Stochastic properties of two general versions of the residual lifetime at random times

This paper studies 2 different versions of the general residual lifetime at random times in the context of statistical dependence between the system lifetime and the random time. We prove that the class of residual lifetimes with a semiindependent random age is equivalent to the class of residual lifetimes at independent random times. Additionally, we conduct stochastic comparisons of the 2 versions of the general residual lifetime at random times. Several numerical examples are presented to illustrate the ordering results.