Large sample nonparametric estimation of the mean residual life

Mean residual life has been applied in a wide variety of areas, including engineering research, biomedical studies, actuarial science, etc. When the functional form of the underlying distribution is given, estimation of the mean residual life is equivalent to estimation of the parameters of the distribution. In this paper, a nonparametric approach for constructing confidence intervals for the mean residual life of a one-unit system is developed. A generalization of the technique to complex systems is addressed. Both censored and uncensored data are considered. Nonparametric confidence intervals for the mean residual life of the lifetime between failures in a stationary renewal process are also derived. Numerical studies and applications of the confidence intervals derived are presented.