Replacement policies with general models

It would be of interest to formulate the general replacement models, combing the constant and random policies to satisfy the commonly planned and randomly needed replacement times. This paper takes up age and periodic replacement models again to formulate their general models when replacement actions are also conducted at random times The classic approach of whichever occurs first and the newly proposed approach of whichever occurs last are used for such general models, whose models are named as replacement first, modified replacement first, replacement last and modified replacement last, respectively. We compare all of the replacement models analytically and numerically to find which policy should be selected from the viewpoint of cost. It is shown that the modified replacement policies with combined approaches of whichever occurs first and last are more economical than others. In addition, the replacement models with different replacement costs are extended for further studies.