Abstract
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.
Highlights
High-precision machining refers to cutting metal or other rigid materials with tolerances in the single-digit micron range; it is used in many areas with stringent quality requirements such as aerospace, electronics, defense, and medical technology (Groover, 2016)
We study the inspection and retirement decisions for machine tools that go through a hidden defective phase that can only be detected via costly inspections
The products processed by a defective tool do not necessarily generate the same reward obtained from a normal tool and a tool failure can be very costly
Summary
High-precision machining refers to cutting metal or other rigid materials with tolerances in the single-digit micron range; it is used in many areas with stringent quality requirements such as aerospace, electronics, defense, and medical technology (Groover, 2016). The company faces the problem of finding the optimal tool usage policy, which specifies when to execute an inspection based on the number of products produced since the tool’s last inspection and during its entire lifetime. This problem is relevant for many other applications where capital assets generate a reward at every unit of usage under the risk of a costly failure and require inspections to reveal their true conditions. Assuming that the amount of products the tool can process in the normal and defective phases have general probability distributions, we provide a structural analysis of the optimal tool-usage policy.
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