Generalized orderings of excess lifetimes of renewal processes

Several concepts of generalized orderings and generalized ageing classes have been considered in the literature (see Fagiuoli and Pellerey, 1993, Nav Res Logist 40: 829–842). They have been used in reliability, economics and actuarial sciences. These generalized notions provide a knowledge of the intrinsic structure of the ageing and ordering properties of random variables and have become an important tool in applied probability. In this paper, we provide new results about generalized orderings of excess lifetimes at different times of a renewal process when the underlying distribution belongs to some generalized ageing class. We also derive some interpretations and give some discussions of these results.