On the asymptotic behaviour of mean residual life function

The mean residual life (MRL) function is very useful in defining a good decision-making criterion for replacement policies and in solving burn-in problems. Furthermore it provides a more descriptive measure of the ageing process than the hazard rate. In this paper a useful relationship between the asymptotic values of the mean residual life function and the hazard rate of a generic continuous distribution function is derived. It is also shown that the derivative of the MRL function of a positive random variable always tends to zero as t approaches infinity.