A New Generalization of the Class of NBU Distributions

It is well-known that the increasing-failure-rate-average (IFRA), new-better-than-used (NBU), and new-better-than-used-in-expectation (NBUE) classes of life distributions are successive generalizations of the class of increasing-failure-rate (IFR) distributions. Further, each of the IFR, IFRA and NBU classes can be characterized in terms of the exponential distribution and certain partial orderings on the family of all distributions. It is not known, however, if the same holds for the NBUE class. This paper introduces a new generalization (called NBAFR) of the NBU class that allows a characterization in terms of the exponential distribution and a (new) partial ordering. The NBAFR class neither contains nor is contained in the NBUE class. Like the latter, the NBAFR class is preserved under the reliability operation of addition of life lengths. But unlike the NBUE, the NBAFR class is also preserved under formation of s-coherent systems - just like the IFR, IFRA, and NBU classes.