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Modeling dependent series systems with q-Weibull distribution and Clayton copula

机译:使用Q-Weibull分布和Clayton Copula建模依赖系列系统

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摘要

In this paper, we propose using the q-Weibull distribution to directly model the failure time of a series system composed of dependent components, discuss the connection between the q-Weibull distribution and the Clayton copula, and show that their parameters are equivalent. Moreover, we propose a Nonhomogeneous Poisson Process with q-Weibull as the underlying time to first failure distribution for reliability analysis of a series system composed of dependent components. The proposed model has fewer parameters and is an approximation to the Clayton copula approach. The maximum likelihood estimators are developed for the parameters of the proposed model. Confidence intervals based on the maximum likelihood asymptotic theory are also developed. The results of simulation experiments demonstrate the accuracy of the proposed model; moreover, estimating the parameters of the proposed model does not require information about which components failed, which is necessary for accurately estimating the parameters of the Clayton model. The procedure is applied to a data set of real failure times for a load-haul-dump machine that is characterized by a bathtub-shaped hazard rate.
机译:在本文中,我们建议使用Q-Weibull分布直接模拟由依赖组件组成的系列系统的故障时间,讨论Q-Weibull分布与Clayton Copula之间的连接,并显示其参数是等效的。此外,我们提出了一种与Q-Weibull的非均匀泊松过程,作为首次故障分布的潜在时间,以便对由依赖组件组成的系列系统的可靠性分析。所提出的模型具有较少的参数,并且是克莱顿copula方法的近似值。为提出模型的参数开发了最大似然估计器。还开发了基于最大似然渐近理论的置信区间。仿真实验结果表明了所提出的模型的准确性;此外,估计所提出的模型的参数不需要关于哪个组件失败的信息,这对于准确地估计Clayton模型的参数是必要的。该过程应用于负载式危险率的负载荷载机器的真正故障时间的数据集。

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