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