The cost function for the preventive - maintenance replacement problem

Abstract

Let a discounted continuous review preventive-maintenance replacement model be such that its total
discounted cost is given by means of two functional equations. We assume that downtime is caused by
equipment breakdowns, and the length of a given downtime is the time necessary to repair the equipment
and set it back in operation. The periodic preventive replacement policy is to replace the equipment by a
new identical equipment when service age X is reached, or when the equipment fails.