Delay-time modelling of a critical system subject to random inspections

We model the inspection-maintenance of a critical system in which the execution of inspections is random. The models we develop are interesting because they mimic realities in which production is prioritised over maintenance, so that inspections might be impeded or they might be opportunistic. Random maintenance has been modelled by others but there is little in the literature that relates to inspection of a critical system. We suppose that the critical system can be good, defective or failed, and that failure impacts on production, so that a failure is immediately revealed, but a defect does not. A defect, if revealed at inspection, is a trigger for replacement We compare the cost and reliability of random inspections with scheduled periodic inspections and discuss the implications for practice. Our results indicate that inspections that are performed opportunistically rather than scheduled periodically may offer an economic advantage provided opportunities are sufficiently frequent and convenient. A hybrid inspection and replacement policy, with inspections subject to impediments, is robust to departure from its inspection schedule. (C) 2019 Elsevier B.V. All rights reserved.