Global reliability sensitivity estimation based on failure samples

Global reliability sensitivity analysis (RSA) can help to assess the effects of input random variables X on the probability of failure Pr(F) of an engineering system. Conventionally, this requires repeated evaluations of the conditional failure probability Pr(F vertical bar X-i = x(i)) for multiple values of the input random variable X-i and for all X-i of interest. Such a solution is straightforward but computationally expensive. In this paper, we propose a new method to perform global RSA, which requires as an input only samples of X that fall in the failure domain. Such samples are a by-product of many sampling-based reliability analysis methods. The proposed method constructs the Pr(F vertical bar X-i = x(i)) by application of Bayes' rule, based on the probability density function (PDF) of X conditioned on system failure F. This conditional PDF is approximated with a kernel density estimation from the failure samples. In this way, the reliability sensitivities of all the input random variables can be computed following a sampling-based reliability analysis with no additional computation cost. The approach is investigated on numerical examples in conjunction with crude Monte Carlo simulation, importance sampling and subset simulation. The results demonstrate the computational advantages over existing single-loop sampling methods for global RSA.