centro de metrologia quimica. calculation of uncertainties for the results reported in sim.qm-p2
TRANSCRIPT
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CENTRO DE METROLOGIA QUIMICA
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CALCULATION OF
UNCERTAINTIES
FOR THE RESULTS
REPORTED IN SIM.QM-P2
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ANALYTICAL MEASUREMENT
As, Cu, Fe, Mn, Ni, Pb, (Zn)
Perkin-Elmer AAnalyst700 Atomic Absorption Spectrophotometer
equipped with a longitudinal graphite
furnace
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Cd
Flame Atomic Absorption Spectrophotometry
Perkin-Elmer AAnalyst100 and using high
sensitivity nebulizer
ANALYTICAL MEASUREMENT
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• NIST-SRMs were used for the preparation of calibration standards.
• The quantification method used was bracketing
• Four independent aliquots of the sample were analyzed, in all cases.
• NIST-SMR 1643d was used as control (except for Cd)
ANALYTICAL MEASUREMENT
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Identify Uncertainty Sources
THE UNCERTAINTY ESTIMATION PROCESS
Calculate combined standard uncertainty
Specify associated model
Quantify Uncertainty Sources
Reporting Uncertainty
Convert to standard uncertainty
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ASSOCIATED MODEL:
BRACKETING
CL CH
AL
AH
CS
AS
LS
LS
LH
LH
CC
AA
CC
AA
Sample concentration is calculated through the equation
dCCC
AA
AAC LLH
LH
LS
S
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IDENTYFING UNCERTAINTY SOURCES
repeatability
calibration
temperature
Csample
dAL, AH, As
repeatability
repeatability
CL, CH
calibration
temperature
F(dil)
U-SMR
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QUANTIFYING UNCERTAINTY SOURCES
repeatability
calibration
temperature
Csample
dAL, AH, As
repeatability
repeatability
CL, CH
calibration
temperature
F(dil)
U-SMR
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Repeatability of A(S,L,H)
n
su )(A Std)(S,
The uncertainty due to random variation of the EAA signal measurement of samples and bracketing standards was
calculated as:
QUANTIFYING UNCERTAINTY SOURCES
Fe Determination Std Low Std High SIM
Average Signal 0,1704 0,2448 0,1955
Std desv 0,0002 0,0019 0,0030
n 3 3 4
ui 0,00011 0,00107 0,00150
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repeatability
calibration
temperature
Csample
dAL, AH, As
repeatability
repeatability
CL, CH
calibration
temperature
F(dil)
U-SMR
QUANTIFYING UNCERTAINTY SOURCES
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Csample
repeatability
CL, CH
calibrationtemperature
F(dil)
n(dil)FCC SMRH,L
n
22
F
u
C
uCu
SMR*
(dil)
(F(dil))(SMR)
H)(L,)(C HL,
Equation for concentration assessment
Equation for the uncertainty calculation
U-SMR
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22
V
u
V
uFdilu
fin
(Vfin)
in
(Vin)
(Fdil)
Csample
repeatability
CL, CH
calibrationtemperature
F(dil)
SMRC
u (SMR)
3
Uu
(certif)
(SMR)
Fdil
u )Fdil(
222 uuu TrepcerfVi,
u
U-SMR
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22 3
1 Fdil
u
C
uCu *
(Fdil)
SMR)(C
(SMR)
(L)L
321SMR FdilFdilFdilCCL
CL = 9.827 g/L
uC = 0.055 g/L
PREPARATION OF STANDARDS
Values and uncertaintiesDescription Nominal value standard uncertainty Relative std (u (x) /x)
2
u (x) uncertainty u (x) /x
CSMR (mg/L) 109,83 0,19 0,00173 2,99E-06
Fdil 1 0,0090 3,63E-05 4,04E-03 1,63E-05
Fdil 2 0,0998 1,42E-04 1,42E-03 2,03E-06
Fdil 3 0,0998 3,19E-04 3,20E-03 1,02E-05
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repeatability
calibration
temperature
Csample
dAL, AH, As
repeatability
repeatability
CL, CH
calibration
