中文摘要：

讨论了一种特殊的δ冲击模型，假设系统受到到达时间间隔服从泊松分布的冲击，当连续两次冲击的时间间隔超过门限值δ时，系统失效。我们计算了此类δ冲击模型系统冲击到达次数和冲击到达时刻的分布，并且进一步求出了系统寿命的概率分布和期望。

英文摘要：

This paper discusses a kind of δ-shock model, assuming that the system suffer from shock which interarrival time follows the Poisson distribution. The system will failure if some interarrival time between two successive shocks is less than some threshold δ. This paper calculate the distribution of shock number and shock arrival times and find the probability distribution and expectations of system lifetime using induction method.