Repair policies for additively degrading machines

This paper describes a method for determining repair policies for machines whose output degrades additively over time. The novelty of the models is that they consider both the state of the machines as well as the state of the repair facility when making repair decisions. The objective in the models is to maximize long-run production. In one model, we approximate the queue waiting time by a geometric random variable, while in the second model we approximate the waiting time by a sequence of geometric random variables (with different means). We show that as the average repair queue increases, the decision to repair must be made earlier. In addition, we show empirically that the simple geometric waiting time approximation becomes less accurate as the queue length increases and that the approximation understates the expected long-run output of the machine. A plastic moulding facility is used to motivate the problem. Computational results using industry supplied data are presented. The results indicate that substantial (10-20%) productivity improvement can be realized using the derived repair policies instead of policies that do not consider the repair queue.