Uncertainty in Analytical Measurements: Approaches, Evaluation Methods and Their Comparison Based on a Case Study of Arsenic Determination in Rice


All measurements have uncertainty and they are not absolute. Therefore, identification, determination and evaluation of critical influencing factors based on recent approaches are important and necessary. Laboratories shall identify and evaluate all components and contributions to measurement uncertainty. In this article, two different approaches for evaluation of measurement uncertainty of arsenic in rice are studied and compared. These different approaches are GUM approach and Monte Carlo approach. The results clarified, evaluated uncertainty for the measurand was the same in the GUM and MCA, statistically and it is clarified that evaluated uncertainty by these approaches have no significant difference.

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Fig. 1


\(\rho\) :






u :

Standard uncertainty

u c :

Combined standard uncertainty


Expanded uncertainty

Ci :

Sensitivity coefficient


Coverage factor

ucal :

Calibration uncertainty

u rep :

Repeatability uncertainty

u temp :

Temperature effect uncertainty

u v :

Volume uncertainty

u m :

Mass uncertainty

u Ccal :

Calibration curve uncertainty


Temperature deviation from 20 °C

\(C_{{C_{cal} }}\) :

Sensitivity coefficient of calibration curve

Cv :

Sensitivity coefficient of volume

Cm :

Sensitivity coefficient of mass

Ccal :

Concentration from calibration curve

CF :

Final concentration


Number of measurements to determine c0


Number of measurements for the calibration

Sm :

residual standard deviation



\(s_{{\overline{x}}}\) :

standard deviation of the averages


Mean square


Degree of freedom


Sum of square


F statistics


P value

Sr :

Within-laboratory (Repeatability) standard deviation

Sl :

Between-laboratory (Intermediate) standard deviation

SR :

Reproducibility standard deviation


Number of subgroups


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  2. [2]

    ISO/IEC GUIDE 99 (2007) International Vocabulary of Metrology - Basic and General Concepts and Associated Terms (VIM).

  3. [3]

    ISO/IEC GUIDE 98-3 (2008) Uncertainty of measurement - Part 3: Guide to the expression of uncertainty in measurement.

  4. [4]

    ISO 21748 (2017) Guidance for the Use of Repeatability, Reproducibility and Trueness Estimates in Measurement Uncertainty Evaluation.

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    EURACHEM / CITAC Guide CG 4, QUAM (2012) Quantifying Uncertainty in Analytical Measurement.

  6. [6]

    EURACHEM/CITAC, Produced Jointly with EUROLAB, Nordtest and the UK RSC Analytical Methods Committee (2007) Guide Measurement Uncertainty Arising from Sampling: A Guide to Methods and Approaches.

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The authors are grateful for financial support from the Meyar Danesh Pars Company and also the University of Kashan with Grant No. of 52798.

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Correspondence to Sayed Mehdi Ghoreishi.

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Nabi, M., Ghoreishi, S.M. & Behpour, M. Uncertainty in Analytical Measurements: Approaches, Evaluation Methods and Their Comparison Based on a Case Study of Arsenic Determination in Rice. MAPAN (2021). https://doi.org/10.1007/s12647-020-00422-0

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  • Uncertainty
  • GUM approach
  • Monte Carlo approach