Abstract: The attributes of a structural system in engineering and the external loads acting on it are often characterized by randomness and fuzziness. For a problem with performance functions which include random variables with fuzzy distribution parameters (FDP), it is important to evaluate their reliability accurately and rapidly. Based on the concepts of randomness and fuzziness, a fuzzy reliability analysis method of probability density function equivalent is proposed in this article. Based on the membership function of an FDP, the prior distribution of the FDP is built. Then the probability density function equivalent of random variables with FDP can be obtained by using Bayes theory. Moreover, the mathematical expectation and variance of random variables are also deduced with FDP of traditional membership functions. In this way, random variables with FDP are turned to traditional random variables,and structural reliability can be analyzed by the traditional reliability analysis approaches. The method proposed in this article solves fuzzy probability problem of performance functions with many random variables whose FDP is hard to obtain. Finally, an example is given to prove the validity of the proposed method by comparing it with the traditional reliability analysis method of fuzzy probability.

Key words: small sample, membership functions, fuzzy distribution parameters, probability density function equivalent, fuzzy probability, reliability