A model of multiple nested inspections at different intervals

Abstract

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. Scope and purpose The performance of a production plant can be improved by appropriate inspection scheduling. This paper presents a novel model and an associated algorithm for obtaining the optimal solution of an inspection scheduling problem of a production plant, that is, for determining the optimal inspection intervals in terms of a criterion of interest. It is assumed that multiple nested inspections at different intervals are performed and the modelling objective is to find the optimal multiple nested inspection intervals, which minimize the long-term expected total cost per unit time. The model established is based upon the delay time concept and is the very first to address and optimize multiple nested inspection simultaneously. The model and algorithm developed in this paper are useful both to researchers and practitioners in which mathematics behind the model and algorithm are fully explored and the algorithm can be readily used as a tool in aid of inspection decision making if the modelling assumptions are satisfied.