A model of multiple nested inspections at different intervals

Although much has been published concerning the optimality of a single‐type inspection process, relatively little attention has been paid in the literature of maintenance modelling to the practice of multiple nested inspections. In this paper a novel model addressing multiple nested inspections of production plant at different intervals is established based upon the delay time concept. A branch‐and‐bound algorithm is developed for finding the optimal intervals for all the inspections which minimizes the long‐term expected total cost per unit time. The modelling can be readily extended to model downtime or reliability. Necessary mathematics is presented and proofs are given. A numerical example is also given to illustrate the modelling and solution processes.