基于饱和泊松分布的网络边的Birnbaum重要度计算方法

Network Birnbaum Importance Measure under Saturated Poisson Distribution

重要度是系统可靠性领域用以识别系统薄弱环节的主要方法之一,也是系统可靠性优化的前提和基础。在对传统Birnbaum重要度计算方法研究的基础上,假设网络边故障个数概率分布已知的前提下,基于网络结构谱,给出了一种基于概率分布的Birnbaum重要度计算方法,重点探讨了网络故障边个数服从饱和泊松分布时Birnbaum重要度的性质。最后,结合算例给出了基于饱和泊松分布的Birnbaum重要度的应用方法。

Network reliability analysis aim to quantify the impact of component failures on the network failure and to identify the weakness in a network. Importance measures provides numerical indicator to determine which compo- nents are more important for network reliability improvement or more critical for network failure. In this paper, the number of failed components is introduced, which is a random variable having a distribution. Under the condition of the distribution have been known, based on the structural spectrum, a new method to compute Birnbaum importance measure is derived. In particularly, when the number of failed components follows a saturated Poisson distribution, several results concerning ranking of components according to Birnbaum importance measure is presen- ted. Finally, an example is presented to explain the application of the results.