Developing and testing the delay-time model

This paper further develops the basic delay-time model for inspections of repairable machinery described in a recent paper by Baker and Wang. In the author’s earlier work, one of a set of simple models was selected and fitted to objective data by minimizing the Akaike Information Criterion. In the present work, several extensions to the basic model are derived, which relax earlier model assumptions, and are designed to cope with the complexities of real-world situations. These extensions include allowing the age of a machine to influence both the period u from replacement of a component to visibility of a defect, and the subsequent period h to failure; allowing an inspection to have a hazardous or beneficial effect on the lifetime of a component; and allowing several mechanisms that induce a correlation between the two hitherto independent periods u and h. The resulting models were fitted to objective data, and it was found that some model extensions improved the fit for particular components. In general, the authors conclude that a broad range of models should be explored. This is necessary both to capture the complexity of real data, and also to give confidence in the adequacy of simpler models.