This paper considers an N-unit series system supported by a warm standby unit and a single repair facility. Suppose that the operating units and the standby unit have constant failure rates a and a1, respectively. When the system is down, all the operable units have constant failure rate a2. The repair time of a failed unit has an arbitrary distribution. Using Takács’ method and a Markov renewal process, the paper discusses the stochastic behavior of this system and obtains the explicit formulae of the system availability and failure frequency.
