Maintenance of a device with age-dependent exponential failures

The paper considers a device that deteriorates over time according to a Markov process so that the failure rate at each state is constant. The reliability of the device is characterized by a Markov renewal equation, and an IFRA (increasing failure rate on average) property of the lifetime is obtained. The opitmal replacement and repair problems are analyzed under various cost structures. Furthermore, intuitive and counterintuitive characterizations of the optimal policies and results on some interesting special problems are presented.