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In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Calibration and Detection Limits
Rüdiger KausThomas Nagel
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Contents
1 Introduction
2 Basics of Calibration
3 Excel-charts for calibration
4 Limits of detection, determination
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
1 Introduction
Calibration is an important process in
establishing traceability
method validation to get the
performance characteristics
the routine use of modern analytical
equipment
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
What is Calibration?
Calibration is the process of establishing how the response of a measurement process varies with respect to the parameter being measured.
The usual way to perform calibration is to subject known amounts of the parameter (e.g. using a measurement standard or reference material) to the measurement process and monitor the measurement response.
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Calibration has Two Major Aims:
Establishing a mathematical function which describes the dependency of the system’s parameter (e. g. concentration) on the measured value Gaining statistical information of the analytical system, e. g. sensitivity, precision
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Calibration Concepts
External standard
Internal standard
Standard addition
Definitive calibration methods
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Goals of Calibration
“Ability to calculate a (measurement) result in a secure (safe) working range”
Funk, W., Dammann, V., and Donnevert, G., “Quality Assurance in Analytical Chemistry”,
VCH Weinheim 1995
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
First Steps to the Goal:
Establishing the calibration function Choosing the working range Measuring several calibration standards Linear regression Test of non linear regression Test of variance homogeneity Calculate performance characteristics
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Next Steps to the Goal:
Calculating the (measurement) results Conversion of the calibration function Reporting the measurement results
Calculating the statistical limits Securing the lower working range critical value of detection limit calculation of the quantitation limit Securing the higher working range
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
2 Basics of CalibrationMathematical Functions
simple linear function with intercept in zero originy = m x
linear function with intercept a and slope by = ax + b
quadratic functiony = ax2 + bx + c
cubic functiony = ax3 + bx2 + ax + d
exponential functiony = a ebx
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Principle of Linear Regression
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Simple Example of Linear Regression
No. x y x2 y2 yx
1 0,5 0,47 0,25 0,221 0,235 0,491
2 1,0 1,01 1,00 1,020 1,010 0,997
3 1,5 1,54 2,25 2,372 2,310 1,503
4 2,0 1,98 4,00 3,920 3,960 2,009
Xm=1,25 ym=1,25 Σ=7,5 Σ=7,533 Σ=7,515
a = 1,012 b = -0,015
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Simple Example of Linear RegressionNo. x
mg/Ly
1 1,0 37
2 2,0 120
3 3,0 170
4 4,0 205
Xm=2,50 ym=133
Calibration
0,000
50,000
100,000
150,000
200,000
250,000
0,000 0,500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000
mg/L
regression curve confidence interval
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
International Standards
ISO 8466 “Water quality– Calibration and evaluation of analytical methods and estimation of performance characteristics
- Part 1: Statistical evaluation of the linear calibration function”
- Part 2: Calibration strategy for non-linear second order calibration functions”
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
3 Excel-charts for CalibrationUniversity of Applied SciencesDepartment of Physical ChemistryProf Dr. R. Kaus
QA-guideline: QA_04_N10
Calibration and process data for the determination of Test data
method
Calibration data measured at
x y_1
mg/L Area / 1000 Process data of a calibration function ... of 1. order ... 2. ordervalue 1 0,050 3,060 Testing linearity: regression 2. Ordnung is significant not better
value 2 0,100 3,522 correlation coefficient 0,995 c = 0,362
value 3 0,150 3,707 slope 0,342 b = 9,487 b = 9,288
value 4 0,200 4,280 intercept 0,106 a = 2,508 a = 2,528
value 5 0,250 5,058 residual standard deviation s(y) = 0,155 s(y) = 0,166
value 6 0,300 5,510 process standard deviation s(x0) = 0,016 s(x0) = 0,017
value 7 0,350 5,703 process variation coeff icient V(x0) = 0,060 E = 9,487
value 8 0,400 6,205 0,206
value 9 0,450 6,950 auxiliary value for the determination of x_P y_P = 2,858 t(95%, single-sided) 1,86
value 10 0,500 7,178 testing value to secure the low er range limit x_P = 0,071 t(95%, single-sided) 1,86
number mean MDL = LC XN = 0,057 t(99%, single-sided) 2,90 sums10 0,275 5,117 detection limit (DIN 32645) XE = 0,115 t(99%, double-sided) 3,36
quantitation limit (DIN 32645) XB = 0,177k = 3
Calibration function 1.O: y =2,508 + 9,487 x
SampleData factor of Results
confidence interval for
resultsStandard uncertainty
no. Area / 1000 dilution mg/L ± mg/L rel. in % e.g. double probelowest 3,06 0,0581 1 0,058 ± 0,035 0,0351 60,3% M = 2
mean 5,12 0,275 1 0,275 ± 0,032 0,0319 11,6% Standard relative expanded
highest 7,18 0,4922 1 0,492 ± 0,035 0,0351 7,1% uncertainty S.U. S.U.
