Note on relations between criteria for ageing

This work is focused on proving implications between criteria for ageing of a system with a well-defined survival time distribution. Specifically, two reliability measures, the mean residual lifetime (MRL) and the hazard rate (HR) are considered. The current article deals with the question of whether a specific property or criterion for ageing with respect to a reliability measure implies the same property or some other criterion with another reliability measure. Implications of various criteria, additional consequences regarding various non-parametric classes of life distributions and particular features of MRL functions are derived and discussed using a characterization result of such functions.