The exact lower confidence limit of reliability for normal stress and normal strength

For stress and strength obey normal distribution and their distributed parameters are unknown, some researchers have given approximate lower confidence limits of its reliability under these conditions. But the error of approximately confidence limits is large in the case of small samples. Based on stress-strength model and relevant statistical knowledge, the exact lower confidence limit of its reliability is presented. The proposed method is compared with three kinds of approximate limits methods. The result shows that no matter large or small the size of the sample is, the accuracy of the method mentioned in this paper is higher than those other three methods. When the size of the sample is small, it is recommended to use this proposed method; when the size of the sample is large, these three methods can be used for approximate calculation. This proposed method provides a new approach for the assessment of the reliability.