The NBUL class of life distribution and replacement policy comparisons

Let X and X τ denote the lifetime and the residual life at age τ of a system, respectively. X is said to be a NBUL random variable if X τ is smaller than X in Laplace order, i.e., X τ ≤ L X . We obtain some characterizations for this class of life distribution by means of the lifetime of a series system and the residual life at random time. We also discuss preservation properties for this class of life distribution under shock models. Finally, under the assumption that the lifetimes have the NBUL property, we make stochastic comparisons between some basic replacement policies.