Transient Analysis of a Two-Unit Standby System with Markovian Degrading Units

A two-unit cold standby system with Markovian degrading units and one repair facility is considered. Two types of repair are possible: preventive and corrective, where the latter is supposed to be more time consuming than the first. The system is controlled by a repair policy of control limit type: a preventive repair on the working unit is carried out as soon as the state of this unit exceeds a certain threshold unless the repair facility is occupied by the other unit. In this paper we derive explicit expressions for the Laplace transforms of the up- and down-periods of this system, which provide insight in the availability of the system and which can be used to obtain approximations for the interval availability distribution. An iterative numerical procedure is presented for the special case of generalized Erlangian distributed repair times.