A well known sufficient condition for the mean residual life order of two random variables is the hazard rate order of the two random variables. The hazard rate order is characterized by the monotonicity of the ratio of the two survival functions. However in many cases this ratio is non monotone...

The total time on test transform has been used in reliability to compare two random lifetimes. Despite that it has been used widely in this context, it is not very clear in which sense the random variables are being compared. In this paper we provide a characterization which reveals the true...