Reliability sensitivity analysis for structural systems in interval probability form

Reliability sensitivity analysis is used to find the rate of change in the probability of failure (or reliability) due to the changes in distribution parameters such as the means and standard deviations. Most of the existing reliability sensitivity analysis methods assume that all the probabilities and distribution parameters are precisely known. That is, every statistical parameter involved is perfectly determined. However, there are two types of uncertainties, epistemic and aleatory uncertainties that may not be perfectly determined in engineering practices. In this paper, both epistemic and aleatory uncertainties are considered in reliability sensitivity analysis and modeled using P-boxes. The proposed method is based on Monte Carlo simulation (MCS), weighted regression, interval algorithm and first order reliability method (FORM). We linearize original non-linear limit-state function by MCS rather than by expansion as a first order Taylor series at most probable point (MPP) because the MPP search is an iterative optimization process. Finally, we introduce an optimization model for sensitivity analysis under both aleatory and epistemic uncertainties. Four numerical examples are presented to demonstrate the proposed method.