1 5,00 0,2626 1 0,263 ± 0,032 0,0319 12,2% 0,0127 4,8% 0,0252 1 ±
3 1 ±
4 1 ±
5 1 ±
6 1 ±
7 1 ±
8 1 ±
9 1 ±
10 1 ±
Quality Management Manual
Page: 1 von 3 PagesPart B
Version:Date : proved:
released:
2.0
Ka
13.04.2001
Calibration
x_P
XB
0,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/L
regression curve confidence interval
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
3 Excel-charts for CalibrationUniversity of Applied Sciences Version: 2.0
Department of Physical Chemistry Date : 13.04.01
Prof Dr. R. Kaus Part B proved:
QA-guideline: QA_04_N10 Page: 1 von 3 Pages released: Ka
data sheet with the complete data
x y residuals
mg/L Area / 1000
i_01 0,05 3,06i_02 0,1 3,522i_03 0,15 3,707i_04 0,2 4,28i_05 0,25 5,058i_06 0,3 5,51i_07 0,35 5,703i_08 0,4 6,205i_09 0,45 6,95i_10 0,5 7,178
number mean
10 0,275 5,117
Outlier testing data pair with suspected outlier i_03 0,15 3,707F(f1=1,f2=N-2)= 5,317645 no outlier above above above
F-Test PW = 1 no outlier for testing: line 33 should be eliminatedt-Test VB(yA) = 4,245976 Process data of the new linear calibration function (no outlier)
3,616836 slope b = 9,487intercept a = 2,508residual standard deviation s(y)_a = 0,155
data sheet with the reduced data process standard deviation s(x0) _a= 0,016x y process variation coefficient V(x0)_a = 6,0 %
i_01 0,05 3,06i_02 0,1 3,522i_03 0,15 3,707i_04 0,2 4,28i_05 0,25 5,058i_06 0,3 5,51i_07 0,35 5,703i_08 0,4 6,205i_09 0,45 6,95i_10 0,5 7,178
number mean
10 0,28 5,117test datas: y_P = 2,858 x_P = 0,07138Relevance: Comparing the slopes 0,00% deviation
Quality Management Manual
residual analysis
-0,25
-0,2
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5mg/L
residual analysis
-0,3
-0,2
-0,2
-0,1
-0,1
0,0
0,1
0,1
0,2
0,2
0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5mg/L
0
1
2
3
4
5
6
7
8
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/L
Are
a / 1
000 x_P
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
3 Excel-charts for CalibrationUniversity of Applied Sciences Quality Management Manual Version: 2.0
Department of Physical Chemistry Date : 13.04.2001
Prof Dr. R. Kaus Part B proved:
QA-guideline: QA_04_N10 Page: 1 von 3 Pages released: Ka
Validation of an analytical method
for the determination of Test data
Principal calibrationProcess data of a calibration function of ...1. Order ... 2. Ordernumber of data N = 10 c = 0,362slope b = 9,487 b = 9,288intercept a = 2,508 a = 2,528residual standard deviation s(y) = 0,155 s(y) = 0,166process standard deviation s(x0) = 0,016 s(x0) = 0,017process variation coefficient V(x0) = 5,95% E = 9,487
calibration function 1.O: y = 2,508 + 9,487 x
Testing linearity: regression 2. order is not significant better
Securing the lower range limit range statistically secure
auxiliary value for the determination of x_P y_P = 2,8580 t(95%, einseitig) 1,86
testing value to secure the lower range limit x_P = 0,071 t(95%, einseitig) 1,86
capability of detection (DIN 32465) NG = 0,057 t(99%, einseitig) 2,90
quantitation limit BG = 0,115 t(99%, zw eiseitig) 3,36
k = 3
VB_x1 = 0,19
Relative analytical imprecision VB_x1(rel) = 381,73 %
1 0,025 770,12 0,05 381,73 0,075 252,34 0,1 187,65 0,125 148,76 0,15 122,87 0,175 104,38 0,2 90,59 0,225 79,7
10 0,25 71,111 0,275 64,012 0,3 58,113 0,325 53,114 0,35 48,915 0,375 45,216 0,4 41,917 0,425 39,118 0,45 36,619 0,475 34,320 0,5 32,221 0,525 30,422 0,55 28,723 0,575 27,224 0,6 25,825 0,625 24,5
confidence interval VB(x)rel in %
0,0
100,0
200,0
300,0
400,0
500,0
600,0
700,0
800,0
900,0
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7mg/ L
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Calibration data
x y_1
mg/L Area / 1000
value 1 0,050 3,060value 2 0,100 3,522value 3 0,150 3,707value 4 0,200 4,280value 5 0,250 5,058value 6 0,300 5,510value 7 0,350 5,703value 8 0,400 6,205value 9 0,450 6,950value 10 0,500 7,178number mean
10 0,275 5,117
3 Excel-charts for calibration3.1 Insert Data
University of Applied SciencesDepartment of Physical ChemistryProf Dr. R. Kaus
QA-guideline: QA_04_N10
Calibration and process data for the determination of Test data
method
Calibration data measured at
x y_1
mg/l Area / 1000 Process data of a calibration function ... of 1. order ... 2. Order
value 1 0,050 3,060 Testing linearity: regression 2. Ordnung is significant not better
value 2 0,100 3,522 correlation coefficient 0,995 c = 0,362
value 3 0,150 3,707 slope 0,342 b = 9,487 b = 9,288
value 4 0,200 4,280 intercept 0,106 a = 2,508 a = 2,528
value 5 0,250 5,058 residual standard deviation s(y) = 0,155 s(y) = 0,166
value 6 0,300 5,510 process standard deviation s(x0) = 0,016 s(x0) = 0,017
value 7 0,350 5,703 process variation coefficient V(x0) = 0,060 E = 9,487
value 8 0,400 6,205 0,206
value 9 0,450 6,950 auxiliary value for the determination of x_P y_P = 2,858 t(95%, single-sided) 1,86
value 10 0,500 7,178 testing value to secure the lower range limit x_P = 0,071 t(95%, single-sided) 1,86
number mean MDL = LC XN = 0,057 t(99%, single-sided) 2,90 sums
10 0,275 5,117 detection limit (DIN 32645) XE = 0,115 t(99%, double-sided) 3,36
quantitation limit (DIN 32645) XB = 0,177k = 3
Calibration function 1.O: y =2,508 + 9,487 x
SampleData factor of Results
confidence interval for
resultsStandard uncertainty
Nr. Area / 1000 dilution mg/l ± ... mg/l rel. in % e.g. double probelowest 3,06 0,0581 1 0,058 ± 0,035 0,0351 60,3% M = 2
mean 5,12 0,275 1 0,275 ± 0,032 0,0319 11,6% Standard- relative expanded
highest 7,18 0,4922 1 0,492 ± 0,035 0,0351 7,1% uncertainty S.U. S.U.
