中文摘要：

本文研究泊松冲击下的单部件可修系统,假设系统并非“修复如新”.系统失效有可能由于外部冲击或者内部因素引起,并且冲击到达服从一个泊松过程.当冲击量大于系统的预先定好的一个阈值,则系统就会失效.假设系统在维修以后相邻之间的阈值形成一个几何过程,而系统的修理时间服从α-幂过程.利用更新过程理论,求出系统经长期运行单位时间内的期望损失及相应的最优更换策略.最终通过数值案例验证了模型中的结果.

英文摘要：

This article studies a one-component repairable system under Poisson shock. It＇s assumed that the system after repair is not ＂as good as new＂. The system＇s failure may be due to external shocks or intrinsic factors and the shocks arrive according to a Poisson process. Whenever the magnitude of a shock is larger than a pre-specified threshold, the system will fail. Assume that the successive threshold values follow a non-decreasing geometrical process after repair and the repair time of the system is an a-power process. Using the renewal reward theorem, 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 given to illustrate the theoretical results for the proposed model.