Residual Probability Function, Associated Orderings, and Related Aging Classes

Abstract

The concept of residual probability plays an important role in reliability and life testing. In this investigation, we study further the residual probability order and its related aging classes. Several characterizations and preservation properties of this order under some statistical and reliability operations of monotone transformation, mixture, weighted distributions, and order statistics are discussed. In addition, by comparing the original distribution with its associated equilibrium distribution with respect to the residual probability order, new aging classes of life distributions are proposed and studied. Finally, a test of exponentiality against such classes is derived and sets of real data are used as examples to elucidate the use of the proposed test for practical problems.