1 5,00 0,2626 1 0,263 ± 0,032 0,0319 12,2% 0,0127 4,8% 0,0252 1 ±
3 1 ±
4 1 ±
5 1 ±
6 1 ±
7 1 ±
8 1 ±
9 1 ±
10 1 ±
Ka
13.04.2001
Quality Management Manual
Page: 1 von 3 PagesPart B
Version:Date : proved:
released:
2.0
Calibration
x_P
XB
0,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/l
Are
a /
10
00
regression curve confidence interval
part from sheet: Insert data & presenting result
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
3 Excel-charts for calibration3.2 Linear regression and performance characteristics
t(95%, single-sided) 1,86
t(95%, single-sided) 1,86
t(99%, single-sided) 2,90
t(99%, double-sided) 3,36
University of Applied SciencesDepartment of Physical ChemistryProf Dr. R. Kaus
QA-guideline: QA_04_N10
Calibration and process data for the determination of Test data
method
Calibration data measured at
x y_1
mg/l Area / 1000 Process data of a calibration function ... of 1. order ... 2. Order
value 1 0,050 3,060 Testing linearity: regression 2. Ordnung is significant not better
value 2 0,100 3,522 correlation coefficient 0,995 c = 0,362
value 3 0,150 3,707 slope 0,342 b = 9,487 b = 9,288
value 4 0,200 4,280 intercept 0,106 a = 2,508 a = 2,528
value 5 0,250 5,058 residual standard deviation s(y) = 0,155 s(y) = 0,166
value 6 0,300 5,510 process standard deviation s(x0) = 0,016 s(x0) = 0,017
value 7 0,350 5,703 process variation coefficient V(x0) = 0,060 E = 9,487
value 8 0,400 6,205 0,206
value 9 0,450 6,950 auxiliary value for the determination of x_P y_P = 2,858 t(95%, single-sided) 1,86
value 10 0,500 7,178 testing value to secure the lower range limit x_P = 0,071 t(95%, single-sided) 1,86
number mean MDL = LC XN = 0,057 t(99%, single-sided) 2,90 sums
10 0,275 5,117 detection limit (DIN 32645) XE = 0,115 t(99%, double-sided) 3,36
quantitation limit (DIN 32645) XB = 0,177k = 3
Calibration function 1.O: y =2,508 + 9,487 x
SampleData factor of Results
confidence interval for
resultsStandard uncertainty
Nr. Area / 1000 dilution mg/l ± ... mg/l rel. in % e.g. double probelowest 3,06 0,0581 1 0,058 ± 0,035 0,0351 60,3% M = 2
mean 5,12 0,275 1 0,275 ± 0,032 0,0319 11,6% Standard- relative expanded
highest 7,18 0,4922 1 0,492 ± 0,035 0,0351 7,1% uncertainty S.U. S.U.
1 5,00 0,2626 1 0,263 ± 0,032 0,0319 12,2% 0,0127 4,8% 0,0252 1 ±
3 1 ±
4 1 ±
5 1 ±
6 1 ±
7 1 ±
8 1 ±
9 1 ±
10 1 ±
Ka
13.04.2001
Quality Management Manual
Page: 1 von 3 PagesPart B
Version:Date : proved:
released:
2.0
Calibration
x_P
XB
0,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/l
Are
a /
10
00
regression curve confidence interval
Process data of a calibration function of 1. order
correlation coefficient 0,995
slope b = 9,487intercept a = 2,508residual standard deviation s(y) = 0,155process standard deviation s(x0) = 0,016process variation coefficient V(x0) = 0,060
0,206
auxiliary value for the determination of x_P y_P = 2,858testing value to secure the lower range limit x_P = 0,071MDL = LC XN = 0,057detection limit (DIN 32645) XE = 0,115quantitation limit (DIN 32645) XB = 0,177
k = 3
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
22
2
2
2
)(
)(112
)(
11
xxb
yy
Ntsx
xx
x
Ntsay
i
PxoP
iYP
22
2
2
2
)(
)(11
)(
)(11
xxb
xXNk
NtskXB
xx
xx
NtsXN
ixo
ixo
3 Excel-charts for Calibration3.2 Linear Regression and Performance Characteristics
slope b = =SLOPE(C4:C13;B4:B13)
intercept a = =INTERCEPT(C4:C13;B4:B13)
residual standard deviation s(y) = =STEYX(C4:C13;B4:B13)
process standard deviation s(x0) = =s_y/b
process variation coefficient V(x0) = =s_x0/x_m
Q= =SUMQUADABW(B4:B12)
auxillary value for the determination of x_P y_P = =a+t*s_y*SQRT(1+1/N+x_m^2/Q)
testing value to secure the lower range limit x_P = =2*s_x0*t*SQRT(1/N+1+(y_P-y_m)^2/b^2/Q)
detection limit (DIN 32645) XN ==s_x0*t99e*SQRT(1+1/N+x_m^2/Q)
quantiation limit (DIN 32645) XB ==k*s_x0*t99z*SQRT(1+1/N+(k*NG-x_m)^2/Q)
k = 3
Performance characteristics of the calibration function (DIN 38402 Teil 51)
y a s tN
x
x x
x s tN
y y
b x x
P Y
i
P xoP
i
11
2 11
2
2
2
2 2
( )
( )
( )
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
part from sheet: Insert data & presenting result
t(95%, single-sided) 1,86
t(95%, single-sided) 1,86
t(99%, single-sided) 2,90
t(99%, double-sided) 3,36
Do we need tables of statistics?
