We consider the reliability of one random variable relative to another, when the variables are continuous and take values in an interval [a, b). We give definitions and characterizations for the exponential property and the standard aging properties IFR, IFRA, and NBU. The exponential property defines an equivalence relation on the distributions, and then each of these aging properties defines a partial order on the distributions, modulo the exponential equivalence. We give a set of conditions that must be satisfied for a general aging property to define such a partial order and show that these conditions are not satisfied by the NBUE property. Several parametric families of distributions are considered.
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