中文摘要：

传统的故障树分析方法依据底事件失效概率计算顶事件失效概率，而实际中常因统计数据不足，难以对底事件失效概率进行有效估计。模糊故障树分析方法用模糊数表示事件失效概率，能够充分利用统计数据，改善分析效果。但因计算量巨大，以往的研究中常用简单运算法则进行近似。本文提出一种数值算法，采用扩张原理，高精度地进行模糊故障树分析，并通过隶属度差分连续性自适应控制搜索步长，减少计算代价。应用于某内燃机故障树，结果表明，该方法能够快速高精度求解模糊故障树。

英文摘要：

In conventional fault tree analysis, the failure probabilities of the element events are difficult to evaluate effectively in common cases for insufficiency in observation data. Fuzzy fault tree analysis algorithms make better use of existing data to gain better outputs. However, for the huge computational costs, in recent works, the analyses are performed by approximation formulae. A numerical algorithm is presented that solves the fuzzy fauh tree problem with high accuracy by the extension principle, and adjust the search step by a self-adaption scheme according to the differential continuity of the membership function to save computational costs. An internal-combustion engine fault tree was solved by the algorithm, the result illustrates that the method is highly accurate and efficient.