There is a well established literature on delay-time models of regular inspection policies where inspections may or may not be perfect, and where the initial point u of a defect arises as a homogeneous Poisson process. This paper extends the modelling in two ways. The first is to include the observed practice where the multi-component system is inspected not only on a planned basis, but also when a component fails. The second extension is to use a nonhomogeneous Poisson process to describe defect arrivals in the system. An inspection–replacement model based upon these two extensions is then developed for a multi-component system. The total expected cost per unit time is minimized with respect to the inspection intervals and the system replacement time. The likelihood function of the time of failures and the number of defects found at inspections is established, in order to estimate model parameters based upon routinely collected maintenance data. As a special case of the general model, an inspection model – based upon a homogeneous Poisson process of defects arising – is also proposed, which has a relatively simple structure. Both simulated and real-life data of failures and defects identified at inspections are used to test the models and parameter-estimating procedure.
