有关正态分布的小样本可靠性评估

Reliability assessment based on small samples of normal distribution

当可靠度特征量满足正态分布时,其分布参数(μ,h)的共轭型先验分布为正态伽玛分布。特征量的主观先验信息及其随机自变量的试验信息可被利用以克服小样本统计推断的困难,借助于最大信息熵原理和矩拟合法,将这两类信息转化为分布参数(μ,h)的贝叶斯先验分布,然后利用该先验分布或它与试验信息结合而形成的后验分布进行可靠性评估。介绍了计算方法并给出两个算例。

When the pertinent parameter involved in reliability definition complies with normal distribution, the conjugate prior of its distributing parameters (μ,h) is of normal-gamma distribution. With the help of maximum entropy and the moments-equivalence principles, the subjective information of the parameter and the sampling data of its independent variables are transformed to a Bayesian prior of (μ,h). The desired estimates are obtained from either the prior or the posterior which is formed by combining the prior and sampling data. Computing methods are. described and examples are presented to give demonstrations.