This paper characterizes the general behaviors of the MRL (mean residual li
ves) for both continuous & discrete lifetime distributions, with respect to
their failure rates. For the continuous lifetime distribution with failure
rates with only one or two change-points, the characteristic of the MRL de
pends only on its mean and failure rate at time zero. For failure rates wit
h "roller coaster" behavior, the subsequent behavior of the MRL depends on
its MRL and failure-rates at the change points. Using the characterization,
their behaviors for the,
Weibull,
lognormal,
Birnbaum-Saunders,
inverse Gaussian,
bathtub-failure-rate,
distributions are tabulated in terms of their shape parameters. For discret
e lifetime distributions, for upside-down bathtub-failure-rate with only on
e change point, the characteristic of the MRL depends only on its mean and
the probability mass function at time zero.