Machine tools with hidden defects: optimal usage for maximum lifetime value

We consider randomly failing high-precision machine tools in a discrete manufacturing setting. Before a tool fails, it goes through a defective phase where it can continue processing new products. However, the products processed by a defective tool do not necessarily generate the same reward obtained from the ones processed by a normal tool. The defective phase of the tool is not visible and can only be detected by a costly inspection. The tool can be retired from production to avoid a tool failure and save its salvage value; however, doing so too early causes not fully using the production potential of the tool. We build a Markov decision model and study when it is the right moment to inspect or retire a tool with the objective of maximizing the total expected reward obtained from an individual tool. The structure of the optimal policy is characterized. The implementation of our model by using the real-world maintenance logs at the Philips shaver factory shows that the value of the optimal policy can be substantial compared to the policy currently used in practice.