Confidence Intervals for Reliability Estimated Using Response Surface Methods

In this paper, two approaches for computing statistical confidence intervals for reliability estimated using response surface methods (RSM) are presented. In the first method, three limit states are used to obtain the upper, mean and lower probability of failure at the design point of interest. This approach is integrated with popular probabilistic design algorithms like the MeanValue First-Order-Second-Moment (MV-FOSM), Monte Carlo (MC) and Hazofer-Lind-RackwitzFiessler (HLRF) algorithms. In the second approach, a close form solution to predict confidence intervals for reliability obtained using the MV-FOSM approach is proposed. Analytical derivations for both methods are presented and the methods are validated via a representative case study. The proposed methods are applicable to any quadratic response surface approximation obtained using design-of-experiment methods.