A Bayesian positive dependence of survival times based on the multivariate arrangement increasing property

We introduce a new notion of positive dependence of survival times of system components using the multivariate arrangement increasing property. Following the spirit of Barlow and Mendel (J. Amer. Statist. Assoc. 87, 1116–1122), who introduced a new univariate aging notion relative to exchangeable populations of components, we characterize a multivariate positive dependence with respect to exchangeable multicomponent systems. Closure properties of such a class of distributions under some reliability operations are discussed. For an infinite population of systems our definition of multivariate positive dependence can be considered in the frequentist’s paradigm as multivariate totally positive of order 2 with an independence condition. de Finetti(-type) representations for a particular class of survival functions are also given.