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EURACHEM / CITAC Guide
Use of uncertainty information
in compliance assessment
First Edition 2007
EURACHEM/CITAC Guide:
Use of uncertainty
information in compliance
assessment
First edition 2007
Editors
S L R Ellison (LGC, UK)
A Williams (UK)
Composition of the Working Group
EURACHEM Members
A Williams
Chairman
UK
S Ellison
Secretary
LGC, Teddington, UK
A Chow Hong-Jiun
Shell Global Solutions International BV
P Gowik
BVL, Germany
W Haesselbarth
BAM Germany
R Kaarls
Nmi, The Netherlands
R Kaus
Germany
Acknowledgements
This document has been produced primarily by a
joint EURACHEM/CITAC Working Group with the
composition shown (right). The editors are
grateful to all these individuals and organisations
and to others who have contributed comments,
advice and assistance.
B Magnusson
SP, Sweden
P Robouch
IRMM, EU
M Roesslein
EMPA, Switzerland
M Walsh
Ireland
W Wegscheider
University of Leoben, Austria
R Wood
Food Standards Agency, UK
Production of this Guide was in part supported
under contract with the UK Department of Trade
and Industry as part of the National Measurement
System Valid Analytical Measurement (VAM)
Programme.
CITAC Members
I Kuselman
INPL, Israel
M Salit
National Institute of Standards and Technology
USA
A Squirrell
NATA, Australia
CONTENTS
1. Introduction
1
2. Scope
1
3. Definitions
2
4. Decision rules and Acceptance zones
2
5. Choosing Acceptance and Rejection Zone limits
5
6. Specifying an acceptable value for u
5
7. Recommendations
6
8. References
7
Appendix A. Determining the size of the Guard Band
8
Appendix B. Examples
13
Appendix C: Definitions
14
Interpretation with expanded uncertainty - Published 2007 - v1a.doc
Use of uncertainty information in compliance assessment
1. Introduction
In order to utilise a result to decide whether it indicates compliance or non-compliance with a
specification, it is necessary to take into account the measurement uncertainty. Figure 1 shows
typical scenarios arising when measurement results, for example on the concentration of analyte,
are used to assess compliance with an upper specification limit. The vertical lines show the
expanded uncertainty ±
U
on each result and the associated curve indicates the inferred
probability density function for the value of the measurand, showing that there is a larger
probability of the value of the measurand lying near the centre of the expanded uncertainty
interval than near the ends. Cases i) and iv) are reasonably clear; the measurement results and
their uncertainties provide good evidence that the value of the measurand is well above or well
below the limit, respectively. In case (ii), however, there is a high probability that the value of
the measurand is above the limit, but the limit is nonetheless within the expanded uncertainty
interval. Depending on the circumstances, and particularly on the risks associated with making a
wrong decision, the probability of an incorrect decision may be or may not be sufficiently small
to justify a decision of non-compliance. Similarly, in case (iii) the probability that the value of
the measurand is below the limit may or may not be sufficient to take the result to justify
compliance. Without further information, which has to be based on the risks associated with
making a wrong decision, it is not possible to use these two results to make a decision on
compliance.
Some guidance is already available on such issues, but it is usually limited to advice to consult
with the client and/or regulator as to the appropriate action to take in cases such as ii) and iii).
This document provides additional guidance on setting appropriate criteria for unambiguous
decisions on compliance given results with associated uncertainty information. Since a great deal
of work on compliance assessment has been carried out in other areas, particularly for the testing
of electrical and mechanical products, this document follows the principles outlined in existing
guidance for electronics and engineering measurement, particularly that set out in ASME
B89.7.3.1-2001
1
.
2. Scope
This guide is applicable to decisions on compliance with regulatory or manufacturing limits
where a decision is made on the basis of a measurement result accompanied by information on
the uncertainty associated with the result. It covers cases where the uncertainty does not depend
on the value of the measurand, and cases where the uncertainty is proportional to the value of the
measurand.
This guide assumes that the uncertainty has been evaluated by an appropriate method that takes
all relevant contributions into account. Guidance on appropriate methods of evaluating
uncertainty is provided by the Eurachem
2
and ISO
3
guides on the subject.
When the decision on compliance is applied to all the tested lot or batch of a substance or
material, the contribution to measurement uncertainty arising from the sampling could be
important. This guide assumes that where the measurand implies a sampling requirement, the
1
Interpretation with expanded uncertainty 2007:v1
 uncertainty includes components arising from sampling. Further guidance on uncertainty in
sampling is given in a related Guide.
4
This document does not consider cases involving decisions based on multiple measurands.
Figure 1 Assessment of Compliance with an Upper Limit
Upper
Limit
(i)
Result minus
expanded
uncertainty
above limit
(ii)
Result above
limit: limit
within
expanded
uncertainty
interval
(iii)
Result below
limit; limit
within
expanded
uncertainty
interval
(iv)
Result plus
expanded
uncertainty
below limit
3. Definitions
Terms used in this guide generally follow those of the International Vocabulary of Basic and
General Terms in Metrology
5
(“the VIM”) and the ISO/IEC Guide to the Expression of
Uncertainty in Measurement
3
(“the GUM”). Additional terms are taken from ASME B89.7.3.1-
2001.
1
A summary of the most important definitions used in this document is provided in
Appendix C.
4. Decision rules and Acceptance zones
The key to the assessment of compliance is the concept of “Decision rules”. These rules give a
prescription for the acceptance or rejection of a product based on the measurement result, its
uncertainty and the specification limit or limits, taking into account the acceptable level of the
probability of making a wrong decision. On the basis of the Decision rules, an “Acceptance
zone” and a “Rejection zone” are determined, such that if the measurement result lies in the
acceptance zone the product is declared compliant and if in the rejection zone it is declared non-
compliant.
2
Interpretation with expanded uncertainty 2007:v1
Upper
Limit
Upper
Limit
(i)
Result minus
expanded
uncertainty
above limit
(i)
Result minus
expanded
uncertainty
above limit
(ii)
Result above
limit: limit
within
expanded
uncertainty
interval
(ii)
Result above
limit: limit
within
expanded
uncertainty
interval
(iii)
Result below
limit; limit
within
expanded
uncertainty
interval
(iii)
Result below
limit; limit
within
expanded
uncertainty
interval
(iv)
Result plus
expanded
uncertainty
below limit
(iv)
Result plus
expanded
uncertainty
below limit
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