Aging in varying environment

An impact of environment on mortality rates is often modeled by a proportional hazards model. This model describes the memory-less property, when the mortality rate at a given instant of time depends only on current environment and does not depend on a history. In the presence of aging (degradation) this assumption is usually unrealistic and historydependent models should be considered. The simplest stochastic degradation model is the accelerated life model. We discuss both models and their generalizations for the cohort setting and apply the developed approach to the period setting for the case when environment (stress) is modeled by functions with switching points (jumps in the level of stress). We also consider notions of individual and population aging in a variable environment and suggest some stochastic measures suitable for the corresponding stochastic ordering.