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Membership function analysis of fuzzy reliability by adaptive truncated sampling with copula theory. (Chinese. English summary) Zbl 1265.62023

Summary: For engineering reliability problems with fuzzy variables and random variables under incomplete probability information, copula theory is employed to approximate the joint distribution functions and joint probability density functions of the random variables, where 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 values of fuzzy variables and design points which let the performance function take extreme values by optimization and iterating strategies, by 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. 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 be completed efficiently. Then the model concepts and solutions are given for the established method, and several examples are presented to demonstrate the appropriatenes of the model and the feasibility of the solutions.

MSC:

62N05 Reliability and life testing
62D05 Sampling theory, sample surveys
03E72 Theory of fuzzy sets, etc.
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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