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CENTRO DE METROLOGIA QUIMICA. CALCULATION OF UNCERTAINTIES FOR THE RESULTS REPORTED IN SIM.QM-P2. As, Cu, Fe, Mn, Ni, Pb, (Zn) Perkin-Elmer AAnalyst700 Atomic Absorption Spectrophotometer equipped with a longitudinal graphite furnace. ANALYTICAL MEASUREMENT. Cd - PowerPoint PPT Presentation
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CENTRO DE METROLOGIA QUIMICA
CALCULATION OF
UNCERTAINTIES
FOR THE RESULTS
REPORTED IN SIM.QM-P2
ANALYTICAL MEASUREMENT
As, Cu, Fe, Mn, Ni, Pb, (Zn)
Perkin-Elmer AAnalyst700 Atomic Absorption Spectrophotometer
equipped with a longitudinal graphite
furnace
Cd
Flame Atomic Absorption Spectrophotometry
Perkin-Elmer AAnalyst100 and using high
sensitivity nebulizer
ANALYTICAL MEASUREMENT
• 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
Identify Uncertainty Sources
THE UNCERTAINTY ESTIMATION PROCESS
Calculate combined standard uncertainty
Specify associated model
Quantify Uncertainty Sources
Reporting Uncertainty
Convert to standard uncertainty
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
IDENTYFING UNCERTAINTY SOURCES
repeatability
calibration
temperature
Csample
dAL, AH, As
repeatability
repeatability
CL, CH
calibration
temperature
F(dil)
U-SMR
QUANTIFYING UNCERTAINTY SOURCES
repeatability
calibration
temperature
Csample
dAL, AH, As
repeatability
repeatability
CL, CH
calibration
temperature
F(dil)
U-SMR
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
repeatability
calibration
temperature
Csample
dAL, AH, As
repeatability
repeatability
CL, CH
calibration
temperature
F(dil)
U-SMR
QUANTIFYING UNCERTAINTY SOURCES
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
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
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
repeatability
calibration
temperature
Csample
dAL, AH, As
repeatability
repeatability
CL, CH
calibration
temperature
F(dil)
QUANTIFYING UNCERTAINTY SOURCES
U-SMR
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
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
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)
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
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)
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%)
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
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
)
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
)
CENTRO DE METROLOGIA QUIMICA