一类具有储备部件的人-机可修复系统算子性质

Properties of the System Operator of a Repairable Standby Human-Machine System

针对一类具有运行部件和储备部件,故障修复时间服从一般分布的人-机系统模型.运用C0半群的理论,证明了系统算子是稠定的预解正算子,得出了系统算子的共轭算子及其定义域,并证明了系统算子的增长界为0,最后运用预解正算子中共尾的概念及其相关理论,证明了系统算子的谱上界也是0.

This paper presents a model representing a two units active and one unit on standby human -machine system with general failed system repair time distribution .Using C0-semigroup theory , we first prove the system operator is a densely defined resolvent positive operator .Then, we obtain the adjoint operator of the system operator and its domain .Furthermore, we prove that 0 is the growth bound of the system operator .Finally, we show that0is also the upper spectral bound of the system operator using the concept of cofinal and relative theory .