A delay-time model to integrate the sequence of resumable jobs, inspection policy, and quality for a single-component system

This study proposes a model that integrates the schedule of a sequence of resumable jobs and inspection policy in a critical single-component system, following a deterioration process modeled with a delay-time concept. Thus, the system can be in a good, defective or failed state. When the system is in a defective state, it decreases in product quality, which leads to an increase in the proportion of non-conforming items and rework activities. If the system fails, a minimal repair is required to restore the system to an operational condition but in a defective state. Consequently, we established a limit of m consecutive minimal repairs to prevent the system from producing a substantial proportion of non-conforming items. So, we propose a mathematical framework and a simulation model to minimize the expected total costs. Also, we develop a Genetic Algorithm to tackle medium-size instances and analyze some special cases of the model. Therefore, we solved a numerical case and performed a sensitive analysis. We compare the Genetic Algorithm with a heuristic algorithm, and our model with its straight simplification. In this last comparison, in the worst case tested, the "ignorance cost'' could reach 335%.