Convergence of fuzzy reliability models and an improved cut-set distribution

The basic fuzzy reliability model of mechanical structures based on cut-set method has been applied to various engineering problems, and some specific models have been formed, such as stress-strength interference model, fatigue life model and avoid-resonance model. A convergence theorem of the model with commonly used cut-set distributions was proposed and proved, and then two corresponding inferences were obtained for the models with unilateral-infinite and bilateral-infinite safety domains respectively. The theorem indicates that when the cut-set becomes longer gradually, the reliability assessments of the fuzzy models with these commonly used cut-set distributions converge to a fixed value which has nothing to do with the specific mechanical structures and thus is unreasonable. In order to avoid this deficiency, a new cut-set distribution called modified truncated normal distribution was proposed. Meanwhile, three specific examples were carried out to verify that the fuzzy reliability model with the proposed cut-set distribution converges well to the corresponding random reliability model, which indicates it is of better convergence and wider applicability.