中文摘要：

研究了泊松冲击下的单部件可修系统。系统失效由外部冲击和内部原因引起，且冲击到达服从泊松过程。当某次冲击的冲击量太大，超过了系统的阈值时，系统就会失效。假设相继周期间部件的阈值形成一个递减的几何过程，而修理过程为α－幂过程，利用更新报酬定理求出系统长期运行下单位时间的平均成本率函数的数学表达式，从分析方法和数值方法上证明最优更换策略的存在和唯一性。最后，通过数值例子验证了模型的相关理论结果。

英文摘要：

A one-component repairable system under Poisson shock is considered.The system＆#39;s failure may be due to external shocks or intrinsic factors.The shocks arrive according to a Poisson process.Whenever the mag-nitude of a shock is larger than a pre-specified threshold, the system will fail.Assume that the successive thresh-old values follow a non-decreasing geometrical process after repair and the repair time of the system is α-power process.Using the theory of renewal process, the explicit expression of the expected long run cost rate is derived and the corresponding optimal policy can be determined analytically or numerically.A numerical example is giv-en to illustrate the theoretical results for the proposed model.