Poisson冲击下的$k/n(G)$系统的可靠性分析

本文研究了一类Poisson冲击下的$k/n(G)$系统(即$k$-out-of-$n$: $G$系统). 假定冲击的到达数形成一个参数为$\lambda$的Poisson过程, 且冲击的量服从某一分布. 当每次冲击到达时, 对系统中工作的部件独立地产生影响. 进而假定每一部件以一定的概率故障, 概率值是冲击量的函数. 且各次冲击独立地对系统造成损失, 直到工作部件数少于$k$系统故障为止. 在这些假定下, 我们获得了系统的可靠度函数和系统的平均工作时间. 进一步, 假定系统是可修的, 系统中有一个维修工, 并根据``先坏先修’’的维修规则对故障部件进行维修. 在维修时间服从指数分布的假设下, 系统状态转移服从Markov过程. 对该系统我们建立了状态转移方程, 并求得了系统可用度、稳态下的平均工作时间、平均停工时间和系统失效频率等可靠性指标. 最后, 我们还给出了一个简单例子来演示讨论的模型.

Reliability Analysis for $k/n(G)$ System under Poisson Shock

In this paper, a $k/n(G)$ system (i.e. $k$-out-of-$n$: $G$ system) under Poisson shock is studied. Assume that the number of the shock arrivals forms a Poisson process with parameter $\lambda$, and the shock value submits to certain distribution. When a shock arrives, all working components in this system will independently produce a random effect. Assume further that the failure probability of the working component under the shock is the function of the shock value, and each shock will independently produce the system loss until the system failure happen when the number of working components in this system is less than $k$. Under these assumptions, we can obtain the system reliability function and the system average working time. Further, if the system is repairable, and there is a repairman in this system. We can assume that repair rule is "first in first out", and each failure component after repair can be "as good as new". When the time of repairs is an exponential distribution, the state transfer of the system submits to Markov process. Thereafter, we can establish the state transfer equations of the system, and obtain some reliability indices such as the system availability and the system average working time, the system average stopping time and the system failure frequency under the steady state. Finally, a simple example is given to illustrate the model proposed.