Study of cut-set distributions in the fuzzy reliability evaluation models

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.