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Aiming to resolve the problems of a variety of uncertainty variables that coexist in the engineering structure reliability analysis, a new hybrid reliability index to evaluate structural hybrid reliability, based on the random–fuzzy–interval model, is proposed in this article. The convergent solving method is also presented. First, the truncated probability reliability model, the fuzzy random reliability model, and the non-probabilistic interval reliability model are introduced. Then, the new hybrid reliability index definition is presented based on the random–fuzzy–interval model. Furthermore, the calculation flowchart of the hybrid reliability index is presented and it is solved using the modified limit-step length iterative algorithm, which ensures convergence. And the validity of convergent algorithm for the hybrid reliability model is verified through the calculation examples in literature. In the end, a numerical example is demonstrated to show that the hybrid reliability index is applicable for the wear reliability assessment of mechanisms, where truncated random variables, fuzzy random variables, and interval variables coexist. The demonstration also shows the good convergence of the iterative algorithm proposed in this article

Structural hybrid reliability index and its convergent solving method based on random–fuzzy–interval reliability model