可修复系统的稳定性、可靠性和数值解

项目名称： 可修复系统的稳定性、可靠性和数值解

项目编号： No.11201037

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 郑福

作者单位： 渤海大学

项目金额： 22万元

中文摘要： 可修复系统是可靠性数学的主要研究对象之一，其研究成果广泛应用于航天、军事、通信、交通等各个领域。但是，随着科学技术的发展，现有模型和结果已不能满足实际问题的需要。因此，建立新模型并对可靠性理论中存在的若干问题进行研究是非常必要的。在本课题，我们除了建立两类三部件串并联休假可修复系统的新模型并对其适定性、渐近稳定性、指数稳定性和可靠性研究外，还给出系统方程的数值解和稳态解代替动态解的精确误差估计。在此基础上，进一步得到系统瞬时可用度，修理工的休假策略和部件的最优更换策略，并通过数值模拟分析参数的敏感度，验证本课题的结论和方法的正确性。这些研究不但给出系统性能的判断与评估，揭示修理工休假对系统性能的影响机制，为研究者进一步研究这类系统奠定严格的理论基础，而且可帮助决策者制定科学合理的决策，指导工程技术人员合理使用及维护设备，提高系统的经济效益和安全性。

中文关键词： 可修复系统；稳定性；可靠性；数值解；算子半群理论

英文摘要： Repairable system is one of the main research objectes in the thoery of reliability mathematics，its research results were widely utilized in the fileds of aerospace, military science, comminucations engineering, transportation business,etc.However, with the constant development of science technology, the existing models and related results are hard to cope with the complexity of the real world. Therefore, it is stringent to establish new models and solve the existed problems in the reliability theory. In this progect, we shall establish new models of the serie-parallel repairable system with three units and vacation and discuss the well-posed-ness, asymptotic stability, exponential stability and reliability of the repairable system. In addition, the numerical solutions to the system equations and the precise error estimates of the stead-state solution in substituion for the dynamic solution are given. Furthermore, on the basis of the reults above, the instantaneous availability of the system, the vacation strategy of the repairman and the optimal replacement strategy of the unit are to be obtained, numerical simulations are also performed to testfy the sensitivity of the system parameter and verify the rationality of results and the soundness of the methods of this project. These research results of this p

英文关键词： Repairable system；Stability；Reliability；Numerical solution；theory of operator semigroups