Analytical Method to Determine Uncertainty Propagation in Fault Trees by Means of Binary Decision Diagrams
Analytical Method to Determine Uncertainty Propagation in Fault Trees by Means of Binary Decision Diagrams
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DOI：
10.1109/tr.2012.2182812
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发表时间：
2012-02
影响因子：
5.9
通讯作者：
A. Ulmeanu
中科院分区：
文献类型：
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作者：
A. Ulmeanu
提出了一种通过故障树将由连续概率密度函数描述的不确定性从低层次（基本事件）传播到高层次（顶事件）的分析方法。它的基础是利用二元决策图计算顶事件概率的期望值和方差。这种方法可以精确地计算出顶事件概率的期望值和方差。在真实故障树的基准上，我们表明，无论何时存在不同的不确定性来源，我们的方法都可以在工业系统的安全分析中得到定量和定性的改进，特别是那些关于安全完整性水平（SIL）的准确评估。解析法的数值结果与蒙特卡罗法的数值结果吻合较好。
An analytical method is presented which enables one to propagate uncertainties described by continuous probability density functions through fault trees from the lower level (basic event) to the higher level (top-event) of a stochastic binary system. It is based on calculating the expected value and the variance of the top-event probability by means of Binary Decision Diagrams (BDD). This method allows an accurate computation of both the expected value and the variance of the top-event probability. We show, on a benchmark of real fault trees, that our method results in a quantitative and qualitative improvement in safety analysis of industrial systems, especially those concerning accurate evaluation of Safety Integrity Levels (SIL), whenever different sources of uncertainties are present. The numerical results of the analytical method are in good agreement with those of the Monte Carlo method.