Inactivity Time With Applications In Reliability And Auction Theories

In this thesis, it is shown that the characterizations for DRHR class in Shaked and Shanthikumar (1994) are in fact sufficient conditions by a counter example. Sufficient conditions for DRHR and IMIT classes are given. We also investigate the inactivity time of k-out-of-n systems based on DRHR and IMIT classes. In addition, by using inactivity time to characterize the second-price closed-seal auction rent, we investigate how the variation of the auction rents reals that of populations.