Abstract The performances of the cut-set distributions in the fuzzy reliability evaluation are studied based on cut-set method. Firstly, a theorem is proved to indicate the convergence defect of the model with the three commonly used cut-set distributions, including uniform distribution, linear distribution and truncated normal distribution. Secondly, a general method is proposed to construct a new family of cut-set distributions named intrinsic cut-set distributions, and three specific intrinsic cut-set distributions are obtained based on this method, including modified truncated normal distribution, truncated lognormal distribution and truncated Weibull distribution. Thirdly, numerical examples are carried out to verify the above theoretical results. It is shown that, compared with the three commonly used cut-set distributions, the proposed intrinsic cut-set distributions make the evaluation more stable and the fuzzy reliability model achieve good convergence at the boundary cases, which could effectively improve the evaluation accuracy and broaden the application of the model. Finally, some recommendations are given to show how to choose a suitable cut-set distribution in practice.

中文翻译：

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模糊可靠性评估模型中割集分布的研究

摘要 基于割集方法研究了割集分布在模糊可靠性评估中的性能。首先，证明了一个定理表明该模型的收敛缺陷与三种常用的割集分布，包括均匀分布、线性分布和截断正态分布。其次，提出了构造一类新的割集分布的通用方法，称为内在割集分布，并基于该方法得到了三种具体的内在割集分布，包括修正截断正态分布、截断对数正态分布和截断威布尔分布。第三，通过数值算例验证了上述理论结果。结果表明，与常用的三种割集分布相比，所提出的内在割集分布使得评价更加稳定，模糊可靠性模型在边界情况下实现了良好的收敛性，可以有效提高评价精度，拓宽模型的应用范围。最后，给出了一些建议以展示如何在实践中选择合适的割集分布。