Reliability sensitivity analysis with mixture of random and fuzzy variables

The reliability analysis and reliability sensitivity analysis are two important works in modern engineering design. Because the reliability membership function presented previously is difficult to compute the reliability sensitivity, a new reliability index is proposed to cope with the reliability model with mixture of random and fuzzy variables. Firstly, the fuzzy variables at λ membership level are transformed into uniformly distributed variables within the λ-cuts, and the reliability model with mixed variables is transformed into one with random variables. Secondly, the reliability or the failure probability are computed by traditional reliability analysis methods, then the reliability index with mixed variables is obtained by use of the decomposition theorem of the fuzzy theory. Based on that, the reliability sensitivity analysis with respect to distribution parameter of random variable can be derived to evaluate the effect of distribution parameter on the new reliability index. The new reliability index not only provides an intuitive and compact index instead of the reliability membership function to describe the fault of reliability model, but also offers an approach to compute the reliability sensitivity with mixed variables. What´s more, the point estimated method and the saddlepoint approximate method are suggested to solve the above indices because they have high precision without too much computational cost in computing the reliability and reliability sensitivity. At last, Two examples including a speed reducer and X-type compressor mechanism are used to testify the feasibility and reasonable of the proposed index. Their computational results verify that the presented methods in their corresponding application fields have high efficiency and acceptable accuracy.