Uncertainty estmation approach
based on validation and Quality
Control Data
“the Nordtest approach"
Single-laboratory validation approach
Effects contributing to
uncertainty
Random
Systematic
The two groups of uncertainty contributions are
quantified separately and then combined:
Ivo Leito
University of Tartu
Institute of Chemistry
uc  u1  u 2
2
2013
Uncertainty arising from
random effects
Nordtest Technical Report 537, 3rd ed (2011)
http://www.nordtest.info/
Single lab validation approach: in practice
(1)
2
uc  u ( Rw )  u (bias )
2
Absolute vs relative uncertainties:
Rules of Thumb
• At low concentrations (near detection limit, trace
level) use absolute uncertainties
2
– Uncertainty is not much dependent on analyte level
Within-laboratory
reproducibility
Uncertainty of the estimate of the
laboratory and the method bias
This component accounts for
the random effects
This component accounts for the
systematic effects
This and subsequent equations work with absolute
and relative values
Nordtest Technical Report 537, 3rd ed (2011)
http://www.nordtest.info/
Uncertainty accounting
for possible bias
at „long term“ level!
1
The main equation:
2
3
Single lab validation approach: in practice
Steps of the process:
• At medium and higher concentrations use relative
uncertainties
– Uncertainty is roughly proportional to analyte level
• In general: whichever is more constant
Appendix E.4 from Quantifying Uncertainty in Analytical Measurement,
EURACHEM/CITAC Guide, Second Edition (2000)
Available from : http://www.eurachem.org/
4
• u(Rw) is the uncertainty component that u(Rw)
takes into account long-term variation of
results within lab, that means: within-lab
reproducibility (sRw)
Include sample
• Ideally:
preparation!
– The same sample
1. Specify measurand
• Sample similar to test samples – matrix,
concentration, homogeneity
2. Quantify Rw component u(Rw)
3. Quantify bias component u(bias)
4. Convert components to standard uncertainties u(x)
5. Calculate combined standard uncertainty uc
6. Calculate expanded uncertainty U
5
–
–
–
–
–
–
The same lab
The same procedure
Different days (preferably over 1 year)
Different persons
Different reagent batches
…
6
1
u(bias)
u(Rw)
• The possible bias of lab’s results from the
best estimate of true value is taken into
account
u(Rw) = sRw
Include sample
preparation!
• u(bias) can be found:
– From repeated analysis of the same samples with a
reference procedure
– From repeated analysis of certified reference materials
(CRMs)
– From repeated interlaboratory comparison measurements
– From repeated spiking experiments
The control sample
analysis has to cover
the whole analytical
process
Ideally: separately for
different matrices and
different concentration
levels!
7
Ideally: several reference materials, several PTs because
the bias will in most cases vary with matrix and
concentration range
8
u(bias)
u(bias)
• The averaging is done using the root mean
square:
u (bias )  RMS bias  u (Cref ) 2
 (biasi ) 2
2
This component accounts
for the average bias of the
laboratory results from
the Cref
biasi  Clabi  Cref i
This component accounts
for the average
uncertainty of the
reference values Cref
u (Cref i ) 
si
ni
RMSbias 
u (Cref ) 
n
 u(Cref )
2
i
n
• n: the number of bias estimates used
– If n is too small then the bias component will include a
large share of random effects and may be
overestimated
9
u(bias): only one CRM
10
Uncertainty due to possible bias
• If only one single CRM is used:
Evaluation of uncertainty due to bias,
ideally:
2
u (bias )  RMS bias  sbias
/ n  u (Cref ) 2
2
– Separately for different sample matrices
– Separately for different concentration
levels
11
12
2
Roadmap:
Possible bias u (Cref i ) from certificates
u (Cref i ) 
biasi  Clabi  Cref i
RMSbias 
si
u (Cref ) 
ni
 u(Cref )
2
i
n
 (biasi ) 2
n
u (bias )  RMS bias  u (Cref ) 2
2
Uncertainty due to
random effects
Combined standard
uncertainty
u ( Rw )  sRW
uc  u ( Rw ) 2  u (bias ) 2
13
3