An overview of the recent advances in delay‐time‐based maintenance modelling

Industrial plant maintenance is an area which has enormous potential to be improved. It is also an area attracted significant attention from mathematical modellers because of the random phenomenon of plant failures. This paper reviews the recent advances in delay‐time‐based maintenance modelling, which is one of the mathematical techniques for optimising inspection planning and related problems. The delay‐time is a concept that divides a plant failure process into two stages: from new until the point of an identifiable defect, and then from this point to failure. The first stage is called the normal working stage and the second stage is called the failure delay‐time stage. If the distributions of the two stages can be quantified, the relationship between the number of failures and the inspection interval can be readily established. This can then be used for optimizing the inspection interval and other related decision variables. In this review, we pay particular attention to new methodological developments and industrial applications of the delay‐time‐based models over the last few decades. The use of the delay‐time concept and modeling techniques in other areas rather than in maintenance is also reviewed. Future research directions are also highlighted.