疲劳影响可忽略的聚合马尔可夫可修系统的可靠性分析

The reliability analysis for aggregated Markov repairable system with fatigue time omission

在经典马尔可夫可修系统模型的基础上,把系统的状态空间分为工作状态集与故障状态集,根据系统运行水平的不同,又把工作状态集划分为完全工作状态集与疲劳工作状态集。当系统在疲劳工作状态集运行的时间小于给定的常数τ时,可以认为系统在这段时间也是处于完全工作状态,即疲劳影响可以忽略,而当系统在疲劳工作状态集运行的时间大于给定的常数τ,则这段时间不能被忽略,从而建立了疲劳影响可忽略的可修系统新模型。运用Laplace变换方法以及生物药理学的离子通道建模理论,求得了原模型与新模型的一些可靠性指标。最后用一个数值算例对所得结论进行了模拟实现。

Based on the classical Markov repairable system, the state space of the system is divided into the set of working states and the set of failure states. Further, the set of the working states is divided into the set of the fully working states and the set of the fatigue working states based on the different working levels. If the sojourn time that the system is in the fatigue working states is less than a given constant τ, then this fatigue working time can be omitted, i.e. the system is thought of as excellent working during this fatigue working time. Otherwise, If the sojourn time that the system is in the fatigue working states is more than the given constant τ, then this fatigue working time can’t be omitted. Based on this assumption, aggregated Markov repairable system with fatigue time omission is modeled. Some reliability indexes of the original model and the new model are derived by using Laplace transform and the IonChannel modeling theory. Finally, a numerical example is given to illustrate these results obtained in the paper.