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The Role of Proficiency Tests in the Estimation of Measurement Uncertainty of
PCDD/PCDF and PCB Determination by Isotope Dilution Methods
e-mail: stefano@raccanelli.eu
Stefano Raccanelli, Environmental Ethical Chemist, Italy
Measuring uncertainty
For the official food and feed control for levels of PCDD/Fs and PCBs non-compliance is defined as exceedance of legal limits beyond reasonable doubt taking into account the measurement uncertainty.
Courtesy of G. Scortichini
As a consequence when checking for non-compliance in official control, the same results of different laboratories can cause different assessment of results due to application of different measurement uncertainties.
Measuring uncertainty
Courtesy of G. Scortichini
(2) Top-down approach Global approach, which combines precision (within-laboratory reproducibility), trueness (bias) and proficiency tests (PTs) studies to calculate measurement uncertainty.
(1) Bottom-up approach Metrological approach based on the identification of the sources of uncertainty and the calculation of their standard uncertainties, then adequately combined. Suggested by ISO and adapted by EURACHEM to the analytical chemistry.
Measuring uncertainty
(0) Empirical general approach Based on 10000 measurements, the Horwitz curve. Mentioned also by ISO.
Empirical equation that relate the concentration of chemical to percentual variation coefficient (uncertainty)
For concentrations below 120 ppb Thompson proposed
(0) Horwitz relation
Type A evaluation (of uncertainty) Evaluation of uncertainty by the statistical analysis of series of observations.
Type B evaluation (of uncertainty): Evaluation of uncertainty from probability density functions based on experience or other information.
(1) Bottom-up approach
Uncertainty sources identified
• repeatability/reproducibility (type A) • calibration curve (type A) • calibration curve drift (type B) • volume (type B) • standard purity (type B) • sample weighing (type B)
Quantifying uncertainty components (Type A) EXAMPLE: PCB-126 in beef fat
Repeatability uncertainty
Number of tests = 18 Mean recovery = 112.3 % Standard deviation = 7.0% Relative standard deviation = 6.2%
Courtesy of G. Scortichini
ni
s ) x ( u i r =
Relative uncertainty = 0.0147
Intercept = -0.0396 Slope = 1.0364 R = 1.0000 Residual standard deviation = 0.2611
Calibration curve uncertainty
Injected amount (pg) Signal ratio
0 0.00
0.5 0.49
2 2.10
10 9.93
40 41.74
200 207.19
Quantifying uncertainty components (Type A) EXAMPLE: PCB-126 in beef fat
Courtesy of G. Scortichini
[ ]
21
2
/ −
−=∑=
n
yys
n
iii
xy
Relative uncertainty = 0.0109
Maximum acceptable variation of RRFi from in-house method:
± 20%
Calibration curve drift uncertainty
Maximum acceptable variation of RRFi from EPA method 1668B 2008 ± 30%
Quantifying uncertainty components (Type B) EXAMPLE: PCB-126 in beef fat
Courtesy of G. Scortichini
( )3
id
xxu ∆= Relative uncertainty = 0.0577
Labelled compound solution (dilution 1): Relative uncertainty = 0.0128
Labelled compound solution (dilution 2): Relative uncertainty = 0.0173
Labelled compound solution (spiking): Relative uncertainty = 0.0173
Relative uncertainty (sum) = 0.0277
Spiking volume uncertainty
Quantifying uncertainty components (Type B) EXAMPLE: PCB-126 in beef fat
Courtesy of G. Scortichini
( )6
iv
xxu ∆=
12
Standard purity uncertainty Standard solution tolerance taken from analytical certificate: ± 5%
Quantifying uncertainty components (Type B) EXAMPLE: PCB-126 in beef fat
Courtesy of G. Scortichini
( )3
ip
xxu ∆=
Relative uncertainty = 0.0289
Sample weighing uncertainty Maximum tolerance taken from calibration certificate of analytical balance: ± 0.3 mg
Quantifying uncertainty components (Type B) EXAMPLE: PCB-126 in beef fat
Courtesy of G. Scortichini
( )3
iw
xxu ∆=
Relative uncertainty = 0.000049
222222)()()()()()()()(
+
+
+
+
+
==
•
wwu
ppu
vvu
ddu
ccu
rru
yyuyu c
c
For models involving only a product or a quotient, the combined standard uncertainty is given by:
Where etc., are the uncertainties of the parameters
expressed as relative standard deviations. rru )(
Calculating the combined expanded uncertainty
The expanded uncertainty is usually calculated using a coverage factor k = 2. ) y ( u k ) y ( U c × =
Uncertainty source Relative uncertainty
Repeatability 0.062*
Calibration curve 0.046*
Calibration curve drift 0.058
Volume 0.028
Standard purity 0.029
Sample weighing 0.0005
Relative combined uncertainty
0.105
Relative expanded uncertainty (k=2)
0.209
* In routine analysis u(xr) and u(xc) are related to the number of replicates
Quantifying TOTAL uncertainty EXAMPLE: PCB-126 in beef fat
Courtesy of G. Scortichini
* In routine analysis u(xr) and u(xc) are related to the number of replicates
Combined and expanded uncertainty
PCB-126 in beef fat
r
prsampler N
Nxuxu ×= )()(
r
pcsamplec N
Nxuxu ×= )()(
Np: number of replicates in
precision study
Nr: number of replicates in
routine analysis
Repeatability
Calibration curve
Courtesy of G. Scortichini
Four approaches can potentially be used
How uncertainty estimated for each individual congener could be propagated to TEQ?
