部件寿命服从威布尔分布时典型系统的寿命与剩余寿命估计

在实际工程中,对系统寿命以及剩余寿命的估计非常重要。在已知系统中部件寿命与可靠度的前提下,关于如何快速得到系统级寿命与剩余寿命的相关研究比较缺乏。针对这一问题,首先研究了可靠度、寿命以及剩余寿命的关系,进一步假设部件寿命服从同一威布尔分布,根据部件的寿命与可靠度函数,推导得到串联、并联和表决系统寿命与剩余寿命期望的封闭表达式,并给出了相应的计算方法。对于冷备系统,当部件寿命服从同一指数分布时,推得了系统寿命及剩余寿命期望的封闭表达式,而当部件寿命服从同一威布尔分布时,给出了系统寿命与剩余寿命的数值计算方法。仿真试验证明本文所提出的方法是准确高效的。最后,以卫星中的动量轮r/n(G)表决系统为例开展了实例研究,证明了该方法在工程实践中的有效性。

Estimation of lifetime and residual life of typical system with Weibull distributed components

In practical engineering, it is significant to estimate the lifetime and residual life of a system. The research is limited for how to obtain the lifetime and residual life of a system efficiently by using the lifetime and reliability of components. Motivated by this problem, relationship between reliability, lifetime and residual life is analyzed in this paper. Further, on the assumption that the components are identically and independently Weibull distributed, the closed forms for lifetime and residual life of series, parallel and r/n(G) systems are derived based on lifetime and reliability function of components, respectively. And the calculation method is presented accordingly. Next, for the lifetime and residual life of the cold standby system, the closed-form is obtained when the components lifetime are identically exponentially distributed and numerical method is proposed when components follow Weibull distributions. The numerical examples prove the proposed method is accurate and efficient. Finally, a r/n(G) system composed by momentum wheels is taken as an example and the results shows that this method is worth learning in engineering practice.