基于小样本的试验系统可信度评估方法

针对小样本试验数据信息匮乏、难以利用概率统计方法进行可信度评估的问题，将重抽样方法与小样本区间估计方法相融合，提出了小样本试验系统新型可信度评估方法。利用重抽样理论，获取多个具有相同样本量的相似小样本。根据灰色系统理论，提出了改进的灰色置信度及置信区间的定义及计算方法。并在此基础上通过求公共区间的方式计算原小样本数据的灰色置信区间。该置信区间在相同的置信度下，区间宽度更窄，精度更高。通过算例仿真，验证了上述方法的合理性、有效性，对工程试验中的小样本数据系统评估提供了一定的方法指导。 

Approach of credibility evaluation for testing system with small samples

Aimed at the problem that the small sample test data are lack of information and it is difficult to use probability statistic method for interval estimation, a novel approach of credibility evaluation for small sample testing system is proposed by integrating the repeated sampling method and the small sample interval estimation method. Many similar small samples with the same sample size are obtained using the theory of repeated sampling. According to the grey system theory, an improved definition and calculation method for grey confidence level and grey confidence interval is proposed. On this basis, the common area of the grey confidence intervals of many small samples is calculated, which is the grey confidence interval for the original small sample data. Under the same confidence level, the above confidence interval has narrower interval width and higher precision. The rationality and validity of the above method is verified through example simulation, which provides certain method guidance for small sample data system evaluation in engineering test.