正态应力-正态强度下可靠度精确置信下限

The Exact Lower Confidence Limit of Reliability for Normal Stress and Normal Strength

针对应力和强度均服从正态分布,且二者的分布参数均未知的情况,有些学者给出了此条件下可靠度的近似置信下限,但是可靠度的近似置信下限在小样本情况下误差较大。基于应力-强度模型,结合相关统计学知识,给出可靠度的精确置信下限,同时与3种近似限方法进行了对比。结果表明:无论样本量大或者小,文中方法计算出的精度均高于3种近似限方法。当样本量较小时,推荐使用文中所给方法;当样本量较大时,可采用3种近似限方法进行近似计算。文中提出的方法可为可靠性评估提供一种新的途径。

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 stressstrength 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.