The single machine repairable system with service breakdown

This paper studies the single machine repair system, There are one unreliable machines and one unreliable servicing facility in the system. The servicing facility maintain the failure machines and may breakdown itself. The distributions of time lasting are exponential distributions. The servicing facility breakdown rates may be different between busy and idle time. The steady state and transient state characters of the system are given. An illustrative numerical example is presented.