No, in EXCEL are a lot of functions integrated
Example: =TINV(0,1;N-2)= 1,86
3 Excel-charts for Calibration3.2 Linear Regression and Performance Characteristics
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
3 Excel-charts for Calibration3.3 Variance Homogeneity (Heteroscedasticity)
from sheet: Calibration (10 values) with test for homogeneity of the variances
Calibration and process dataunit: mg/L extinction
Values no. x y_1 0,05 0,14 y_4 y_5 y_6 y_7 y_8 y_9 y_10
1 0,05 0,140 0,143 0,140 0,146 0,144 0,145 0,144 0,146 0,145 0,148 0,14412 0,1 0,2813 0,15 0,4054 0,2 0,5355 0,25 0,6626 0,3 0,7897 0,35 0,9168 0,4 1,0589 0,45 1,17310 0,5 1,303 1,302 1,303 1,304 1,300 1,296 1,295 1,301 1,296 1,306 1,3006
10 0,275 0,7262
test for homogeneity of the variances
o.k.
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
part from sheet: Insert data & presenting result
3 Excel-charts for calibration3.4 Comparing function of 1. order with function of 2. order
University of Applied SciencesDepartment of Physical ChemistryProf Dr. R. Kaus
QA-guideline: QA_04_N10
Calibration and process data for the determination of Test data
method
Calibration data measured at
x y_1
mg/l Area / 1000 Process data of a calibration function ... of 1. order ... 2. Order
value 1 0,050 3,060 Testing linearity: regression 2. Ordnung is significant not better
value 2 0,100 3,522 correlation coefficient 0,995 c = 0,362
value 3 0,150 3,707 slope 0,342 b = 9,487 b = 9,288
value 4 0,200 4,280 intercept 0,106 a = 2,508 a = 2,528
value 5 0,250 5,058 residual standard deviation s(y) = 0,155 s(y) = 0,166
value 6 0,300 5,510 process standard deviation s(x0) = 0,016 s(x0) = 0,017
value 7 0,350 5,703 process variation coefficient V(x0) = 0,060 E = 9,487
value 8 0,400 6,205 0,206
value 9 0,450 6,950 auxiliary value for the determination of x_P y_P = 2,858 t(95%, single-sided) 1,86
value 10 0,500 7,178 testing value to secure the lower range limit x_P = 0,071 t(95%, single-sided) 1,86
number mean MDL = LC XN = 0,057 t(99%, single-sided) 2,90 sums
10 0,275 5,117 detection limit (DIN 32645) XE = 0,115 t(99%, double-sided) 3,36
quantitation limit (DIN 32645) XB = 0,177k = 3
Calibration function 1.O: y =2,508 + 9,487 x
SampleData factor of Results
confidence interval for
resultsStandard uncertainty
Nr. Area / 1000 dilution mg/l ± ... mg/l rel. in % e.g. double probelowest 3,06 0,0581 1 0,058 ± 0,035 0,0351 60,3% M = 2
mean 5,12 0,275 1 0,275 ± 0,032 0,0319 11,6% Standard- relative expanded
highest 7,18 0,4922 1 0,492 ± 0,035 0,0351 7,1% uncertainty S.U. S.U.
1 5,00 0,2626 1 0,263 ± 0,032 0,0319 12,2% 0,0127 4,8% 0,0252 1 ±
3 1 ±
4 1 ±
5 1 ±
6 1 ±
7 1 ±
8 1 ±
9 1 ±
10 1 ±
Ka
13.04.2001
Quality Management Manual
Page: 1 von 3 PagesPart B
Version:Date : proved:
released:
2.0
Calibration
x_P
XB
0,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/l
Are
a /
10
00
regression curve confidence interval
Process data of a calibration function ... of 1. order ... 2. orderTesting linearity: regression of 2. order is not significantly better
correlation coefficient 0,995 c = 0,362
slope 0,342 b = 9,487 b = 9,288
intercept 0,106 a = 2,508 a = 2,528
residual standard deviation s(y) = 0,155 s(y) = 0,166
process standard deviation s(x0) = 0,016 s(x0) = 0,017
process variation coefficient V(x0) = 0,060 E = 9,487
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Calibration function: y = a+ b *x (+ c* x2)
3 Excel-charts for calibration3.5 Calculating the function
University of Applied SciencesDepartment of Physical ChemistryProf Dr. R. Kaus
QA-guideline: QA_04_N10
Calibration and process data for the determination of Test data
method
Calibration data measured at
x y_1
mg/l Area / 1000 Process data of a calibration function ... of 1. order ... 2. Order
value 1 0,050 3,060 Testing linearity: regression 2. Ordnung is significant not better
value 2 0,100 3,522 correlation coefficient 0,995 c = 0,362
value 3 0,150 3,707 slope 0,342 b = 9,487 b = 9,288
value 4 0,200 4,280 intercept 0,106 a = 2,508 a = 2,528
value 5 0,250 5,058 residual standard deviation s(y) = 0,155 s(y) = 0,166
value 6 0,300 5,510 process standard deviation s(x0) = 0,016 s(x0) = 0,017
value 7 0,350 5,703 process variation coefficient V(x0) = 0,060 E = 9,487
value 8 0,400 6,205 0,206
value 9 0,450 6,950 auxiliary value for the determination of x_P y_P = 2,858 t(95%, single-sided) 1,86
value 10 0,500 7,178 testing value to secure the lower range limit x_P = 0,071 t(95%, single-sided) 1,86
number mean MDL = LC XN = 0,057 t(99%, single-sided) 2,90 sums
10 0,275 5,117 detection limit (DIN 32645) XE = 0,115 t(99%, double-sided) 3,36
quantitation limit (DIN 32645) XB = 0,177k = 3
Calibration function 1.O: y =2,508 + 9,487 x
SampleData factor of Results
confidence interval for
resultsStandard uncertainty
Nr. Area / 1000 dilution mg/l ± ... mg/l rel. in % e.g. double probelowest 3,06 0,0581 1 0,058 ± 0,035 0,0351 60,3% M = 2
mean 5,12 0,275 1 0,275 ± 0,032 0,0319 11,6% Standard- relative expanded
highest 7,18 0,4922 1 0,492 ± 0,035 0,0351 7,1% uncertainty S.U. S.U.
