Optimization normal availability of a cold standby system with priority

摘要

In this paper we consider an optimization problem for a deteriorating cold standby repairable system that consists of two dissimilar components and one repairman. Suppose that the life of each component satisfies the exponentially distribution and repair time of the component satisfies the general distribution, the component 1 has priority in use and repair. Firstly, a mathematical model is built via the differential and partial differential equations, and some basic result such as the existence and uniqueness of the solution, the non-negative steady-state solution and the exponential stability of the system are derived. Based on the stability result, we discuss an optimization problem about the normal availability of the system.