Optimal periodic preventive maintenance policy for a system subject to failures/repairs which follow the non-homogeneous pure birth process

This paper considers a periodic preventive maintenance policy for a deteriorating and repairable system. The system is subject to random failures and is repaired at each failure. To improve the reliability, at periodic timesiT(i= 1, 2, horizontal ellipsis N-1), the system is preventively maintained (PM). At the timeNTthe system is replaced. The failure/repair process between two PMs follows the Non-Homogeneous Pure Birth Process (NHPBP) which is a generalized version of the Non-homogeneous Poisson process (NHPP). The reliability improvement made by a PM action is stochastically modeled based on the properties of NHPBP. The cost for each PM depends on the reliability condition of the system at that PM time. The PM policy is characterized by the two parameters (N, T). We develop a two-stage procedure to find the optimal (N*, T*) which minimizes the long-run expected cost rate. Numerical examples are presented to illustrate the properties of the optimal policies.