Fault tree analysis (FTA) is a widely used methodology in the process industries. FTA is used for the development of failure mechanisms, computation of failure frequencies and the determination of the probability of failure on demand of safety systems. Much of the data used in a FTA study are uncertain. For example, the failure rate of a pump is often not known with great precision. Likewise the failure rates of instrumentation are often known only within some defined limits. The common practice, used by analysts in the quantification of a fault tree, is to use the most likely or best guess as to the needed failure rate data. The use of best guess values as data inputs to the quantification of a fault tree creates uncertainty in the computed results. This paper presents a general methodology for the determination of the impact of uncertainty on the results of a fault tree study. The general methodology is based on the mathematics of propagation of error and variance contribution analysis. For a fault tree that contains 10 event minimal cut sets, the methodology will compute the variance in the probability (or frequency) of the top event with a maximum error of 5%. For five event minimal cut sets the error in variance of the top event probability (or frequency) will be no more than 2%. An example is presented to illustrate the application of the fault tree uncertainty analysis methodology to a real world problem.

中文翻译：

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一种利用误差传播方法进行故障树不确定性分析的新方法

故障树分析 (FTA) 是过程工业中广泛使用的方法。FTA 用于开发故障机制、计算故障频率以及根据安全系统的要求确定故障概率。FTA 研究中使用的大部分数据都是不确定的。例如，泵的故障率通常无法非常精确地获知。同样，仪器的故障率通常仅在某些定义的范围内才知道。分析师在量化故障树时使用的常见做法是对所需的故障率数据使用最可能或最佳的猜测。使用最佳猜测值作为故障树量化的数据输入会在计算结果中产生不确定性。本文介绍了确定不确定性对故障树研究结果的影响的一般方法。一般方法基于误差传播和方差贡献分析的数学。对于包含 10 个事件最小割集的故障树，该方法将计算最大误差为 5% 的顶级事件的概率（或频率）方差。对于五个事件最小割集，顶部事件概率（或频率）的方差误差将不超过 2%。给出了一个例子来说明故障树不确定性分析方法在现实世界问题中的应用。对于包含 10 个事件最小割集的故障树，该方法将计算最大误差为 5% 的顶级事件的概率（或频率）方差。对于五个事件最小割集，顶部事件概率（或频率）的方差误差将不超过 2%。给出了一个例子来说明故障树不确定性分析方法在现实世界问题中的应用。对于包含 10 个事件最小割集的故障树，该方法将计算最大误差为 5% 的顶级事件的概率（或频率）方差。对于五个事件最小割集，顶部事件概率（或频率）的方差误差将不超过 2%。给出了一个例子来说明故障树不确定性分析方法在现实世界问题中的应用。