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Quantitative analysis of a fault tree with priority AND gates

机译:具有优先级AND门的故障树的定量分析

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A method for calculating the exact top event probability of a fault tree with priority AND gates and repeated basic events is proposed when the minimal cut sets are given. A priority AND gate is an AND gate where the input events must occur in a prescribed order for the occurrence of the output event. It is known that the top event probability of such a dynamic fault tree is obtained by converting the tree into an equivalent Markov model. However, this method is not realistic for a complex system model because the number of states which should be considered in the Markov analysis increases explosively as the number of basic events increases. To overcome the shortcomings of the Markov model, we propose an alternative method to obtain the top event probability in this paper. We assume that the basic events occur independently, exponentially distributed, and the component whose failure corresponds to the occurrence of the basic event is non-repairable. First, we obtain the probability of occurrence of the output event of a single priority AND gate by Markov analysis. Then, the top event probability is given by a cut set approach and the inclusion-exclusion formula. An efficient procedure to obtain the probabilities corresponding to logical products in the inclusion-exclusion formula is proposed. The logical product which is composed of two or more priority AND gates having at least one common basic event as their inputs is transformed into the sum of disjoint events which are equivalent to a priority AND gate in the procedure. Numerical examples show that our method works well for complex systems.
机译:当给出最小割集时,提出了一种计算具有优先级“与”门和重复基本事件的故障树的精确顶部事件概率的方法。优先级“与”门是一个“与”门,其中输入事件必须按照规定的顺序发生,以发生输出事件。众所周知,这种动态故障树的最高事件概率是通过将其转换为等效的马尔可夫模型而获得的。但是,此方法对于复杂的系统模型不切实际,因为随着基本事件数量的增加,在马尔可夫分析中应考虑的状态数量急剧增加。为了克服马尔可夫模型的缺点,本文提出了一种替代方法来获得最高事件概率。我们假设基本事件是独立发生,呈指数分布的,并且其故障与基本事件的发生相对应的组件是不可修复的。首先,通过马尔可夫分析获得单个优先级与门输出事件发生的概率。然后,通过割集方法和包含-排除公式给出最高事件概率。提出了一种有效的程序来获取包含与排除公式中的逻辑乘积相对应的概率。由具有至少一个共同基本事件作为输入的两个或多个优先级AND门组成的逻辑乘积被转换为与该过程中的优先级AND门等效的不相交事件之和。数值例子表明,我们的方法适用于复杂的系统。

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