1 5,00 0,2626 1 0,263 ± 0,032 0,0319 12,2% 0,0127 4,8% 0,0252 1 ±
3 1 ±
4 1 ±
5 1 ±
6 1 ±
7 1 ±
8 1 ±
9 1 ±
10 1 ±
Ka
13.04.2001
Quality Management Manual
Page: 1 von 3 PagesPart B
Version:Date : proved:
released:
2.0
Calibration
x_P
XB
0,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/l
Are
a /
10
00
regression curve confidence interval
Calibration function 1.O: y =2,508 + 9,487 x
part from sheet: Insert data & presenting result
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
3 Excel-charts for calibration3.6 Graphically representation the data
part from sheet: Insert data & presenting resultUniversity of Applied SciencesDepartment of Physical ChemistryProf Dr. R. Kaus
QA-guideline: QA_04_N10
Calibration and process data for the determination of Test data
method
Calibration data measured at
x y_1
mg/l Area / 1000 Process data of a calibration function ... of 1. order ... 2. Order
value 1 0,050 3,060 Testing linearity: regression 2. Ordnung is significant not better
value 2 0,100 3,522 correlation coefficient 0,995 c = 0,362
value 3 0,150 3,707 slope 0,342 b = 9,487 b = 9,288
value 4 0,200 4,280 intercept 0,106 a = 2,508 a = 2,528
value 5 0,250 5,058 residual standard deviation s(y) = 0,155 s(y) = 0,166
value 6 0,300 5,510 process standard deviation s(x0) = 0,016 s(x0) = 0,017
value 7 0,350 5,703 process variation coefficient V(x0) = 0,060 E = 9,487
value 8 0,400 6,205 0,206
value 9 0,450 6,950 auxiliary value for the determination of x_P y_P = 2,858 t(95%, single-sided) 1,86
value 10 0,500 7,178 testing value to secure the lower range limit x_P = 0,071 t(95%, single-sided) 1,86
number mean MDL = LC XN = 0,057 t(99%, single-sided) 2,90 sums
10 0,275 5,117 detection limit (DIN 32645) XE = 0,115 t(99%, double-sided) 3,36
quantitation limit (DIN 32645) XB = 0,177k = 3
Calibration function 1.O: y =2,508 + 9,487 x
SampleData factor of Results
confidence interval for
resultsStandard uncertainty
Nr. Area / 1000 dilution mg/l ± ... mg/l rel. in % e.g. double probelowest 3,06 0,0581 1 0,058 ± 0,035 0,0351 60,3% M = 2
mean 5,12 0,275 1 0,275 ± 0,032 0,0319 11,6% Standard- relative expanded
highest 7,18 0,4922 1 0,492 ± 0,035 0,0351 7,1% uncertainty S.U. S.U.
1 5,00 0,2626 1 0,263 ± 0,032 0,0319 12,2% 0,0127 4,8% 0,0252 1 ±
3 1 ±
4 1 ±
5 1 ±
6 1 ±
7 1 ±
8 1 ±
9 1 ±
10 1 ±
Ka
13.04.2001
Quality Management Manual
Page: 1 von 3 PagesPart B
Version:Date : proved:
released:
2.0
Calibration
x_P
XB
0,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/l
Are
a /
10
00
regression curve confidence interval
Calibration
x_P
XB
0,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/l
regression curve confidence interval
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
part from sheet: Outlier
3 Excel-charts for calibration3.7 Calculating outliers3.8 Graphically representation the outliers
University of Applied Sciences Version: 2.0
Department of Physical Chemistry Date : 13.04.01
Prof Dr. R. Kaus Part B proved:
QA-guideline: QA_04_N10 Page: 1 von 3 Pages released: Ka
data sheet with the complete data
x y residuals
mg/L Area / 1000
i_01 0,05 3,06i_02 0,1 3,522i_03 0,15 3,707i_04 0,2 4,28i_05 0,25 5,058i_06 0,3 5,51i_07 0,35 5,703i_08 0,4 6,205i_09 0,45 6,95i_10 0,5 7,178
number mean
10 0,275 5,117
Outlier testing data pair with suspected outlier i_03 0,15 3,707F(f1=1,f2=N-2)= 5,317645 no outlier above above above
F-Test PW = 1 no outlier for testing: line 33 should be eliminatedt-Test VB(yA) = 4,245976 Process data of the new linear calibration function (no outlier)
3,616836 slope b = 9,487intercept a = 2,508residual standard deviation s(y)_a = 0,155
data sheet with the reduced data process standard deviation s(x0) _a= 0,016x y process variation coefficient V(x0)_a = 6,0 %
i_01 0,05 3,06i_02 0,1 3,522i_03 0,15 3,707i_04 0,2 4,28i_05 0,25 5,058i_06 0,3 5,51i_07 0,35 5,703i_08 0,4 6,205i_09 0,45 6,95i_10 0,5 7,178
number mean
10 0,28 5,117test datas: y_P = 2,858 x_P = 0,07138Relevance: Comparing the slopes 0,00% deviation
Quality Management Manual
residual analysis
-0,25
-0,2
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5mg/L
residual analysis
-0,3
-0,2
-0,2
-0,1
-0,1
0,0
0,1
0,1
0,2
0,2
