Optimal replacement schedule in a deteriorating production system with deterministic, random lead time for replacement

This study investigates the replacement schedule for a production system with a non-repairable key module that deteriorates over time, and is subject to random failure. We examine the case where replacing the key module requires lead time for preparing such replacement. Our aim is to determine the cost-minimizing schedule point that signals the point in time when the preparation of key module replacement shall start. We propose two models with deterministic lead time, and two models with random lead time in response to whether or not a prespecified quality level shall be met during a system operating cycle. The numerical results demonstrate that longer expected lead time advances the optimal schedule points, and increases the expected system costs per unit time in all models, while a higher variation of lead time advances the optimal schedule points, and increases the expected system costs per unit time in the models with random lead time. The numerical results also reveal that, relaxing the constraint of meeting a prespecified quality level, even in the presence of penalty, may be more economical than having this constraint. Our findings shed light on system maintenance with uncertainties in the activities required prior to component replacement.