Estimation of Reliability with Hybrid Uncertainties in the Unified Framework of Random Set Theory

The method of reliability estimation with hybrid uncertainties including random and fuzzy variables is proposed. By means of random set theory, random variables and fuzzy variables are transformed into random set, and then a unified model of reliability is proposed in the unified framework of random set theory. The limit-state function of a structure with hybrid uncertainties is mapped into a random set by using the extension principle of function based on random set, and then the limit cumulative distribution functions (CDFs) of reliability are determined. According to the upper and the lower CDF, the interval estimation of reliability can be obtained. The traditional reliability theory based on probability can be viewed as one of the sub-cases of the method proposed. The proposed method is demonstrated with an example.