Abstract
For $d\geq2$, let $\mathbf{X}=(X_{1},\dots,X_{d})$ be a vector of exchangeable continuous lifetimes with joint survival function $\overline{F}$. For such models, we study
some properties of multivariate ageing of $\overline{F}$ that are described by means of the multivariate ageing function $B_{\overline{F}}$, which is a useful
tool for describing the level curves of $\overline{F}$. 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.