Reliability Analysis of a Cold Standby Repairable System with Repairman Extra Work

作     者：ZHANG Xin 

作者机构：Department of Basic Courses Beijing Union University Academy of Mathematics and Systems Science Chinese Academy of Sciences 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报(英文版))

年 卷 期：2015年第28卷第5期

页      面：1015-1032页

核心收录：

学科分类：080705[工学-制冷及低温工程] 0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 07[理学] 08[工学] 0807[工学-动力工程及工程热物理] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China under Grant No.11201007 

主　　题：C0-semigroup exponential stability repairable system resolvent positive operator 

摘      要：This paper deals with a cold standby repairable system with two identical units and one repairman who can do extra work in idle time. The authors are devoted to studying the unique existence and exponential stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.