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Transcript of Use of Measurement Uncertainty Information in Compliance Assessment of Chemical Results D. Theodorou...
Use of Measurement Uncertainty Information in Compliance
Assessment of Chemical Results
D. Theodorou
Athens, October 2008
What is not uncertainty !
• Accuracy: accuracy is not a quantifiable term
• Error: result of a measurement minus the true value of the measurand
idealized concepts
What is uncertainty
a parameter associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand (ISO Guide to the Expression of Uncertainty in Measurement)
Result: 20 ± 3 mg
Uncertainty = tolerance interval
The true amount is between 17 and 23 mg
Uncertainty of Chemical Measurements
There is always experimental variations when we make a measurement
Typical Sources of Uncertainty in Chemical Analyses•SamplingStorage ConditionsInstrument effects (e.g. calibration, accuracy, carry over effects)Reagent purityAssumed stoichiometry (e.g. incomplete or side reactions)Measurement conditions (e.g temperature, humidity)Sample effects (e.g. recovery - matrix effects)Computational effects (e.g calibration model, truncation / round off)Blank correctionOperator effectsRandom effects
Type A &Type B contributions
Overall Estimate of Uncertaintyor Expanded Uncertainty
Eurachem/CITAC Guide
Combined Uncertainty
coverage factor, k
Typical Uncertainty Statement
Total cadmium content (Cd): 328 μg·kg-1
Measurement Uncertainty: 27 μg·kg-1 (8,2%)
The stated uncertainty is an expanded measurement uncertainty (U). It was obtained by multiplying the combined standard uncertainty uc with a coverage factor k equal to 2. This corresponds approximately to a 95 % confidence interval.
Procedures for the Estimation of Measurement Uncertainty
• ISO Guide to the expression of measurement uncertainty (ISO GUM)
• EURACHEM Guide to quantifying uncertainty in analytical measurement
• Use of collaborative trial data – ISO 5725 critical differences
• ISO/TS 21748 – Guide to the Use of Repeatability, Reproducibility and Trueness Estimates in Measurement Uncertainty Estimation
• Concept established by Commission Decision 2002/657/EC implementing Council Directive 96/23/EC concerning the performance of analytical methods and the interpretation of results
• AOAC INTERNATIONAL approach
• Internal quality control approach
• NMKL (Nordic Committee on Food Analysis) approach
• Microbiological Analyses (ISO/TS 19036, Niemelä Guide)
• Monte Carlo Simulation (ISO GUM Supplement 1)
Why is it important?
10,6
11,6
10,6
11,6
10,6
11,6
10
10,5
11
11,5
12
12,5
Lab A Lab B Lab A Lab B Lab A Lab B
mg
/kg
repeatability
uncertainty
Uncertainty = Confidence Informed Decision
Uncertainty and limiting values
Many analyses are made to assure that limiting values are not exceeded (e.g. for drinking water quality)
Without information about the measurement uncertainty it may appear to be very easy to make decisions, but these decisions may be incorrect
Uncertainty and limiting values
AN EXAMPLE
Drinking water -> Pb content
Parametric value: 10 μg/l (COUNCIL DIRECTIVE 98/83/EC)
Laboratory uncertainty at that level: ± 0,8 μg/l (Expanded uncertainty, 95% confidence interval)
Uncertainty and limiting values
11,2
10,4
9,6
8,8
8
10
12
(i) Result lessuncertaintyabove limit
(ii)Result abovelimit but limit
withinuncertainty
(iii)Result belowlimit but limit
withinuncertainty
(iv)Result plusuncertaintybelow limit
Pb
co
nte
nt
(μg
/l)
Uncertainty and limiting values
Straightforward Approach
1. If possible use a method producing more accurate results
2. Report the result and uncertainty with a statement that compliance (or non-compliance) could not be demonstrated
(for a suggested statement see UKAS Guide, M3003, The Expression of Uncertainty and Confidence in Measurement)
10,4
9,6
8
10
12
(ii) (iii)
Pb
co
nte
nt
(μg
/l)
Uncertainty and limiting values
10,4
9,6
8
10
12
(ii) (iii)
Pb
co
nte
nt
(μg
/l)
Detailed Approach• Set up probability based decision
rules• Select a decision limit (critical
value) taking into account what the end user expects:
i. low probability of false rejection, α
ii. low probability of false acceptance, β
Acceptance zone Rejection zone
Decision Limit
guard band
Upper limit
Acceptance zone Rejection zone
Decision Limitguard band
Upper limit
guard band, g = 2∙uc= U95%
Uncertainty and limiting values
Acceptance Zone Rejection Zone
Upper Limit
U95%
DL
2,5% of the values under the curve are inside the specification limit
High confidence of correct rejectionDecision limit DL is chosen so that the risk of false rejection (α) is less than 2,5%.
guard band, g = 2∙uc= U95%
Uncertainty and limiting values
Upper Limit
U95%
Acceptance Zone
DL
Rejection Zone
2,5% of the values under the curve are outside the specification limit
High confidence of correct acceptanceDecision limit DL is chosen so that the risk of false acceptance (β) is less than 2,5%.
EURACHEM / CITAC Guide
USE OF UNCERTAINTY INFORMATION IN COMPIANCE
ASSESSMENT, Edition 1(2007)
The Guide describes many aspects of the matter.
It covers cases of:
- Simultaneous upper and lower limits
- Uncertainties depending on the value of the measurand
- Asymmetric distributions of the measurand
- Standard uncertainties with effective degrees of freedom
Different decision rules are compared.
Conclusions
-Need for consistent way of reporting test results
-Uncertainty: quantitative measure of the reliability of a result
-Decisions for compliance or non-compliance with a specification
should take into account uncertainty
-When the state of compliance is not clear, appropriate judgments
should be based on probability-based decision criteria
-Decision criteria should be based on risks associated with making
wrong decision i.e. false rejection or false acceptance
Thank you for your attention !!!
Dimitris Theodorou, MSc, [email protected]
PRIORITY S.A. Business Consultant
Laboratory Accreditation Dept.