【作者】 胡林敏；

【导师】 岳德权；

【作者基本信息】 燕山大学 ， 运筹学与控制论， 2006， 硕士

【摘要】 具有两类失效状态的可修系统是可靠性理论中的一类典型系统。修理工是可修系统中必不可少的一部分，而修理工休假或者从事其它的工作对系统的可靠性指标和经济效益会产生重要的影响。因此，在具有两类失效状态的可修系统中考虑修理工休假或者从事其它的工作具有重要的理论意义和应用价值。本文研究了三个具有两类失效状态部件且修理工可多重休假的可修系统模型。这三个模型是以往文献中相关模型的推广，是具有重要研究价值的新模型。首先，研究了修理工可多重休假的具有两类失效状态N部件串联可修系统。通过对系统模型的分析，得到了系统的可靠度和首次故障前平均时间，并利用向量Markov过程理论和Laplace变换的方法，求出了系统的可用度、故障频度和修理工处于休假状态的概率等可靠性指标。此外，还对系统进行了效益分析。其次，研究了修理工可多重休假的具有两类失效状态两部件并联可修系统。应用向量Markov过程理论和Laplace变换的方法，求出了系统的可用度、故障频度和修理工处于休假状态的概率等可靠性指标，以及系统可靠度的Laplace变换式和首次故障前平均时间的表达式，同时还对系统进行了效益分析，确定了修理工是否休假的策略。最后，研究了修理工可多重休假的具有两类失效状态三部件串并联可修系统。应用向量Markov过程理论和Laplace变换的方法，求出了系统可靠度的Laplace变换式和首次故障前平均时间的表达式，并得到了系统的可用度、故障频度及修理工处于休假状态的概率等可靠性指标。此外，还对系统部分可靠性指标和效益进行了数值分析，为在实际工作中的决策者提供了制定系统工作方案的重要依据。更多还原

【Abstract】 Repairable system with two types of failure is a typical system in reliability theory. Repairman is one of the essential parts of a repairable system, while repairman has vacation or is engaged in other work, which can have the important influence to the system reliability expressions and the economic benefit of the system. Therefore, it has the important theory significance and the application value to consider that repairman has vacation or is engaged in other work in repairable system with two types of failure.This paper studies three repairable system models with two types of failure and multiple vacations of a repairman. These are new ones, which are the spread of the related models in the references and have the important research value.Firstly, a n-unit series repairable system with multiple vacations of a repairman and two types of failure is studied, we obtain the reliability and the mean time to first failure of this system, and using vector Markov process theory and Laplace transform method, we obtain the availability, the failure frequency of this system and the probability of repairman being vacation condition, and so on. In addition, we also discuss the benefit of this system.Secondly, we study a two-unit parallel repairable system with multiple vacations of a repairman and two types of failure. By using vector Markov process theory and Laplace transform method, we obtain the availability, the failure frequency of this system and the probability of repairman being vacation condition, and so on. Then we obtain the Laplace transformation of the reliability and the expressions of the mean time to first failure, and analyze the benefit of this system and determine whether repairman is on vacation strategy.Finally, we discuss a three-unit serie-parallel repairable system with multiple vacations of a repairman and two types of failure. By using vector Markov process theory and Laplace transform method, we obtain the Laplace transformation of the reliability, the expressions of the mean time to first failure, the availability, the failure frequency of this system and the probability of repairman being vacation condition, and so on. Additionally, we also carry on the numerical analysis to the system partial reliability indices and the benefit, and provide the formulation system work plan important basis to the practical work policy-maker.更多还原