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.