Aging functions and multivariate notions of NBU and IFR

For d≥2, let X=(X1, , Xd) be a vector of exchangeable continuous lifetimes with joint survival function F̄. For such models, we study some properties of multivariate aging of F̄ that are described by means of the multivariate aging function BF̄, which is a useful tool for describing the level curves of F̄. Specifically, the attention is devoted to notions that generalize the univariate concepts of New Better than Used and Increasing Failure Rate. These multivariate notions are satisfied by random vectors whose components are conditionally independent and identically distributed having univariate conditional survival function that is New Better than Used (respectively, Increasing Failure Rate). Furthermore, they also have an interpretation in terms of comparisons among conditional survival functions of residual lifetimes, given a same history of observed survivals. Copyright © Cambridge University Press 2010.