On bending (down and up) property of reliability measures in mixtures

Abstract

In this paper, we study the bending property of the failure rate, reversed hazard rate, mean residual life and mean inactivity time in mixtures. For those four reliability measures, the weak and strong bending properties are studied and discussed, respectively. The results are illustrated with suitable examples, where most of them are relative to the model of proportional reliability measures. © 2017, Springer-Verlag Berlin Heidelberg.