边界扰动法在修理工可休假的可修系统可靠性分析中的应用

由于休假可修系统的可靠性研究在不同领域有着广泛的应用, 近二十多年来休假可修系统的可靠性研究受到了越来越多的关注。本项目重点研究各类修理工休假的可修复系统，特别是对修理工可有限休假的带有一个冷贮备部件的并联系统、修理工可多重休假的N 个不同部件串联可修复系统、修理工可单重休假的三部件串并联可修复系统及修理工可多重休假的退化可修系统进行深入的研究。研究系统的适定性、非负动态解的存在唯一性、稳态解的存在性、动态解的渐近稳定性和动态解的指数稳定性。进一步研究系统的最优控制问题,并利用数值计算和数值模拟的方法对本项目所得部分理论结果进行数值实验。这对系统的可靠性有非常重要的科学意义。本项目的目标是建立各类可修系统的适定性、动态解的存在性、动态解的渐近稳定性和动态解指数稳定性的简单、合理、并且易于验证的判别准则，从事这方面的研究工作的科研人员提供理论框架和方法。

Repairable systems with vacation have been received increasing attention during nearly two decades due to their wide applications in various fields. In this project we focus on the various types of repairable systems attended by a repairman with vacations, especially, we study a parallel system with a cold standby unit and finite vacations, N-dissimilar unit series system attended by a repairman with multiple vacations, a three-unit series-parallel repairable system attended by a repairman with single vacation and a deteriorating system attended by a repairman with multiple vacations. We study the well-posedness, the existence and uniqueness of the non-negative dynamic solution, the existence of the steady state solution and the asymptotic stability as well as the exponential stability of the systems. Furthermore,we study the problem of optimal control of the systems, and by using the numerical calculation and the numerical simulation method, we execute numerical experiments on some theoretical results obtained in this project, which are very important scientific significance in the reliability of the systems. Main goal of this project is to build a simple and reasonable criterion for studying well-posedness, the existence and uniqueness of the dynamic solution, and the asymptotic stability as well as the exponential stability of various types of repairable systems, and to provide a theoretical framework and methodology to the researchers in this area.