Dynamic proportional hazard rate and reversed hazard rate models

Cox (1972) proportional hazard (PH) model has been used to model failure time data in Reliability and Survival Analysis. Recently, proportional reversed hazard model has been analyzed in the literature. Sometimes, the hazard rate (or the reversed hazard rate) may not be proportional over the whole time interval, but may be proportional differently in different intervals. In order to take care of this kind of problems, in this paper, we introduce the dynamic proportional hazard rate model, and the dynamic proportional reversed hazard rate model, and study their properties for different aging classes. The closure of the models under different stochastic orders has also been studied. Examples are presented to illustrate different properties of the models.