﻿ 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

Pure Mathematics
Vol.05 No.05(2015), Article ID:16093,6 pages
10.12677/PM.2015.55032

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

Shuang Yuan, Hui Wang

Harbin Normal University, Harbin Heilongjiang

Email: yuanshuang0556@126.com

Received: Sep. 5th, 2015; accepted: Sep. 22nd, 2015; published: Sep. 25th, 2015

ABSTRACT

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.

Keywords:Repairable Systems, Resolvent Positive Operator, Growth Bound, Cofinal, Upper Spectral Bound

Email: yuanshuang0556@126.com

1. 引言

2. 系统介绍

1)

2)

3)

，则存在使。令，显然 (i=3,4)。根据文献[8] 知：

，因，故，所以当时，

X的共轭空间为，其中，显然为Banach空间(文献[7] )。因为A + E为X的子空间，X存在共轭空间，则不妨假设的共轭空间且的子空间。

Properties of the System Operator of the Repairable System under Common-Cause Failure and Critical Human Error[J]. 理论数学, 2015, 05(05): 227-232. http://dx.doi.org/10.12677/PM.2015.55032

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