Mean residual life of lifetime distributions

Abstract

This paper characterizes the general behaviors of the MRL (mean residual lives) 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 depends only on its mean and failure rate at time zero. For failure rates with `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 discrete lifetime distributions, for upside-down bathtub-failure-rate with only one change point, the characteristic of the MRL depends only on its mean and the probability mass function at time zero.