中文摘要：

定义了一类新的离散随机过程（Poisson-Negative-Binomial，PNB过程）．首先通过推导给出了该过程的概率分布、矩母函数、期望与方差的表达式．其次，以PNB过程作为基础过程，建立了一类累积冲击模型；在损伤可加情形下．给出了系统寿命T的生存函数和T的高阶矩的计算公式，以推论形式给出寿命T的期望和方差的表达式；此外还给出了系统累积损伤的期望和方差的计算公式．最后在冲击强度服从指数分布条件下，给出一个应用实例．

英文摘要：

A new class of discrete random process Poisson-Negative-Binomial （PNB） Process was defined. Firstly, the probability distribution and moment generating function of the process were researched, the expressions of expec- tation and variance were derived. Secondly, in the PNB process as a basis process, a model of cumulative impact damage was established;in the case of impact damage could be added, the calculation formulas of survival function and the higher order moment of lifetime T were given, the expressions for the expectation and variance about lifetime T of the system were given in the form of inference ;In addition, the formulas for calculating the expectation and vari- ance of the cumulative damage were also derived. Finally, under the condition of the impact damage obey exponential distribution, an applied example was given