On the optimal policies of an exponential machine repair problem

We consider an exponential repair model with s machines and one repairman. The machines' failure rates are equal but the repair rate may change from machine to machine. The repairman repairs the failed machines one at a time and in the course of his work he may even interrupt repairing one machine and start another. We compare repair policies and prove an optimality result by means of stochastic order. The proof is based on representing the compared models simultaneously in a special way and comparing then the sample paths of the interesting stochastic processes.