• 论文 •

### 弧$k/n(G)$与节点$k/n(G)$网络模型可靠性估计的对偶变量蒙特罗洛方法

1. 西南交通大学交通运输与物流学院, 成都 610031
• 出版日期:2018-01-25 发布日期:2018-03-06

DING Heng, LI Yanlan. Monte Carlo Simulation with Antithetic Variable for Reliability Evaluation of $k$-out-of-$n$ Network Models Based on Arcs and Nodes[J]. Journal of Systems Science and Mathematical Sciences, 2018, 38(1): 86-100.

### Monte Carlo Simulation with Antithetic Variable for Reliability Evaluation of $k$-out-of-$n$ Network Models Based on Arcs and Nodes

DING Heng, LI Yanlan

1. School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610031
• Online:2018-01-25 Published:2018-03-06

A new kind of $k$-out-of-$n$ network model based on nodes was proposed to fix the problem that the input requirements from upstream nodes cannot be well modeled in the $k$-out-of-$n$ network based on arcs. In a $k$-out-of-$n$ network based on nodes, the $k$-out-of-$n$ property of nodes are developed further by letting nodes work only when there are at least $k$ inputs from its operating-input set, which makes it easy to deal with the input requirements from any upstream node. And the connectedness algorithms based on random adjacency matrix were designed for the Monte Carlo simulation plans of $k$-out-of-$n$ networks based on arcs and nodes respectively. Considered the monotonicity of the structure function of $k$-out-of-$n$ network models, variance-reducing technique with antithetic variables was used in the progress of the Monte Carlo reliability evaluation. Finally, the simulation results show the effectiveness of the simulation plans for reliability evaluation. And the Monte Carlo simulation using antithetic variables makes the time cost reduced and accuracy improved when compared with crude Monte Carlo method.

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