由常规故障和临界人为错误引起系统故障的可修复系统的算子性质

Properties of the System Operator of the Repairable System under Common-Cause Failure and Critical Human Error

本文讨论了由常规故障和临界人为错误引起系统故障的可修复系统,通过运用C0半群的理论,证明该系统的预解正算子是稠定的,从而证明了系统算子的增长界为0。最后运用共尾概念和相关理论,证明了该系统算子的谱上界也为0。

The objective of this paper is to research a stochastic model representing system under common- cause failure and critical human error. Using C0 semigroup theory, we first prove that the system operator is a densely defined resolvent positive operator. Then, we set the adjoint operator of the system operator and its domain. So, we can prove that 0 is the growth bound of the system operator. At last, by using the concept of cofinal and relative theory we can prove that 0 is also spectral bound of the system operator.