【摘要】 "JCGM 100:2008"的温度计修正值不确定度评定案例中,模型为bt=y1+y2(t-20),自变量(t-20)与因变量修正值bt=(tR-t)间不独立,实质上选温度计示值t作自变量、标准值tR作因变量,前者的误差影响显著大于后者,这与应选误差影响可忽略的作自变量的原则相悖.案例中评定b(t′)的不确定度ubt′错用了求预测值置信区间的预测模型,应先改用tR作自变量拟合、再求反预测值tR(t′)及其置信区间的校准模型,我们在预测和校准两种情况下计算了ubt′以作比较.案例中limn→∞ubt′=0有逻辑性瑕疵.对自变量等距分布、自变量在区间两端集中各半这两种情形,算出其斜率标准差的期望值之比约槡3,否证了"测散布数据最小二乘拟合主要为减小因变量的独立同分布随机误差影响"的命题,初步导出"主要为减小因变量的具有随机性的未定系差分量影响"的推论,质疑了高斯-马尔科夫假定的普适性.考虑因变量标准差包含两类分量,提出了预测或校准(反预测)模型下的置信区间的调和近似算式.更多还原

【Abstract】 In the hand book JCGM 100:2008(i.e.,GUM 2008,the revised version of GUM 1995),the uncertainty evaluation of the correction to thermometer calibration was an exemplary case,where the model bt=y1+y2(t-20)was adopted.In this model,however,the correction of the dependent variable,bt=(tR-t),was correlated to the argument(t-20).In actual applications,the uncertainty of thermometer readout t used as the argument was evidently larger than that of the standard reference tRused as the dependent variable.This contradicts with the principle that the uncertainty of the argument was usually small or negligible.In addition,the uncertainty of b(t′),ubt′in the case was evaluated by improperly using the model which was indeed applicable for predicting the confidential interval of the predicted value.Now,it was suggested to use the standard procedure in which the linear fit was conducted using tR as the argument and the inverse predictedvalue tR(t′)and its confidential interval were then evaluated.We further compared the calculated ubt′between the two situations,i.e.,the prediction and the calibration.It was further pointed out that the conclusion of lim n→∞ubt′=0,was logically incorrect.It was demonstrated that the expected value of the standard deviation of the slope was larger in the case where the arguments distributed equidistantly by a factor of 31/2 compared to the case where the arguments situate in the vicinity of the two ends of the fitting range.The results clarify that the leasts quare fitting to separately distributed data points is mainly to reduce the influence originating from the undefined systematic error components instead of from the random error components.The universality of the Gaussian-Markov assumption was questioned.Consideringthatthestandard deviation ofthe dependent variableincludestwocomponents,we propose a novel approximate formula to derive the confidential interval in the prediction model and the calibration model(inverse prediction model).更多还原