Computation of Reliability with Both Aleatory and Epistemic Uncertainty Based on Random Sets Theory
A method to handle hybrid uncertainties including aleatory and epistemic uncertainty is proposed for the computation of reliability. The aleatory uncertainty is modeled as random variable and the epistemic uncertainty is modeled with evidence theory. The two types of uncertainty are firstly transformed into random set, and the limit-state function of a product is mapped into a random set by using the extension principle of random set. Then, the belief function and the plausibility function of safety event are determined. The two functions are viewed as the lower and the upper cumulative distribution functions of reliability, respectively. The reliability of a product will be bounded by two cumulative distribution functions, and then an interval estimation of reliability can be obtained. The proposed method is demonstrated with an example.
H. X. Guo et al., "Computation of Reliability with Both Aleatory and Epistemic Uncertainty Based on Random Sets Theory", Applied Mechanics and Materials, Vols. 29-32, pp. 1252-1257, 2010