The main purpose of this work is to model a continuously monitored deteriorating system by using a bivariate Birth/Birth-Death process. The system consists of M identical, independent units and the deterioration process of each unit is a three-state continuous time-homogeneous Markov chain with two working states and a failure state. The production rate of each unit varies in different working states and the demand rate of the system is assumed to be constant. The cost of sending maintenance crew to perform maintenance is high, so simultaneous replacement of several units can be cost-effective. Maintenance is initiated when the process makes a transition into a state with a pre-specified number of failed units. The maintenance policy prescribes corrective replacement of failed units as well as preventive maintenance of unhealthy units. The optimal maintenance policy is derived such that the long-run expected average cost per unit time is minimized, according to the renewal theory. Finally, a numerical example of a multi-unit system is provided.
