Where does “whichever occurs first” hold for preventive maintenance modelings?

The purpose of this paper is to observe where the classical assumption “whichever occurs first” holds for preventive maintenance (PM) modelings. We firstly take up a bivariate maintenance policy where “whichever occurs first” and the newly proposed “whichever occurs last” are respectively used. Modification of PM performance is introduced into modelings to avoid interruptions of job executions, that is, PMs are done only at the end of working cycles. From the points of performability and maintenance cost, we secondly compare the optimized “first” and “last” policies in detail and find two critical points of comparisons analytically. Further, by comparing the “first” and “last” policies with the standard maintenance, modified PM costs are obtained to observe whether it is easy to save PM cost for “whichever occurs first”. For a trivariate maintenance policy, we thirdly propose an entirely new assumption “whichever occurs middle” and give another one model that considers both assumptions of “first” and “last”. We analyze maintenance probabilities for each model and then obtain directly their expected maintenance cost rates for further studies.