中文摘要：

在假定的修理过程为α-幂过程的基础上,利用马尔科夫过程和拉普拉斯变换求出冲击环境下单部件可修系统的可用度、系统故障频度等可靠性指标,并通过更新报酬定理求出系统的长期运行下单位时间的平均成本率函数的数学表达式,以分析方法和数值方法证明最优更换策略的存在和唯一性;最后,通过数值例子证明我们导出的结论的正确性,并在所有参数都给定的条件下,通过数值例子求出系统的最优更换策略.

英文摘要：

A one-component repairable system under Poisson shock is considered.The system＇s failure may be due to external shocks.The shocks arrive according to a Poisson process.Whenever the magnitude of a shock is larger than a pre-specified threshold,the system fails.Assuming that the repair time of the system is α-power process,the system availability and the rate of occurrence of failures etc.are derived to indicate the importance of the reliability.The paper aims at the optimized number of failures of the system before a replacement is carried out.The explicit expression of the expected long term running cost rate is derived and the corresponding optimal policy is determined analytically and numerically.A numerical example is given to illustrate the theoretical results for the proposed model.