Measurement Uncertainty
Alex Williams
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Uncertainty
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Is a fundamental property of a result
It is not an optional extra
It is not just as an additional burden
All results have an uncertainty on their
value
 Needs to be evaluated irrespective of
requirements of 17025
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Overview
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What is meant by Uncertainty?
What information is it intended to give ?
Why is it important?
How is uncertainty evaluated?
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
What is Uncertainty?
 There will always be an uncertainty
about the value of a result
 Even when correction factors have been
applied
 Because there will be an uncertainty on
these factors
 There will also be an uncertainty arising
from random effects.
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Lab A Lab B Lab C
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
Lab D Lab E
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Units
Lab A
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
Lab B Lab C
Lab D Lab E
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Why Uncertainty is Important
 to assess the reliability of the result
 to know the confidence that can be
placed in any decisions based on its use
 in order to compare measurement
results
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Uncertainty should be Quantified in a
Way that is
 Universal:
applicable to all kinds of measurements
 Internally consistent:
independent of how components are grouped
 Transferable:
use uncertainty on a result in derivation of
uncertainty on dependant results
 Procedures set out in: Guide to the Expression
of Uncertainty in Measurement (GUM)
Published by ISO ISBN 92-67-10188-9
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
1993
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Uncertainty of Measurement Definition
 parameter, associated with the result of
a measurement, that characterizes the
dispersion of the values that could
reasonably be attributed to the
measurand
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Uncertainty of Measurement
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Standard Uncertainty
 Uncertainty of the result expressed as a
Standard Deviation
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Expanded Uncertainty
 ..interval about the result of a measurement
that may be expected to encompass a large
fraction of the distribution of values that could
reasonably be attributed to the measurand.
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Principles of Measurement
 Measurement results are obtained from a
comparison of the unknown with a standard
 In the simplest case, the value VU of the
unknown is VU=f(V1, IU, I1),
Where
 I1 indication, when measuring the standard,
 IU when measuring the unknown and
 V1 the value of the standard
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Evaluating Uncertainty
 Uncertainty on result is: Uncertainty from comparison with standard.
 Plus the uncertainty on the value of the
standard.
 Many sources of uncertainty associated with
the comparison
 Uncertainty on standard usually small
 Traceability is to the value of the standard
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Measurement of Mass
using two pan balance
 Effects to be taken into account:
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buoyancy
equality of arm lengths
sensitivity to position on pan
air temperature gradients
electrostatic forces
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Evaluating Uncertainty
Sources of uncertainty
1. Incomplete definition of the
measurand.
2. Sampling - the sample measured may
not be representative.
3. Incomplete implementation of the
measurement method.
4. Personal bias in reading analogue
instruments.
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Evaluating Uncertainty
Sources of uncertainty
5. Inadequate knowledge of the effects of
environmental conditions on the
measurement procedure or imperfect
measurement of environmental
conditions
6. Instrument calibration uncertainty
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Evaluating Uncertainty
Sources of uncertainty
7. Instrument resolution or discrimination
threshold.
8. Values assigned to measurement
standards and reference materials.
9. Values of constants and other
parameters obtained from external
sources and used in the data reduction
algorithm.
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Evaluating Uncertainty
Sources of uncertainty
10. Instrument approximations and
assumptions incorporated in the
measurement method and procedure.
11. Variations in repeated observations of
the measurand under apparently
identical conditions.
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Evaluating Uncertainty
 Approach depends on information
available
 Cause and effect diagram helps track
components.
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Preparation of a Calibration
Standard
cCd
1000  m  P

V
V
Purity
Temperature
Calibration
Repeatability
c(Cd)
Readability
Readability
m(tare)
m(gross)
Linearity
Sensitivity
Linearity
Repeatability
Calibration
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
Repeatability
Sensitivity
m
Calibration
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Pesticide in Bread
Repeatability
I(op)
Calibration
Linearity
I(op)
I(ref)
c(ref)
V(op)
Purity (ref)
m(ref)
m(ref)
Temperature
Temperature
Calibration
V(ref)
dilution
V(ref)
Calibration
V(op)
m(sample)
Calibration
Calibration
dilution
P(op)
m(gross)
m(tare)
Linearity
Linearity
Calibration
Calibration
Calibration
F(hom)
Recovery
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
I(ref)
m(sample)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Evaluating Uncertainty
 For many types of test, method
validation provides most of required
information
 Identifies and controls parameters that
affect result
 Plus normal QA
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching
Conclusions
 Uncertainty is an essential component of
the result
 Necessary to ensure comparability of
results
 In many cases method validation studies &
QA data provide most of information
required
 More information on
www.measurementuncertainty.org
Williams, A.: Measurement Uncertainty
In: Wenclawiak, Koch, Hadjicostas (eds.)
© Springer-Verlag Berlin Heidelberg 2003
Quality Assurance in Analytical Chemistry – Training and Teaching