Abstract
This paper considers anN-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 ratesa anda1, respectively. When the system is down, all the operable units have constant failure ratea2. The repair time of a failed unit has an arbitrary distribution. Using Takacs' method and a Markov renewal process, we discuss the stochastic behavior of this system and obtain the explicit formulae of the system availability and failure frequency.
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