Abstract: In the process of shock and degradation of reliability systems, it is usually multi-stage and dependent. In order to analyze the dependence of the shock and degradation more accurately, a composite model of multi-stage system with dependent shock and degradation process is established. In the model, a more generalized dependence on shock and degradation processes is proposed. The shock and degradation contribute to the damage accumulation process of the system, which leads to the change of the system stage, and the state transition affects the impact and degradation process. By constructing Markov update process and based on semi Markov kernel, the reliability expression of this impact degradation model is obtained.

Key words: markov renewal process, multi-stage model, degradation process, shock process, reliability modeling

摘要： 系统所遭受的冲击和退化损害过程广泛存在着多阶段特征和相互依赖关系,为了更精确建模和分析系统冲击和退化间的依赖性,论文建立了多阶段冲击和退化过程的复合模型,提出了一种更加广义的冲击和退化过程依赖关系,即二者同时对系统损害累积过程产生贡献,进而导致系统阶段的改变,而状态转移又反馈性地影响冲击和退化过程。通过构造马尔可夫更新过程,基于半马尔科夫核,得到此类冲击退化模型的可靠度解析表达。

关键词: 马尔科夫更新过程, 多阶段模型, 系统退化, 冲击模型, 可靠性