Conservative reliability index for epistemic uncertainty in reliability-based design optimization

In this paper, a simple but efficient concept of epistemic reliability index (ERI) is introduced for sampling uncertainty in input random variables under conditions where the input variables are independent Gaussian, and samples are unbiased. The increased uncertainty due to the added epistemic uncertainty requires a higher level of target reliability, which is called the conservative reliability index (CRI). In this paper, it is assumed that CRI can additively be decomposed into the aleatory part (the target reliability index) and the epistemic part (the ERI). It is shown theoretically and numerically that ERI remains same for different designs, which is critically important for computational efficiency in reliability-based design optimization. Novel features of the proposed ERI include: (a) it is unnecessary to have a double-loop uncertainty quantification for handling both aleatory and epistemic uncertainty; (b) the effect of two different sources of uncertainty can be separated so that designers can better understand the optimization outcome; and (c) the ERI needs to be calculated once and remains the same throughout the design process. The proposed method is demonstrated with two analytical and one numerical examples.