temperature
F(dil)
QUANTIFYING UNCERTAINTY SOURCES
U-SMR
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dCCC
AA
AAC LLH
LH
LS
S
CALCULATING THE CONCENTRATION
Values and uncertainties in determination of Fe on SIM-P2 sample
Description Value x Standard uncertaintyu (x)
AS SIM-P2 sample Absorbance 0,1955 0,0015
AL Low standard Absorbance 0,1704 0,0001
AH High standard Absorbance 0,2448 0,0011
CL Low standard Concentration (g/L) 9,827 0,055
CH High standard Concentration (g/L) 13,780 0,073
d Sample diluted factor 8,349 0,044
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CALCULATING THE COMBINED STANDARD UNCERTAINTY
dCCC
AA
AAC LLH
LH
LS
S
22
C
2
C
222
d
S
H
S
L
S
AH
S
AL
S
AS
S ud
Cu
C
Cu
C
Cu
A
Cu
A
Cu
A
CsCuc
2
H
2
L
2
H
2
L
2
S
2
)Cs(
i
2x
2
i1
ux
fu(y) )(
)x....,x,x(fy i21
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222
)(xn
)(x2
)(x1
n
2
2
2
1
2
ux
y........u
x
yu
x
yu(y)
KRAGTEN(*)
Finally 2
)y(xuxyux
y)(x)(x
2
2
1111
1
)(
)(x
)(x)(x
u
yuxy
x
y
1
111
1
)(
2
2
2
)(x*)(x
)(x)(x)(x u
u
yuxyu
x
y
1
1
111
1
1
)(
(*) J. Kragten, Analyst, 119, 2161-2166 (1994)
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CALCULATION OF COMBINED STANDARD UNCERTAINTY
A S A L A H C L C H d
Value 0,19552 0,17039 0,24483 9,82683 13,78000 8,34912
u 0,00150 0,00011 0,00107 0,05523 0,07262 0,04367
A S 0,1955 0,1970 0,1955 0,1955 0,1955 0,1955 0,1955
= x1 + u (x1)
A L 0,1704 0,1704 0,1705 0,1704 0,1704 0,1704 0,1704
A H 0,2448 0,2448 0,2448 0,2459 0,2448 0,2448 0,2448
C L 9,8268 9,8268 9,8268 9,8268 9,8821 9,8268 9,8268
C H 13,780 13,780 13,780 13,780 13,780 13,853 13,780
d 8,3491 8,3491 8,3491 8,3491 8,3491 8,3491 8,3928
Conc.(mg/L) 93,19 93,853 93,156 93,029 93,493 93,392 93,675
y =equation y'1=y(x1 + u (x1)) idem idem idem idem idem
u(y,xi) 0,6659 -0,0318 -0,1586 0,3054 0,2047 0,4874
= y - y'1 idem idem idem idem idem
u2(y), u
2(y,xi) 0,84236 0,44344 0,00101 0,02515 0,09329 0,04190 0,23757
uncertainty (u ) 0,92
Expanded uncert. (U) 1,84
Relative U (%) 1,97
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UNCERTAINTY CONTRIBUTIONS
Uncertainty contributions
0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00
Cs
A S
A L
A H
C L
C H
d
unce
rta
intie
s so
urce
s
u(y,xi)
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Finally, the concentration and uncertainty values for Fe in the sample SIM.QM-P2 are:
Concentration CS = 93.19 g/L
Combined uncertainty ucom = 0.92
g/L
Expanded uncertainty U = 1.84
g/L U=u*k, (k=2) (1.97%)
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RESULTS OF Intec IN SIM.QM-P2
SUMMARY OF RESULTS OBTAINED ON SAMPLE SIM-P2
Element Average concentration Expanded Uncertainty REU(g/L) (g/L) (%)
Ni 62,86 2,52 4,0
Fe 93,19 1,84 2,0
Cu 17,06 0,44 2,6
As 50,94 1,02 2,0
Pb 21,86 0,66 3,0
Mn 39,44 1,58 4,0
Cd 144 4 2,8
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RESULTS OF SIM.QM-P2
Pb
18
19
20
21
22
23
24
25
26
NISTprep. value
Intec
Co
nce
ntr
atio
n (
g/L
)
Ni
54
56
58
60
62
64
66
68
70
72
74
NISTprep. value
Intec
Co
nce
ntr
atio
n (
g/L
)
As
46
47
48
49
50
51
52
53
54
55
NISTprep. value
Intec
Co
nce
ntr
atio
n (
g/L
)
Fe
8688
909294
9698
100
102104106
NISTprep. value
Intec
Co
nce
ntr
atio
n (
g/L
)
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RESULTS OF SIM.QM-P2
Cu
10
12
14
16
18
20
22
24
26
NISTprep. value
Intec
Co
nce
ntr
atio
n (
g/L
)
Cd
110
117
124
131
138
145
152
159
166
NISTprep. value
Intec
Co
nce
ntr
atio
n (
g/L
)
Mn
35
36
37
38
39
40
41
42
43
44
NISTprep. value
Intec
Co
nce
ntr
atio
n (
g/L
)
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CENTRO DE METROLOGIA QUIMICA
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