两相同部件并联可修系统正解的存在性

Existence of positive solution of repairable system with two identical components

可修系统是可靠性理论研究的主要内容,可修系统包含串联和并联系统,并联系统是指系统中的多个部件有一个完好系统就能正常工作的一类系统.讨论一类两相同部件并联可修系统的数学模型,首先,估计了主算子的预解式;其次,证明了系统的主算子的稠定性;最后,利用强连续算子半群理论证明了并联可修系统的非负解的存在唯一性,并说明了系统的算子生成一个正的强连续算子半群.

<Abstrcat> Repairable system is the main contents of the Reliability theoretical studies, it contains series system and multiple system. If one of the units in a system does work, the system works. Therefore the system is called a multiple system. In this paper, a class of system consisting of two repairable unit are discussed. First, the resolvent of principal operator is estimated. Then the density of principal operator of the system is proved. Finally, by using strongly continuous semi-group theory of functional analysis, the existence of unique positive solution of the system has been proved, and the operator of system generates a positive strongly continuous semi-group is explained.