Fuzzy Structural Reliability Analysis And Hypothesis Testing

In this paper, we discuss the problems for fuzzy structural reliability analysis and a sequential Bayesian approach to fuzzy hypothesis testing based on fuzzy theories.The main results are listed as follows:Firstly, based on the fuzzy theories and fuzzy random theories, the model of fuzzy structural reliability analysis is developed when stress and strength are fuzzy variables and fuzzy random variables. At last, some examples are used to demonstrate the feasibility and reasonability of the presented method.Secondly, when generalized stress and strength follow normal , weibull , Γ-distributions respectively and the parameters of probabilistic distributions are fuzzy variables, the method of structural reliability analysis is developed based on random f--uzzy theories. Some examples are used to demonstrate the feasibility and reasonabili--ty of the presented method.Thirdly, when prior information comes from experts' experience, the method For describing hyper parameters is developed. Then we apply it to the reliability analysis for stress-strength model where stress and strength follow exponential distribution. The discussion focuses on Bayesian analysis adopting conjugate prior. The fuzzy Bayesian estimation for reliability is given with Lindley approximation and random fuzzy simulation.Finally, based on random fuzzy theories, we give the sequential Bayesian rule to fuzzy hypothesis testing for normal, exponential, and binomial distributions with Jefferys prior and conjugate prior.