New better than used in expectation processes

The paper studies the new better than used in expectation (NBUE) and new worse than used in expectation (NWUE) properties of Markov renewal processes. It shows that a Markov renewal process belongs to a more general class of stochastic processes encountered in reliability or maintenance applications. The paper presents sufficient conditions such that the first-passage times of these processes are new better than used in expectation. The results are applied to the study of shock and repair models, random repair time processes, inventory, and queueing models.