If $X$ is a life distribution with finite mean then its mean residual
life function (MRLF) is defined by $M(x)E[X-x|X>x]$. It has been found
to be a very intuitive way of describing the aging process.  Suppose
that $\mone$ and $\mtwo$ are two MRLF's, e.g., those corresponding to
the control and the experimental groups in a clinical trial. It may be
reasonable to assume that the remaining life expectancy for the
experimental group is higher than that of the control group at all
times in the future, i.e., $\mone(x)\le\mtwo(x)$ for all $x$.
Randomness of data will frequently show reversals of this order
restriction in the empirical observations. In this paper we propose
estimators of $\mone$ and $\mtwo$ subject to this order restriction.
They are shown to be strongly uniformly consistent and asymptotically
unbiased. We have also developed the weak convergence theory for these
estimators. Simulations seem to indicate that, even when $\mone\mtwo$,
both of the restricted estimators improve on the empirical
(unrestricted) estimators in terms of mean squared error, uniformly at
all quantiles, and for a variety of distributions.