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

Mehdi Nabi, Sayed Mehdi Ghoreishi &Mohsen Behpour

Abstract

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.

Abbreviations

$ρ$ : Density

m: Mass

V: Volume

u : Standard uncertainty

u _{c :}Combined standard uncertainty

U: Expanded uncertainty

C_i : Sensitivity coefficient

k: Coverage factor

u_cal : Calibration uncertainty

u _rep: Repeatability uncertainty

u _temp: Temperature effect uncertainty

u _v: Volume uncertainty

u _m: Mass uncertainty

u _Ccal: Calibration curve uncertainty

ΔT: Temperature deviation from 20 °C

$C_{C_{c a l}}$ : Sensitivity coefficient of calibration curve

C_v : Sensitivity coefficient of volume

C_m : Sensitivity coefficient of mass

C_cal : Concentration from calibration curve

C_F : Final concentration

M: Number of measurements to determine c₀

N: Number of measurements for the calibration

S_m : residual standard deviation

m: slope

$s_{\bar{x}}$ : standard deviation of the averages

MS: Mean square

DF: Degree of freedom

SS: Sum of square

F: F statistics

P: P value

S_r : Within-laboratory (Repeatability) standard deviation

S_l : Between-laboratory (Intermediate) standard deviation

S_R : Reproducibility standard deviation

p: Number of subgroups

References:

[1] ISO/IEC GUIDE 98-1 (2009) Uncertainty of Measurement – Part 1: Introduction to the expression of uncertainty in measurement.

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

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

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

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

[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.

[7] JCGM 101 (2008) Evaluation of Measurement Data – Supplement 1 to the “Guide to the Expression of Uncertainty in Measurement” – Propagation of Distributions Using a Monte Carlo Method.