On quantile reversed residual lifetime and its aging properties

If the random variable T denotes the lifetime (T > 0, with probability one) of a unit, then the random variable T <Subscript> (t) </Subscript>=[t − T|T ⩽ t],, for a fixed t, is known as the inactivity time or the reversed residual lifetime. In this paper, we define a new class of life distributions based on the quantile of the random variable T(<Subscript> t </Subscript>) and study its reliability properties. Some new results of the proposed class are demonstrated including some closure properties. In particular, the quantile reversed residual lifetime functions of some well-known life distributions are illustrated. Finally, we define a new stochastic ordering based on the quantile reversed residual lifetime and study its reliability properties and closure properties. Copyright Sapienza Università di Roma 2012