可忽略部分维修时间且工作时间服从PH分布的单部件可修系统的可靠性

考虑了一个单部件可修系统,部件的工作时间为phase type分布,修理时间为指数分布,建立了原马尔可夫可修系统模型。在该模型的基础上,如果系统的维修时间不超过给定的非负常数τ,则这段维修时间可以被忽略,认为系统在这段时间内仍处于工作状态,如果系统的维修时间超过了给定的非负常数τ,则这段维修时间不能被忽略,认为系统在这段时间内处于故障状态,从而建立了可忽略部分维修时间的系统模型,并运用聚合随机过程理论,分别推导出两个系统模型的几个可靠性指标。最后用一个数值算例对所得结论进行了模拟实现。

The reliability for a single unit repairable system with repair time omission and working time following PH distribution

A unit repairable system, with the working time follows phase type distribution, and with the repair time is exponentially distributed, was considered. The original Markov repairable system model was modeled. Based on the model, if the system repair time is less than given non negative constant τ, then the repair time can be omitted, we think that the system is also working during the repair time. Otherwise, if the system repair time is greater than given non negative constant τ, then the repair time cannot be omitted, the system is thought of as failure during the repair time. Based on these assumptions, the new system model with repair time omission was modeled. Some reliability indexes of the original model and the new model were respectively derived by using aggregated stochastic process theory. Finally, a numerical example was given to illustrate these results obtained.