具有共同分量的相关数据的加权平均

doi:10.3969/j.issn.1000-1158.2012.06.22

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摘要对比不相关数据的加权平均法,讨论了对具有共同分量的一组相关数据的加权平均法。分析了比对数据的相关性,将相关数据的不确定度分解为共同分量与不相关分量的组合。提出了具有较好可操作性的估计比对数据溯源链共同分量不确定度的简单方法。结论为加权平均应以不相关分量的不确定度为权重因素;共同分量的不确定度是“固有”的,不随参与平均计算的数据数量的增加而减小;忽略数据相关性,不仅影响加权平均的权重,进而影响平均值,也会导致平均值不确定度计算结果偏小。以压力比对为例分析了共同分量的不确定度的评定以及不同取值结果的差异。

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	原遵东
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关键词 ：计量学, 不确定度, 加权平均, 相关性, 共同分量, 比对, 参考值

Abstract：By contrasted with the weighted mean method (WMM) for uncorrelated data, the WMM for a set of correlated data with common components is studied. A simple method with manipuility is presented for estimating the uncertainty of common component of traceability chain. The weights for calculating mean, which are derived, are the uncertainties of only uncorrelated components, not the ones of entire data. The uncertainty of common component for the mean is inherent, which is not decreased with increasing the number of averaged data. It not only influences the weights and thus the mean, but also leads an underestimation for the uncertainty of mean to neglect the influence of the correlation on the weights. Take a pressure comparison for instance, the estimations for the uncertainty of common component are illustrated and their results calculated with different estimated values are given.

Key words： Metrology Uncertainty Weighted mean Correlation Common component Comparison Reference value

PACS:

TB9

作者简介: 原遵东(1960-),福建莆田人,中国计量科学研究院研究员,主要研究方向为温度计量。yuanzd@nim.ac.cn

引用本文:

原遵东,王池,林延东,李燕华. 具有共同分量的相关数据的加权平均[J]. 计量学报, 2012, 33(6): 577-582.
YUAN Zun-dong,WANG Chi,LIN Yan-dong,LI Yan-hua. Weighted Mean for Correlation Data Influenced by Common Components. Acta Metrologica Sinica, 2012, 33(6): 577-582.

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http://jlxb.china-csm.org:81/Jwk_jlxb/CN/10.3969/j.issn.1000-1158.2012.06.22 或 http://jlxb.china-csm.org:81/Jwk_jlxb/CN/Y2012/V33/I6/577