An aperiodic inspection and replacement policy based on the delay-time model with component-lifetime heterogeneity

Inspection of ageing systems is important in practice, and many models have been developed to study inspection policies. However, the state-of-art still imposes strong assumptions. In this paper, we relax the assumption of periodic inspections in the framework of an inspection and age replacement policy for a system with three states: good, defective and failed. The three-state system characterizes the delay-time model. We compare our proposed model (aperiodic inspections) with the industry standard model (periodic inspections) under two different scenarios, i.e. perfect and imperfect inspections, using a numerical example and the cost-rate in a renewal-reward formulation. The results demonstrate savings of up to 6.4% in total maintenance costs, highlighting the importance of flexibility in inspections. This flexibility is particularly useful for accommodating heterogeneity of component lifetimes specially in mixed populations of “weak” and “strong” components. Furthermore, the cost-rate can increase by up to 15% when inspection errors are ignored. These errors have significant impacts as they can result in renewing the component at inappropriate times or missing the opportunity to do so. Also, the impact of defective costs becomes more pronounced when inspection errors are not taken into account.