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Impact of copulas for modeling bivariate distributions on system reliability

机译：copulas用于建模双变量分布对系统可靠性的影响

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摘要

A copula-based method is presented to investigate the impact of copulas for modeling bivariate distributions on system reliability under incomplete probability information. First, the copula theory for modeling bivariate distributions as well as the tail dependence of copulas are briefly introduced. Then, a general parallel system reliability problem is formulated. Thereafter, the system reliability bounds of the parallel systems are generalized in the copula framework. Finally, an illustrative example is presented to demonstrate the proposed method. The results indicate that the system probability of failure of a parallel system under incomplete probability information cannot be determined uniquely. The system probabilities of failure produced by different copulas differ considerably. Such a relative difference in the system probabilities of failure associated with different copulas increases greatly with decreasing component probability of failure. The maximum ratio of the system probabilities of failure for the other copulas to those for the Gaussian copula can happen at an intermediate correlation. The tail dependence of copulas has a significant influence on parallel system reliability. The copula approach provides new insight into the system reliability bounds in a general way. The Gaussian copula, commonly used to describe the dependence structure among variables in practice, produces only one of the many possible solutions of the system reliability and the calculated probability of failure may be severely biased.
机译：提出了一种基于copula的方法，以研究copula在不完全概率信息下建模双变量分布对系统可靠性的影响。首先，简要介绍了建模双变量分布的copula理论以及copula的尾部相关性。然后，提出了一般的并行系统可靠性问题。此后，在copula框架中概括了并行系统的系统可靠性范围。最后，给出一个说明性的例子来说明所提出的方法。结果表明，在不完全概率信息下并行系统故障的系统概率无法唯一确定。由不同的copula引起的系统故障概率差异很大。随着组件故障概率的降低，与不同copula相关的系统故障概率的这种相对差异会大大增加。其他copula与高斯copula的系统故障概率的最大比率可以在中间相关时发生。 copulas的尾部依赖性对并行系统的可靠性有重要影响。 copula方法以一般方式提供了对系统可靠性范围的新见解。在实践中通常用来描述变量之间的依存关系的高斯copula仅产生系统可靠性的许多可能解决方案之一，并且计算出的故障概率可能会严重偏差。

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  • 来源
    《Structural Safety》 |2013年第2013期|80-90|共11页
  • 作者

    Xiao-Song Tang; Dian-Qing Li; Chuang-Bing Zhou; Kok-Kwang Phoon; Li-Min Zhang;

  • 作者单位

    State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, 8 Donghu South Road, Wuhan 430072, PR China;

    State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, 8 Donghu South Road, Wuhan 430072, PR China;

    State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, 8 Donghu South Road, Wuhan 430072, PR China;

    Department of Civil and Environmental Engineering, National University of Singapore, Blk E1A, #07-03, 1 Engineering Drive 2. Singapore 117576, Singapore;

    Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Joint probability distribution; Correlation coefficient; Copulas; Parallel system; System reliability; Reliability analysis;

    机译：联合概率分布;相关系数;科普拉斯;并联系统系统可靠性;可靠性分析;

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