带有贮备部件的多部件串联系统可靠性分析与优化研究

发布时间：2018-08-19 17:22

【摘要】：带有贮备部件的串联系统是可靠性研究中非常重要的一类系统,也是工程上常见的一类系统,其中贮备部件的优化是一类备受关注的问题。如何合理地选择备件并将之贮备在系统中将对系统的可靠性具有较大影响。在一般的可靠性讨论中,通常假设系统中部件之间是相互独立的。然而,根据实践分析可知,系统在工作时其工作部件之间具有一定的相依性。基于适当的Copula函数,根据部件的边缘分布得到联合分布,进而得出整个系统的可靠性指标具有实际意义。对于可修系统,既通过马尔可夫过程,又利用马尔可夫更新过程和补充变量法等工具进行可靠性分析,具有系统性。首先,本文对于带有贮备部件的三部件串联系统的备件优化问题做出了详细讨论。分别从贮备部件与工作部件同型和不同型的两种情形讨论了系统贮备部件基于可靠度的优化问题。在两种情形下又分别对带有冷贮备和温贮备的系统进行了分析,得出相应的可靠度表达式,并通过MATLAB作图得出最优化结果。其次,对上述优化结果中特定的带有两个冷贮备的三部件串联系统,在系统中部件相互独立时和部件相依时的情形下分别进行可靠性分析。部件相依时又引入了FGM Copula,AMH Copula和Clayton Copula三种不同的连接函数进行对比研究。最后,本文针对带有两个冷贮备的三部件串联系统,研究了基于马尔可夫过程和几何过程的可靠性。对于马尔可夫型系统,通过一定的假设,分析得到系统所有的状态,运用马可夫过程理论进行分析求解。对于几何过程的退化系统,在假定系统中工作部件具有优先维修权,特定部件维修时间服从几何过程等条件下,运用补充变量法研究系统的可靠性。
[Abstract]:Series system with spare parts is a very important system in reliability research, and it is also a kind of common system in engineering. Among them, the optimization of spare parts is a kind of problem that attracts much attention. How to reasonably select spare parts and store them in the system will have a great impact on the reliability of the system. In general reliability discussions, it is generally assumed that the components of the system are independent of each other. However, according to the analysis of practice, the system has certain dependence on its working parts. Based on the proper Copula function, the joint distribution is obtained according to the edge distribution of the components, and the reliability index of the whole system is obtained. For repairable systems, reliability analysis is carried out by means of Markov process, Markov renewal process and supplementary variable method. Firstly, this paper discusses in detail the problem of spare parts optimization for three parts series system with spare parts. In this paper, the reliability optimization problem of the system storage components is discussed from the two cases of the same type and different types of the spare parts and the working parts, respectively. In both cases, the system with cold reserve and warm reserve is analyzed, the corresponding reliability expression is obtained, and the optimization result is obtained by MATLAB diagram. Secondly, the reliability analysis of the special three-component series system with two cold reserves in the above optimization results is carried out under the condition that the components are independent of each other and the components are dependent on each other. When components depend on each other, three different connection functions, FGM Copula Copula and Clayton Copula, are introduced for comparative study. Finally, this paper studies the reliability of Markov process and geometric process for the three-component series system with two cold reserves. For Markov systems, all the states of the system are obtained through some assumptions, and the Markov process theory is used to solve the problem. For the degenerate system of geometric process, the reliability of the system is studied by means of supplementary variable method under the assumption that the working part has the priority maintenance right in the system and the maintenance time of the specific component is dependent on the geometric process.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O213.2

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