修理工带休假的两同型部件冷贮备可修系统的指数稳定性
Exponential Stability of a Cold Standby Repairable System with Two Identical Components and a Repairman on Vacation
摘要: 本文假设部件工作时间和修理工空闲时间服从指数分布，部件维修时间和修理工休假时间服从一般分布。把系统方程化为Cauchy问题，通过C
0半群理论得到系统动态解的性质，再分析算子的性质得到算子的本征值，从而得到修理工带休假的两同型部件冷贮备可修系统的指数稳定性。
Abstract:
This paper assumes that component working time and repairman idle time obey exponential distribution, component maintenance time and repairman vacation time obey general distribution. The system equation is transformed into the Cauchy problem, the properties of the dynamic solution of the system are obtained by the theory of C0 semigroups, and then the eigenvalues of the operator are obtained by analyzing the properties of the operator, the exponential stability of the cold standby repairable system with two identical components is obtained.
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