|
|
|
| GUM and Analysis of Measurement Uncertainty Evaluation Using Observation Equation |
| HU Hong-bo,SUN Qiao,DU Lei,FAN Zhe,BAI Jie |
| National Institute of Metrology, Beijing 100029, China |
|
|
|
|
Abstract The process of uncertainty evaluation methods based on GUM serials and Bayesian analysis is compared, and it is derived that GUM uncertainty evaluation is based on measurement equation, and a forward uncertainty evaluation method, while Bayesian analysis is an inverse uncertainty evaluation based on observation equation. A probabilistic approach to analysis and comparison is used to the two approaches. It’s concluded that for linear model and with non-informative prior for the measurand both analysis can be applied and get the same result, but for non-linear model, only GUM S1 method and Bayesian analysis give the same result. The results are illustrated by examples.
|
|
Received: 25 July 2016
Published: 11 August 2017
|
|
|
|
Corresponding Authors:
Hong-Bo HU
E-mail: huhb@nim.ac.cn
|
|
|
|
［1］BIPM, IEC, IFCC, ISO, IUPAC, IUPAP and OIML. Guide to the Expression of Uncertainty in Measurement. International Organization for Standardization, Guide to the Expression of Uncertainty in Measurement［S］.International Organization for Standardization, Geneva, Switzerland, 2008.
［2］BIPM, IEC, IFCC, ISO, IUPAC, IUPAP and OIML. Guide to the Expression of Uncertainty in Measurement. International Organization for Standardization, Evaluation of measurement data-Supplement 1 to the “Guide to the expression of uncertainty in measurement”-, Propagation of Distribution Using a Monte Carlo method［S］. International Organization for Standardization, Geneva, Switzerland, 2008.
［3］BIPM, IEC, IFCC, ISO, IUPAC, IUPAP and OIML. Evaluation of measurement data-Supplement 2 to the “Guide to the expression of uncertainty in measurement”-Extention to any number of output quantities［S］. International Organization for Standardization, Geneva, Switzerland, 2011.
［4］费业泰. 误差理论与数据处理［M］. 北京:机械工业出版社,2015.
［5］倪育才. 实用测量不确定度评定［M］. 北京:中国计量出版社,2004.
［6］Weise K, Wger W. A Bayesian theory of measurement uncertainty［J］. Measurement Science and Technology,1993,4(1):1-11.
［7］Lira I,Grientschnig D. Equivalence of alternative Bayesian procedures for evaluating measurement uncertainty［J］. Metrologia,2010,47(3):334-336.
［8］Lira I, Wger W. Comparison between the conventional and Bayesian approaches to the evaluate measurement data［J］. Metrologia,2006,43(4): 249-259.
［9］Calonico D, Levi F, Michel R, et al. Bayesian inference of a negative quantity from positive measurement results［J］. Metrologia,2009,46(3): 267-271.
［10］胡红波,孙桥,杜磊. GUM S1与基于贝叶斯方法的不确定度评估比较［J］. 计量学报,2017, 38(4): 517-520.
［11］Possolo A, Toman B. Assessment of measurement uncertainty via observation equations［J］. Metrologia,2007,44(6): 464-475.
［12］韦来生,张伟平. 贝叶斯分析［M］. 合肥:中国科学技术大学出版社,2015.
［13］姜瑞,陈晓怀,王汉斌,等. 基于贝叶斯信息融合的测量不确定度评定与实时更新［J］. 计量学报,2017, 38(1): 123-126. |
|
|
|
2017, Vol. 38 
