具有小修和不完全预防性维修的多状态退化系统的可靠度分析

Reliability Analysis of a Multi-State Degraded System with Minimal Repairs and the Incomplete Preventive Maintenance

研究了基于小修和不完全预防性维修混合维修模式下的多状态退化系统.利用可靠性理论与马尔可夫过程理论,分析了系统在一个周期内的运行模式和维修方式,绘制了系统状态概率转移图.根据状态概率转移图,得到状态概率的微分方程组.利用代数中的Crammer法则得到状态概率的Laplace变换式,然后通过Laplace反演得到状态概率的显表达式.最后,由可靠度的概念得到了可靠度重要指标的结果.

A multi-state degraded system based on the mixed maintenance mode of minimal repairs and incomplete preventive maintenance is studied.Based on the reliability theory and Markov process theory,the operation mode and maintenance mode of the system in a period are analyzed,and the probabilistic transition diagram of the system state is drawn.According to the state probabilistic transition diagram,differential equation group of state probability is derived.The Laplace transformations formula of state probability is obtained by using the crammer rule in algebra,and then the explicit expression of state probability is derived by Laplace inversion.Finally,the results of the important index of reliability are obtained from the concept of reliability.