In the theory and practice of life insurance, computing the average future lifetime is very important, under the condition of Balducci assumption, a concrete formula of actuarial calculations of the average future lifetime can be provided, which is very signficant in eslimuting average future lifetime if the sample data is available.

Invariability of orderly connections of decreasing mean residual life;

The mean residual life of complex system is an important reliability index which is focused on very much in engineering, but it is rarely studied so far.

According to the study of unrepairable product residue mean life,based on the mathematical description of the residue mean life and the basic knowledge of reliability and mathematical statistics,a method is deduced to assess the confidence lower limit for the mean residual life,and an engineering instance is analyzed.

In this paper, the quasi-moment estimators of the parameters are proposed based on the zero-failure data in Weibull distribution according to the concept "mean residual lifetime".

When the Weibull distribution is transformed to exponential distribution or uniform distribution under multiply type -I, we can use the mean residual lifetime to construct sample moment.

It is shown that,under homogeneous Poisson shock model,the lives of components will increase in the sense of expectation ordering,reversed failure rate ordering,reversed mean residual life ordering,increase concave ordering and Laplace transform ordering if the number of shocks which cause the failure of the components increases in the sense of corresponding stochastic orderings.

As an application, the rates of consistency for the estimator of mean residual life function are showed.