Comparison among Methods of Modeling Epistemic Uncertainty in Reliability Estimation

Epistemic uncertainty, the lack of knowledge, is often more important than aleatory uncertainty, variability, in estimating reliability of a system. While the probability theory is widely used for modeling aleatory uncertainty, there is no dominant approach to model epistemic uncertainty. Different approaches have been developed to handle epistemic uncertainties using various theories, such as probability theory, fuzzy sets, evidence theory and possibility theory. However, since these methods are developed from different statistics theories, it is difficult to interpret the result from one method to the other. The goal of this paper is to compare different methods in handling epistemic uncertainty in the view point of calculating the probability of failure. In particular, four different methods are compared; the probability method, the combined distribution method, interval analysis method, and the evidence theory. Characteristics of individual methods are compared in the view point of reliability analysis.