冷贮备离散时间状态聚合可修系统的可靠性

对一个离散时间可修系统的可靠性进行了研究,系统由两个部件和一个修理工组成,一个部件在线工作,另一个冷贮备,修理工具有多重休假策略,故障部件修复如新;假设部件正常工作时间、修理时间、修理工的休假时间服从不同参数的离散位相型分布。通过运用kronecker算子和聚合随机过程理论,分别推导出系统在瞬态和稳态情况下的一些可靠性指标:可用度、故障的条件概率以及可靠度。所得结果表明离散时间情形并不是连续时间情形的一个特殊情况。最后用一个数值算例对所得结论进行了验证。

Reliability of a cold standby discrete time state aggregated repairable system

The reliability of a discrete time repairable system is studied. There are two components and one repairman in the system. One component is online, the other is cold standby, and the repairman can take multiple vacations. The failure component can be repaired as good as new. The operational time of the unit online, the repair time and the vacation time of the repairman are governed by different discrete phase type distributions, respectively. The system is studied in a transient and stationary regime. The availability, the conditional probability of failure and the reliability are derived by using the Kronecker operator and the aggregated stochastic process theory. The results show that the discrete case is not a trivial case of the continuous one. Finally, a numerical example is given to illustrate these results.