Abstract
In this paper, two characterizations of the weak bivariate failure rate order over the bivariate Laplace transform order of two-dimensional residual lifetimes are given. The results are applied to characterize the weak bivariate failure rate ordering of random pairs by the weak bivariate mean residual lifetime ordering of the minima of pairs with exponentially distributed random pairs with unspecified mean. Moreover, a well-known bivariate aging term, namely, the bivariate increasing failure rate, is characterized by the weaker bivariate decreasing mean residual lifetime property of a random pair of minima.