Abstract: On the basis of the mathematical transition from fuzzy probability to conventional random probability, a numerical algorithm focusing on mechanical structure system with fuzzy stress and fuzzy strength is presented for the fuzzy reliability analysis. In the presented algorithm, the fuzzy stress and fuzzy strength are truncated to the subsets, which are the common sets, corresponding to the truncated level firstly. The appropriate probability distribution is then introduced on the truncated subsets, and the conventional reliability method is used to calculate the fuzzy failure probability, which is called as the truncated fuzzy failure probability. By using the truncated fuzzy failure probability as the integration function, the fuzzy failure probability can be calculated for the structure system, where the truncated levels of the fuzzy stress and the fuzzy strength are utilized as the integration variables. The fuzzy reliability is formulated for the structure system with fuzzy basic variables and fuzzy states as well. The illustrations are used to investigate the effects of the fuzzy distribution parameters and the introduced probability distributions on the fuzzy failure probability. By the conjunction with the fuzzy linear regression, the presented algorithm can be expanded to solve the fuzzy reliability analysis of the complicated structure system with multiple fuzzy basic variables.

Key words: Fuzzy, Fuzzy state, Reliability