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An approach to detection capabilities estimation of analytical procedures based on measurement uncertainty

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Abstract

Detection capabilities are important performance characteristics of analytical procedures. There are several conceptual approaches on the subject, but in most of them a level of ambiguity is presented. It is not clear which conditions of measurements should be used, and there is a relative lack of definition concerning blanks. Moreover, there are no systematic experimental studies concerning the influence of uncertainty associated with bias evaluation. A new approach based on measurement uncertainty is presented for estimating quantities that characterize capabilities of detection. It can be applied to different conditions of measurement and it is not necessary to perform an additional experiment with blanks. Starting from a modelling process of the combined uncertainty of concentration, it is possible to include in the estimated quantities the effects due to random errors and the uncertainty associated to evaluation of bias. The detection capabilities are then compared with the results obtained using some other relevant approaches. Slightly higher values were obtained with the measurement uncertainty approach due to inclusion of uncertainty associated with bias.

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Abbreviations

ACS:

American Chemical Society

ANOVA:

Analysis of variance

MUA:

Measurement uncertainty approach

OLS:

Ordinary least squares

USEPA:

United States Environmental Protection Agency

VIM 3:

Third edition of the International Vocabulary of Metrology

WLS:

Weighted least squares

A :

A signal

A B :

Mean of the blank signals

A C :

IUPAC’s critical signal value

A D :

Signal of the IUPAC’s detection limit

a 0 :

Intercept of the linear regression model of u c versus concentration

a 1 :

Slope of the linear regression model of u c versus concentration

b 0 :

Regression coefficient of the Zitter and God’s regression model of u c versus concentration

b 1 :

Regression coefficient of the Zitter and God’s regression model of u c versus concentration

c :

Analyte concentration expressed as mass fraction, mass concentration or any other compositional quantity

c B :

Mean of the estimated concentrations of blank

c C :

Critical value

c D :

Detection limit

c KS :

Limit of detection according with the Kuselman and Sherman’s approach

f(cB):

Function u c = f(c) evaluated at the mean of the estimated concentrations of blank (c B)

k :

Coverage factor

MDL :

Method detection limit of the USEPA approach

m 0 :

Intercept of the linear regression model of s versus A in the IUPAC approach

m 1 :

Slope of the linear regression model of s versus A in the IUPAC approach

RSMU :

Relative standard measurement uncertainty

s :

Standard deviation of the signal

s B :

Standard deviation of blank signals

s I(TO) :

Intermediate precision standard deviation with time and operator different

s O :

Standard deviation due to operator

s r :

Repeatability standard deviation

s T :

Standard deviation due to time

t 1−α,ν :

Student’s t percentile for a level of confidence α and ν degrees of freedom

u c :

Combined measurement uncertainty

u(cr):

Uncertainty of a detection capability (c C or c D) estimated at repeatability condition of measurement

u(cTO):

Uncertainty of a detection capability (c C or c D) estimated at intermediate precision condition of measurement

u(δ):

Standard uncertainty bias estimate

α :

Probability of type I error

β :

Probability of type II error

γ r :

Detection capability (γ C or γ D) estimated from repeatability condition of measurement, expressed in mass concentration

γ TO :

Detection capability (γ C or γ D) estimated from intermediate precision condition of measurement time-operator different, expressed in mass concentration

γ USEPA :

Values of the estimated concentrations used to calculate the MDL in accordance with USEPA

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Acknowledgments

The authors express their gratitude to A. Boza, A. Montero, S. Alleyne and O. Collazo for their help in part of the experimental labour. The authors also express their deepest gratitude to the reviewers for manuscript improvement concerning language.

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Authors and Affiliations

  1. Institute of Science and Technology of Materials, University of Havana, Zapata y G, s/n, Havana, Cuba

    Juan Jiménez-Chacón & Manuel Alvarez-Prieto

Authors
  1. Juan Jiménez-Chacón
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  2. Manuel Alvarez-Prieto
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Correspondence to Manuel Alvarez-Prieto.

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Jiménez-Chacón, J., Alvarez-Prieto, M. An approach to detection capabilities estimation of analytical procedures based on measurement uncertainty. Accred Qual Assur 15, 19–28 (2010). https://doi.org/10.1007/s00769-009-0608-6

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