A cold system with two different components and a single vacation of the repairman

In this paper, we model a cold standby repairable system with one repairman. Suppose that the system consists of two dissimilar components and one repairman, in which component 1 is the major working unit and component 2 is the cold stand-by unit, component 1 has priority in use and repair; then the repairman takes a single vacation. Under these assumptions, we derive a model of partial differential equations. Furthermore, using the functional analysis method, we discuss the dynamic asymptotical behavior of the system and get some reliability indices. Finally we analyze a variety for indices of reliability and profit of the system with change of other parameters of the system by numerical simulation.