In many situations where system failures occur the concept of 'minimal repair' is important. A minimal repair occurs when the failed system is not treated so as to return it to 'as new' condition but is instead returned to the average condition for a working system of its age. For a system with decreasing reliability it will become increasingly expensive to maintain operation by minimal repairs, and the question then arises about when the entire system should be replaced.
In this research we suggest the minimal repair/replacement model with down times. The minimal repair/replacement model based on the system passage time: a system undergoes minimal repair during [0,T] with a failure replacement on the first failure during [T, τ], or preventive replacement if the system is still functioning at τ.
We consider three policies with down times. One is age replacement, another is the suggested model based on the system passage time in this research, and the other is the minimal repair/replacement model based on the system operating time. Numerical examples are performed to compare the three models and conclusions are drawn from these comparisons regarding the relative effectiveness of the policies.