Introduction to Measurement Uncertainty

Wolfhard Wegscheider19 November 2019

Outline

What is measurement uncertainty?

Quality from a customer´s perspective

Monte Carlo simulation as a universal tool

Special case of (large) relative uncertainty

Remaining Problems: Inadequate results from

Guidelines and Standards

Error of measurement vs. Uncertainty of measurement

true value,

(total) error of measurement = random error + systematic error

uncertainty

)()()( xxxxii

Decisions under uncertainty

acceptancezone A

acceptancezone B

Burden of proof

Size of guard band g:change k or u

g = k * u = U k (1-)CIk…coverage factor

Greater kleads to better coverage

(subject to pdf)

but impairs decision process

Smaller uleads to better decisions

but makes development ofprocedures and theiroperation more costly

http://www.eurachem.org/index.php/publications/guides/uncertcompliance© W. Wegscheider, Berlin 2019

Outline

Analytical (and difference) vs. Monte Carlo

Influence factors+ uncertainties

Model ofquantity

Quantity value+ uncertainty

Probability distributionfunctions of influence factors

Model ofquantity

Probabilitydistributionfunction ofquantity value

analytical

Monte Carlo

Uncertainty and Distribution from Standard Additions

Textbook wisdom:„extrapolation“ to zero signalasymmetric results for confidence limits

Monte Carlo study with Excel add-inDetermination of Cu by flame AA

Features: preparation of standards fromsolids, partial correlations, errors in x AND y

Modelled Analytical Procedure

1000 mg/l solution

+2 mg/l Cu2+ +4 mg/l Cu2+ +6 mg/l Cu2+ +0 mg/l Cu2+

aliquots from sample

0.06 abs. 0.10 abs. 0.14 abs.0.02 abs.

regression

result

100 mg Cu

20 mg/l solution

17 s for a Monte Carlo simulation

Outline

Large relative uncertaintyHow large is large

RSD = 10%

RSD = 30%

RSD = 100%

Typical contributions touncertainty

sampling

sample preparationmeasurement

𝑠 𝑠 + 𝑠 + 𝑠

Consequences of typicalcontributions to uncertainty

• Sampling requires greatest attention• Errors in sampling cannot be recovered

in a later stage• Only the largest contributions require optimization

(Pythagoras !!!)

𝑠 𝑠 + 𝑠 + 𝑠

Determination of organo-phosphorus pesticides in bread

1. specification of measurand

2. identification of sources of uncertainty

V(op)c(ref)

recovery m(sample)

I(ref)F(homogeneity)

repeatability

m(tare)

linearity

m(gross)

linearity

repeatability

purity

m(ref)

V(ref)

3. Quantification of componentsAmended measurement equation:

)gg(10

yhomogeneit

FRecmI

Proberef

oprefopop

RSD = 27% RSD = 20%

Determination of organo-phosphorus pesticides in bread3. Combining the separate contributions

normal log-normal95% (0.36;1.56) 95% (0.44;1.63)

Outline

Standard on Standard AdditionsDIN 32633 (2013)

5x5 additions

Ideal cases s result DIN M.C.Const. uniform 0.5 a.u. 0.060 a.u. 0.058 a.u.Const. normal 0.5 a.u. 0.027 a.u. 0.026 a.u.

Real cases from DIN/PTB μg/gRh by ICPMS increasing 231.3 12.9 5.6Rh by ICPMS intern. std. 233.7 3.3 2.2

μg/mlBr´by IC variable 24.44 0.54 0.25

ICP-MS Data from DIN

NIR spectra of brick cheeseInfometrix Applications Overview 1996

„best“ wavelengthfor moisture

Calibration on wavelength 9

useless

Multivariate prediction of moisture

h …… leverage

h …… leverage vs. spectra

IUPAC Approach to „uncertainty“Pure Appl. Chem. 78, No. 3, pp. 633–661, 2006

variance of prediction

leverage * var. of conc. of standards

leverage * var. of (signals/sensitivity)

Noise of2% addedto

Spectra ofstandards

Spectra ofunknowns

Concen-tration ofstandards

Sum(IUPAC)

All three

Effect (in %moisture)

0.194 0.429 0.070 0.600 1.21

Effect as extra-RMSEP in % moisture

o The IUPAC-proposed summation does not work

o Expected reason: no allowance for significant correlations

o Full Monte-Carlo procedure is required instead

RMSEP… root mean squared error of prediction

Effect of four sampling proceduresWestad & Marini, 2015

Conclusions

CITAC/Eurachem Guides have been very wellreceivedVery good tools are available for freeRemaining problems should be tackled

Thank you for your interest

Introduction to Measurement Uncertainty - Eurachem · Introduction to Measurement Uncertainty...

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