具有小修和一般型更换策略的多状态退化系统

A multi-state degraded system with minimal repairs and the replacement policy in general distribution

为了解决多状态退化系统问题,利用马尔可夫过程理论及补充变量法建立了微分方程组,并采用Laplace变换法及其反演方法,研究了带有小修和一般型更换维修策略的模型。假定系统连续退化成许多离散状态,在系统退化到失效状态时,实施更换函数为一般分布的更换策略,使系统修复如新;系统在每个退化状态可能随机失效,然后得到小修,得到了可靠度和首次故障前的平均时间的表达式,可用度和首次故障前的平均时间的Laplace变换式等重要的可靠性指标。该成果具有一定的理论和实际意义。

In order to solve the problem associated with multi-state degraded system,this paper investigates a multi-state degraded system with minimal repairs and the replacement policy in general distribution using a system of differential equations established based on Markov process theory and the supplementary variable method and by Laplace transform and its inversion.In this model,it is assumed that the system could degrade consecutively into many discrete states until a complete failure state,then a replacement maintenance policy in general distribution is implemented and the system becomes as good as new.In each degraded state,the system could fail randomly and be restored into a previous state of degradation by minimal repairs.Based on these assumptions,the study derives the reliability indices,such as the reliability function,the mean time to first failure,Laplace transform of the availability and the failure frequency etc.The results have some theoretical and practical significance.