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.

A method is presented to calculate approximate value of confidence lower limits making use of reliability test data of torpedo components.

For the given reliability and confidence level, the point estimate and four approximate confidence lower limits of the storage time are obtained, and their covering ratio to each other is compared.

The estimate and lower confidence limit of reliability for pass-fail component;

The lower confidence limits of storage reliability for exponential type products were studied.

Also the paper discusses the relationship between lower confidence limits and PCIs,as well as the percentage of unqualified products in process.

Under the assumption that every person s loss fee is a random variable which changes in accordance with the distribution E(λ) and the valid times of claim change in accordance with the distribution of random variables,this paper provides the upper confidence limits of mean total insurance loss.

This paper preliminarily studies the distribution of the total loss fees of insurance and the upper confidence limits of the mean total loss fees of insurance.