Evaluating the machine availability of machine repair problem with two failure modes under working vacation policy

This research investigates a machine repair problem consisting of operating and standby machines with heterogeneous failure modes, mode I and mode II. A repairman is responsible for repairing failed machines, and the repair rates for the two failure modes are different. When there are no failed machines in the system, the repairman will take multiple working vacations from the system. Thus, the repairman will not cease repairing failed machines during vacation periods, but instead continue to repair failed machines with a different repair rate. Once the repairman's vacation ends and no failed machines are found in the system, the repairman will take another vacation until a failed machine appears in the system. In this study, we obtain the stationary distribution of the number of failed machines in modes I and II numerically by the R software. We establish the machine availability using the steady-state probabilities and investigate its sensitivity analysis through numerical results to understand the influence of various system parameters on it.