Membership function analysis of fuzzy reliability by adaptive truncated sampling on Copula theory

For engineering reliability problem with fuzzy variables and random variables under incomplete probability information, Copula theory is employed to approximate joint distribution function and joint probability density function of the random variables, on which an adaptive truncated sampling method is established to obtain the membership function of fuzzy reliability. The established model on the Copula approximation can get the value of fuzzy variables and design point which make the performance function take extreme values by optimization and iterating strategy, on which an adaptive truncated sampling is employed to calculate the bounds of the reliability under each given membership level and to get the membership function of the reliability furthermore. In the established method, the advantage of the Copula approximation is combined with the efficiency and robustness of the adaptive truncated sampling, which makes the reliability analysis under incomplete probability information can be completed efficiently. After the model concepts and the solution are given for the established method, several examples are presented to demonstrate the rationality of the model and the feasibility of the solution.