Instantaneous availability model with 2-D discrete characteristics of one-unit repairable systems

The discrete-time one-unit repairable system was studied, whose lifetime, repair delay time, corrective maintenance time and preventive maintenance time are all assumed to be random variables with general discrete distributions. We investigated the relationship of system states including operational state, waiting state for repair, state for preventive maintenance, and state for corrective maintenance. Then the state transition model was built. Furthermore, we established the instantaneous availability model which has the 2-D discrete characteristics, and on the basis, we proposed the optimal maintenance interval model. Finally, numerical examples were given to illustrate the proposed models.