0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5mg/L
0
1
2
3
4
5
6
7
8
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/L
Are
a / 1
000 x_P
residual analysis
-0,25
-0,2
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5
mg/L
data pair with suspected outlier i_03 0,15 3,707no outlier above above aboveno outlier for testing: line 33 should be eliminated
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
part from sheet: Outlier
3 Excel-charts for calibration3.7 Calculating outliers3.8 Graphically representation the outliers
University of Applied Sciences Version: 2.0
Department of Physical Chemistry Date : 13.04.01
Prof Dr. R. Kaus Part B proved:
QA-guideline: QA_04_N10 Page: 1 von 3 Pages released: Ka
data sheet with the complete data
x y residuals
mg/L Area / 1000
i_01 0,05 3,06i_02 0,1 3,522i_03 0,15 3,707i_04 0,2 4,28i_05 0,25 5,058i_06 0,3 5,51i_07 0,35 5,703i_08 0,4 6,205i_09 0,45 6,95i_10 0,5 7,178
number mean
10 0,275 5,117
Outlier testing data pair with suspected outlier i_03 0,15 3,707F(f1=1,f2=N-2)= 5,317645 no outlier above above above
F-Test PW = 1 no outlier for testing: line 33 should be eliminatedt-Test VB(yA) = 4,245976 Process data of the new linear calibration function (no outlier)
3,616836 slope b = 9,487intercept a = 2,508residual standard deviation s(y)_a = 0,155
data sheet with the reduced data process standard deviation s(x0) _a= 0,016x y process variation coefficient V(x0)_a = 6,0 %
i_01 0,05 3,06i_02 0,1 3,522i_03 0,15 3,707i_04 0,2 4,28i_05 0,25 5,058i_06 0,3 5,51i_07 0,35 5,703i_08 0,4 6,205i_09 0,45 6,95i_10 0,5 7,178
number mean
10 0,28 5,117test datas: y_P = 2,858 x_P = 0,07138Relevance: Comparing the slopes 0,00% deviation
Quality Management Manual
residual analysis
-0,25
-0,2
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5mg/L
residual analysis
-0,3
-0,2
-0,2
-0,1
-0,1
0,0
0,1
0,1
0,2
0,2
0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5mg/L
0
1
2
3
4
5
6
7
8
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/L
Are
a / 1
000 x_P
test datas: y_P = 2,86 x_P = 0,07138Relevance: Comparing the slopes 0,00% deviation
residual analysis
-0,3
-0,2
-0,2
-0,1
-0,1
0,0
0,1
0,1
0,2
0,2
0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5mg/L
0
1
2
3
4
5
6
7
8
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/L
Are
a /
1000
0
1
2
3
4
5
6
7
8
0,000 0,100 0,200 0,300 0,400 0,500 0,600
mg/L
Are
a /
1000
x_P
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
The analytical results will be calculated by the inverse of the calibration function: x = (y-a)/b
3 Excel-charts for calibration3.9 Calculating analytical results
University of Applied SciencesDepartment of Physical ChemistryProf Dr. R. Kaus
QA-guideline: QA_04_N10
Calibration and process data for the determination of Test data
method
Calibration data measured at
x y_1
mg/l Area / 1000 Process data of a calibration function ... of 1. order ... 2. Order
value 1 0,050 3,060 Testing linearity: regression 2. Ordnung is significant not better
value 2 0,100 3,522 correlation coefficient 0,995 c = 0,362
value 3 0,150 3,707 slope 0,342 b = 9,487 b = 9,288
value 4 0,200 4,280 intercept 0,106 a = 2,508 a = 2,528
value 5 0,250 5,058 residual standard deviation s(y) = 0,155 s(y) = 0,166
value 6 0,300 5,510 process standard deviation s(x0) = 0,016 s(x0) = 0,017
value 7 0,350 5,703 process variation coefficient V(x0) = 0,060 E = 9,487
value 8 0,400 6,205 0,206
value 9 0,450 6,950 auxiliary value for the determination of x_P y_P = 2,858 t(95%, single-sided) 1,86
value 10 0,500 7,178 testing value to secure the lower range limit x_P = 0,071 t(95%, single-sided) 1,86
number mean MDL = LC XN = 0,057 t(99%, single-sided) 2,90 sums
10 0,275 5,117 detection limit (DIN 32645) XE = 0,115 t(99%, double-sided) 3,36
quantitation limit (DIN 32645) XB = 0,177k = 3
Calibration function 1.O: y =2,508 + 9,487 x
SampleData factor of Results
confidence interval for
resultsStandard uncertainty
Nr. Area / 1000 dilution mg/l ± ... mg/l rel. in % e.g. double probelowest 3,06 0,0581 1 0,058 ± 0,035 0,0351 60,3% M = 2
mean 5,12 0,275 1 0,275 ± 0,032 0,0319 11,6% Standard- relative expanded
highest 7,18 0,4922 1 0,492 ± 0,035 0,0351 7,1% uncertainty S.U. S.U.
