Abstract
This paper concentrates on the component importance measure of a network whose arc failure rates are not deterministic and imprecise ones. Conventionally, a computing method of component importance and a measure method of reliability stability are proposed. Three metrics are analyzed first: Birnbaum measurement, component importance, and component risk growth factor. Based on them, the latter can measure the impact of the component importance on the reliability stability of a system. Examples in some typical structures illustrate how to calculate component importance and reliability stability, including uncertain random series, parallel, parallel-series, series-parallel, and bridge systems. The comprehensive numerical experiments demonstrate that both of these methods can efficiently and accurately evaluate the impact of an arc failure on the reliability of a network system.
Highlights
As a quantitative measure, reliability can be broadly interpreted as the ability of a system to perform its intended function
Lemma 5. e network topology decomposing method based on Cellular Automata in Section decomposes network G, a disjoint set denoted as DB(G) can be calculated, and the Birnbaum measure of any component i in the network can be obtained by the following recursion formula: IiB (t) = Rel (DB (G), i)
Evaluating the importance of components for complex networks is of great significance to the research of survivability and robusticity of networks
Summary
Reliability can be broadly interpreted as the ability of a system to perform its intended function. Network reliability can be estimated using Bayesian approach [1], Monte Carlo simulation [2, 3], genetic algorithm [4], fault-tree analysis [5], etc. To evaluate reliability importance of components in a network system, Zio et al [10] present generalized importance measures based on Monte Carlo simulation. Simulation based on Monte Carlo method [10] often depends more on the convergence of probability than the number of network components; statistical error during reliability analysis may result in slow convergence for achieving acceptable accuracy in low probability estimations. A computing method of component importance (NEA) based on Cellular Automata is designed; in addition, a new measure method of reliability stability (NSA) is proposed in this paper.
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