具有多重严重故障和非严重故障和修复功能的系统的可靠性分析

该文研究一个具有多重严重故障和非严重故障和修复功能的系统的可靠性问题. 在泛函分析理论的框架下,将系统方程组写成一个 Banach 空间中的抽象初值问题,利用算子半群方法,研究了该系统的适定性、稳态解的存在性以及稳定性.表明: 在系统模型的假定下,所研究的系统是适定的,存在非负动态解和稳态解, 特别在范数意义下动态解收敛到稳态解.从而由系统稳态解得到的系统指标是可靠的.

Analysis of Reliability of a System with Repair and Multiple Critical and Noncritical Errors

In this paper the authors study reliability of a system with repair and multiple critical and non-critical errors.Under the functional frame work,they rewrite the system into an eqvolutionary equation in the state Banach space.Using the theory of semigroup of bounded linear operators,they investigate the well-poseness and the stability of the system.They prove that,under certain assumptions,the system is wellposed and associates a positive C_0 semigroup; There is a steady state of the system and solution of the system converges asymptotically to this steady state in the sense of norm.And hence the indices of the system determined by the steady state are reliable.