1 5,00 0,2626 1 0,263 ± 0,032 0,0319 12,2% 0,0127 4,8% 0,0252 1 ±
3 1 ±
4 1 ±
5 1 ±
6 1 ±
7 1 ±
8 1 ±
9 1 ±
10 1 ±
Ka
13.04.2001
Quality Management Manual
Page: 1 von 3 PagesPart B
Version:Date : proved:
released:
2.0
Calibration
x_P
XB
0,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/l
Are
a /
10
00
regression curve confidence interval
SampleData factor of Results
confidence interval for
resultsStandard uncertainty
no. Area / 1000 dilution mg/L ± mg/L
lowest 3,06 0,0581 1 0,058 ± 0,035 0,035mean 5,12 0,275 1 0,275 ± 0,032 0,032
highest 7,18 0,4922 1 0,492 ± 0,035 0,0351 5,00 0,2626 1 0,263 ± 0,032 0,0322 1 ±
3 1 ±
4 1 ±
5 1 ±
6 1 ±
7 1 ±
8 1 ±
9 1 ±
10 1 ±
part from sheet: Insert data & presenting result
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
part from sheet: Insert data & presenting result
3 Excel-charts for calibration3.10 Estimating the uncertainty
University of Applied SciencesDepartment of Physical ChemistryProf Dr. R. Kaus
QA-guideline: QA_04_N10
Calibration and process data for the determination of Test data
method
Calibration data measured at
x y_1
mg/l Area / 1000 Process data of a calibration function ... of 1. order ... 2. Order
value 1 0,050 3,060 Testing linearity: regression 2. Ordnung is significant not better
value 2 0,100 3,522 correlation coefficient 0,995 c = 0,362
value 3 0,150 3,707 slope 0,342 b = 9,487 b = 9,288
value 4 0,200 4,280 intercept 0,106 a = 2,508 a = 2,528
value 5 0,250 5,058 residual standard deviation s(y) = 0,155 s(y) = 0,166
value 6 0,300 5,510 process standard deviation s(x0) = 0,016 s(x0) = 0,017
value 7 0,350 5,703 process variation coefficient V(x0) = 0,060 E = 9,487
value 8 0,400 6,205 0,206
value 9 0,450 6,950 auxiliary value for the determination of x_P y_P = 2,858 t(95%, single-sided) 1,86
value 10 0,500 7,178 testing value to secure the lower range limit x_P = 0,071 t(95%, single-sided) 1,86
number mean MDL = LC XN = 0,057 t(99%, single-sided) 2,90 sums
10 0,275 5,117 detection limit (DIN 32645) XE = 0,115 t(99%, double-sided) 3,36
quantitation limit (DIN 32645) XB = 0,177k = 3
Calibration function 1.O: y =2,508 + 9,487 x
SampleData factor of Results
confidence interval for
resultsStandard uncertainty
Nr. Area / 1000 dilution mg/l ± ... mg/l rel. in % e.g. double probelowest 3,06 0,0581 1 0,058 ± 0,035 0,0351 60,3% M = 2
mean 5,12 0,275 1 0,275 ± 0,032 0,0319 11,6% Standard- relative expanded
highest 7,18 0,4922 1 0,492 ± 0,035 0,0351 7,1% uncertainty S.U. S.U.
1 5,00 0,2626 1 0,263 ± 0,032 0,0319 12,2% 0,0127 4,8% 0,0252 1 ±
3 1 ±
4 1 ±
5 1 ±
6 1 ±
7 1 ±
8 1 ±
9 1 ±
10 1 ±
Ka
13.04.2001
Quality Management Manual
Page: 1 von 3 PagesPart B
Version:Date : proved:
released:
2.0
Calibration
x_P
XB
0,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
0,000 0,100 0,200 0,300 0,400 0,500 0,600mg/l
Are
a /
10
00
regression curve confidence interval
Standard uncertainty
e.g. double measurementM = 2
Standard- relative expanded
uncertainty S.U. S.U.
0,0127 4,8% 0,025
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
4 Limits of Detection, Determination
4.1 Limit of Detection
4.2 Limit of Determination (Quantitation)
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
4. Limits of Detection, Determination4.1Limit of Detection
Detection limit
DIN 32645 from blanks
from calibration data
Funk dynamic model
IUPAC
Coleman recursive formula
explicit formula
2
D x 0 f;αx
1 1 xx s t
m n Q
LD f;α
s 1 1x t
b m n
2
c y n2
ii 1
0 x1y b s t 1
nx x
2
y cD n
22i
i 1
s t y y1x 2 1
a na x x
c 1 α,v 0S t sαβ,v 0 1 α,v 0
D
δ σ 2t σK Kx
A I A I
B A1 α,v
0
σ σK 1 r(B,A) t
σ A
2
A1 α,v
σI 1 t
A
11
2 22 2D
D n 2,1 α n 2,1 βxx xx
x xs 1 x 1x t 1 t 1
a n S n S
1
2 2
D H V
J J 4HKx DL
2H
n 2,1 β
aA
s t
12 2
n 2,1 α
n 2,1 β xx
t 1 xB 1
t n S
2xx
1F B 1 S
n
xxG 2AB S 2 1xxH A S J G 2x 2K F x
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
4. Limits of Detection, Determination4.1Limit of Detection
4.2Limit of Determination (Quantitation)
A) DIN 32645
Detection limit
by fast estimation:
Capability limit
Determination limit
by fast estimation
Factor for fast estimation
2k
D x0 f;ax
y - a 1 1 xx = = s t + +
b m n Q
n;α x0Dx = 1,2 Φ s
2
C NG x0 f;βx
1 1 xx = x + s t + +
m n Q
2
DDT x0 f;α
x
x - x1 1x = k s t + +
m n Q
n;α x0DTx = 1,2 k Φ s
n;α f;α
1Φ = t 1+
n
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
4. Limits of Detection, Determination4.1Limit of Detection
4.2Limit of Determination (Quantitation)
B) Funk
Detection limit dynamic model
Determination limit dynamic model
2
c y n2
ii 1
0 x1y b s t 1
nx x
2
y cD n
22i
i 1
s t y y1x 2 1
a na x x
2y
c n2
ii 1
s t 1 xx 1
a nx x
2
ch y n
2
ii 1
x x1y b 2 s t 1
nx x
2
y hhDT n
22i
i 1
s t y yy b 1x 1
a a na x x
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
4. Limits of Detection, Determination4.1Limit of Detection
4.2Limit of Determination (Quantitation)
C) IUPAC
Detection limitc 1 α,v 0S t s
αβ,v 0 1 α,v 0D
δ σ 2t σK Kx
A I A I
B A1 α,v
0
σ σK 1 r(B,A) t
σ A
2
A1 α,v
σI 1 t
A
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
4. Limits of Detection, Determination4.1Limit of Detection
4.2Limit of Determination (Quantitation)
D) Coleman/HUBAUX-VOS model
Detection limit recursive formula
explicit formula
1
2 2
D H V
J J 4HKx DL
2H
n 2,1 β
aA
s t
12 2
n 2,1 α
n 2,1 β xx
t 1 xB 1
t n S
2xx
1F B 1 S
n
xxG 2AB S 2 1xxH A S J G 2x 2K F x
11
2 22 2D
D n 2,1 α n 2,1 βxx xx
x xs 1 x 1x t 1 t 1
a n S n S
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
FUNK et. al. #BEZUG!
