具有小修和不完全预防性维修的多状态退化系统的可用度分析  

Availability Analysis of A Multi-State Degraded System with Minimal Repairs and the Imperfect Preventive Maintenance

作　　者：王丽花 岳德权[2] WANG Li-hua;YUE De-quan(Faculty of Mathematics Science,Baotou Teachers College,Baotou 014030,China;College of Science,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]内蒙古科技大学包头师范学院,内蒙古包头014030 [2]燕山大学理学院,河北秦皇岛066004

出　　处：《数学的实践与认识》2018年第16期222-226,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71071133);包头师范学院青年科学研究基金项目(BSYKJ2014-21)

摘　　要：研究了一种多状态退化系统,该系统由于在工作过程中逐渐退化,导致系统的效率降低.为了减少系统的失效率和退化率,系统会受到随机失效后的小修和退化到最后一个可接受工作状态时的预防性维修.在这种具有小修和不完全预防性维修的多状态退化系统模型中,假定系统能连续退化成一些离散状态,并且这些离散状态是从正常工作状态一直到完全失效状态.当系统逐渐退化到某个临界值（这里把它称作不可接受状态）时,就视系统完全失效,那么在最后一个可接受状态时系统就会得到预防性维修;当系统从任意的工作状态随机失效后就会得到小修.在这个模型中,基于它是一个连续时间的马尔可夫过程,来计算稳态可用度指标.In this paper, we study a multi-state degraded system, which gradually will degrade in the working process, and the degradation may cause reduction of system efficiency. To reduce the failure rate and degradation rate, the system will be subjected to minimal repairs after the random failure and the preventive maintenance after the degradation which makes the system stop working. Then, in the multi-state degraded systems model with minimal repairs and preventive maintenances, we assume that the system can continuously degraded into a number of discrete states, and these discrete states are from perfect operation state to the complete failure state. When the system is gradually degraded to a critical value （called it unacceptable state here）, regarded as complete failure, then in the final acceptable state, the system will be subjected to preventive maintenance; After the random failure from any work state, the system get minimal repairs. Finally, in this model, we assume that it is a continuous time Markov process to calculate steady state availability indices.

关 键 词：多状态系统 退化 小修 预防性维修 稳态可用度 

分 类 号：O211.62[理学—概率论与数理统计]