verified by comparing the results against those obtained from a Latin Hypercube Sampling. The performance of the proposed method is evaluated in terms of computational costs and accuracy