1) The square root of the sum of squares (RSS):
2) The SUM:
3) The average of (uci*TEFi)i=congener
4) The median of (uci*TEFi)i=congener
∑=
=29
1
2)*()(i
ciic uTEFTEQu
∑=
=29
1)*()(
iciic uTEFTEQu
Only one is statistically correct: in fact the square root of the sum of squares (RSS) provides the most realistic estimates
Is this a simplified
approach?
Black-box approach
(2) Top-down approach
Uncertainty results from combination of two terms: a. Best estimate of global precision (s)
b. Best available estimate of global bias (E) and its uncertainty (uE)
𝑢𝑢𝑐𝑐 = 𝑓𝑓( 𝑠𝑠 ⏟𝑎𝑎
; 𝐸𝐸 ; 𝑢𝑢(𝐸𝐸)�����𝑏𝑏
)
(2) Top-down approach
Global precision is evaluated as the standard deviation of results of repeated measures on the same sample, in a period long enough to include all possible sources than can influence the results: - Different lot of reagents/solvents; - Different analyst; - Different environmental conditions, - Different instrumental calibrations; - Different instrument or after service…..
a) Best estimate of global precision (s)
a) Best estimate of global precision (s)
Same reagent lot
same series
Same instrument
Same Laboratory
Ripetibility (r)
Ripetibility intra-lab. (Rw)
Riproducibility (R)
Same reagent lot
Same instrument
Same Laboratory
Same Laboratory
Different series
Different reagent lot
Same Laboratory
Different series
Different reagent lot Differnt
instruments
Different series
Differnt instruments
Different reagent lot
Different laboratory
Same instrument
Different series
Courtesy of F. Pecoraro
𝑢𝑢𝑐𝑐 = 𝑓𝑓( 𝑠𝑠 ; 𝐸𝐸 ; 𝑢𝑢(𝐸𝐸)�����𝑏𝑏𝑏𝑏𝑎𝑎𝑠𝑠
𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
)
b) Best estimate of global bias and uncertainty
The best estimate of global bias can be obtained in two ways: I) From CRM analysed several times in different days;
II) From participation to Proficiency Tests (PT); The estimates can be provided in similar way, I will present the PT method (Northtest approach)
𝑢𝑢𝑐𝑐 = 𝑓𝑓( 𝑠𝑠𝑅𝑅𝑅𝑅 ; 𝐸𝐸 ; 𝑢𝑢(𝐸𝐸) )
b) Best estimate from participation to PT: of global bias and its uncertainty
Participating to several PTs (minimum 6)
Participating to one PT
Courtesy of F. Pecoraro
𝑢𝑢𝑐𝑐 = � 𝑠𝑠𝑅𝑅𝑅𝑅 2� + 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅2 + 𝑢𝑢(𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 )2�����������
𝑈𝑈 = 2 ∙ 𝑢𝑢𝑐𝑐
Global bias Global precision
Uncertainty of global bias
Calculating the combined expanded uncertainty
Courtesy of F. Pecoraro
(2) Top-down approach Pros: dynamic (updated uncertainty at each PT participation), moderate costs for synergies with other Lab needs (accreditation). Cons: need for participation to some PTs, possible errors in estimation of assigned value and overestimation of assigned uncertainty
(1) Bottom-up approach Pros: rigorous if correctly applied Cons: static (generally done only once), expensive, possible underestimation of error source (e.g. ripetibility)
Pros&Cons of approaches for Measuring uncertainty
(0) Empirical general approach Pros: immediate, no cost Cons: not verified, static, low reliability, possible overestimation
On-going top-down approach
validation data (precision, accuracy)
Quality control (QC)
results from PTs (more than 1 per year)
daily LOQ
white matrix/solvent effect
variation of response factors
Made it a dynamic way to run your Laboratory!
Some features of InterCinD
- the samples are NATURALLY CONTAMINATED MATRIXES (es. soil, sediments, ash, food, wastes…);
- Matrixes are homogeneized and treated in agreement with the international guidelines for reference materials (ISO Guide 34:2009);
- analytes: PCDD/F, PCB-DL, PCB-ICES6, PAH, PBDE, heavy metals;
- Data are required in 3 replicates (evaluation of accuracy & precision).
The interlaboratory circuit InterCinD is organized in agreement with international guidelines and is accreditated ISO 17043
the InterCIND
+ + =
Assessing Performance
j
jjkijki s
xxz
−= ,,
,,
Accuracy: using z-scores
Precision: using “relative range” (r)
ji
jijijijijijiji x
xxxxxxr
,
,3,,2,,1,,3,,2,,1,,
),,min(),,max( −=
Overall objective Is to provide basis for the laboratories to assess their performances evaluated through the z-scores (accuracy) and dispersion of measures (precision).
the participants 2013 (26 countries) 2014 (23 countries)
Num
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