共因故障的冗余系统和一个储备部件的可靠性  

Reliability of Redundant System with Common-Cause Failures and One Standby Unit

作　　者：刘丹红[1] 许跟起[1] 

机构地区：[1]天津大学理学院,天津300072

出　　处：《天津大学学报》2011年第5期458-465,共8页Journal of Tianjin University(Science and Technology)

基　　金：国家自然科学基金资助项目(NSFC-60874034)

摘　　要：储备冗余性用于提高系统的可靠性和可使用性,共因故障是系统可靠性的关键问题.利用泛函分析的方法,在系统模型假定下,证明系统的动态非负解是系统算子的0本征值对应的非负本征向量.通过研究系统算子的谱特征,证明在边界条件含有积分的情况下,系统算子的谱点仍均位于复平面的左半平面且虚轴上除0外无谱,证明了系统存在非负的动态解和稳态解,并在范数意义下收敛到稳态解.研究了系统动态解收敛于系统的定态解的收敛速度问题,并给出了系统可靠性条件.Reserve redundancy is used to improve system reliability and usability.Common-cause failure is a key issue to system reliability.Is is shown by functional analysis method that the non-negative dynamic solution of the system is the non-negative eigenvector corresponding to zero eigenvalue of system operator.By studying the spectral properties of the system operator,it is proved that the spectral points,when boundary conditions contain integral,are still located on the left side of the complex plane and that there is no spectrum on the imaginary axis plane with the exception of zero.The result shows that there exist nonnegative dynamic and steady solutions for the system.The dy-namic solution converges asymptotically to the steady solution under the sense of norm.The convergent rate is studied and the condition of system reliability is presented.

关 键 词：共因故障 C0半群 指数稳定性 可靠性 

分 类 号：O29[理学—应用数学]