NBUE and NWUE properties of increasing Markov processes

Consider a device that deteriorates in time according to an increasing Markov process so that it fails as soon as a critical threshold is exceeded. NBUE and NWUE properties of the lifetime of the device are identified to extend the existing literature on the PFr, IFR, IFRA, and NBU cases. In particular, it is shown that NBUE and NWUE characterizations can be made through a monotonicity property on the potential operator of the Markov process.