Optimal inspection policy for a single-unit system considering two failure modes and production wait time

In many real production systems, a system may be stopped due to a lack of demand or exhaustion of raw materials. This is known as production wait and provides a good opportunity for maintenance. Meanwhile, the increased complexity of the modern machines brings new challenges for modeling and analyzing their failure behaviors. To address these real-world problems, this research considers a single-unit system that may fail due to either hard failures or soft failures. The wait time of a system is utilized to conduct inspections and maintenance. The system is replaced when a defect is found during an inspection, a failure occurred or a pre-specified age threshold is reached, whichever comes first. The cost model, which is the long-run maintenance cost per unit of time, is derived. The optimal periodical inspection interval and the threshold age to minimize the long run maintenance cost per unit of time is then obtained. A case study is conducted to demonstrate the proposed maintenance model. The study shows using the proposed maintenance model can reduce the cost. Sensitivity analysis illustrates how each cost parameter affects the optimal inspection interval and the optimal age threshold.