AGING FUNCTIONS AND MULTIVARIATE NOTIONS OF NBU AND IFR

Ford >= 2, let X = (X(1),...,X(d)) be a vector of exchangeable continuous lifetimes with joint survival function (F) over bar. For such models, we study some properties of multivariate aging of (F) over bar that are described by means of the multivariate aging function B((F) over bar), which is a useful tool for describing the level curves of (F) over bar. 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.