Relative Ageing of Population and Subpopulations in Proportional Hazard Frailty Models

This paper studies various relative ageing notions of the proportional hazard frailty model represented by random variable X with the random variable \(X|\varTheta =\theta \) . In particular, we study how the overall population ages relative to the ageing of its subpopulation with certain frailty under various notions of relative ageing. In addition, we will generalize some of the available results in the literature. The principle developed in the paper could be useful in comparison of ageing any two systems such as sensors, actuators, accessories, while making selection.