Prüfgröße y_P = 2914 t(95%,onesided) 1,86 detection limit x_P = 0,0862 t(95%,onesided) 1,86
quantitation limit BG = 0,1250 mg/l
Figure 1: The values are calculated with the formulas from Funk’s book [6] in an Excel-
sheet
Figure 2: The values are calculated with the formulas from DIN 32645 [5] in an Excel-sheet
4 Limits of Detection, Determination4.3 Critical Discussion
The values are calculated with the formulas from Funks book in an EXCEL sheet
Figure 1: The values are calculated with the formulas from Funk’s book [6] in an Excel-
sheet
DIN 32645
Nachweisgrenze detection limit NG = 0,070 mg/l t(99%,einseitig)2,90
Bestimmungsgrenze BG = 0,212 mg/l t(99%,zweiseitig)3,36 quantitation limit k = 3
Figure 2: The values are calculated with the formulas from DIN 32645 [5] in an Excel-sheet The values are calculated with the formulas from DIN 32645 in an EXCEL sheet
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Which Values of Detection limits and Quantitation limits are correct?
Choosing a confidence range for the quantitation limit:
recommendation of the DIN 32645: k=3 +/- 33% ;
recommendation of the IUPAC: 1/k=0,1 +/- 10%
4 Limits of Detection, Determination4.3 Critical Discussion
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Detection limits from blanks - problems with the normal distribution
detection limits from blanks give very low values, but
- blanks don’t belong to the same statistically population as the calibration and measuring data
- often they are normally distributed
4 Limits of Detection, Determination4.3 Critical Discussion
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Determination of the detection limit from blanks for: Naphthalene(with test of normal distribution)
Sample-Nr. Blank IS Blank/ISBlank/IS sorted x-x_m u=(x-x_m)/s uexpected
1 339 515592 0,0006575 0 -0,00031 -1,068 -1,5382 193 518421 0,00037228 0 -0,00031 -1,068 -0,9993 196 515572 0,00038016 0 -0,00031 -1,068 -0,6594 203 522514 0,00038851 0 -0,00031 -1,068 -0,385 376 529887 0,00070959 0,000372 0,00007 0,233 -0,1216 0 527819 0 0,000380 0,00007 0,261 0,1217 288 525571 0,00054798 0,000389 0,00008 0,290 0,388 0 527309 0 0,000548 0,00024 0,847 0,6599 0 563544 0 0,000657 0,00035 1,230 0,999
10 0 517630 0 0,000710 0,00040 1,412 1,538number mean 0,000306
10 standard deviation 0,000286
standard deviation 0,000286
slope from the clal ibration curve 0,762
detection limit 0,000654 mg/l
referred to the sample weight 0,00245 mg/kg TS
-2,000
-1,500
-1,000
-0,500
0,000
0,500
1,000
1,500
2,000
-2 -1,5 -1 -0,5 0 0,5 1 1,5 2
u expected
u m
ea
su
re
d
4 Limits of Detection, Determination4.3 Critical Discussion
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Quantitation limits and working range
Quantitation limits are often higher than some of the calibration data
(in the procedure suggested by Funk the quantitation limit is always higher than the 1st calibration point).
Now there is the difficulty:
Which is the lowest concentration I'm allowed to record?
4 Limits of Detection, Determination4.3 Critical Discussion
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material
Author: TitelKaus, R., Nagel, T.: Calibration and Detection Limits © Springer-Verlag Berlin Heidelberg 2003
In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching
Fachhochschule Niederrhein Quality management Version: V_1.0
Fachbereich Chemie
Prof. Dr. R. Kaus Date: 30.10.97
Calibration Page: 1 von 4 pages prepared by : Kaus
Calibration and process data for the destination of Carbonx y_1 in water
Calibration data mg/l Area
Wert 1 0,05 3060 (measured data are taken from DIN 32 645)Wert 2 0,1 3522Wert 3 0,15 3707Wert 4 0,2 4280Wert 5 0,25 5058Wert 6 0,3 5510Wert 7 0,35 5703Wert 8 0,4 6205Wert 9 0,45 7156Wert 10 0,5 7178number means
10 0,275 5137,9
Process data of a linear calibration function (DIN 38402 Teil 51)
slope b = 9662intercept a = 2481residual standard deviation s(y) = 192process standard deviation s(x0) = 0,0199process variation coef ficient V(x0) = 7,24%
0,20625aux iliary value for the determination of x_P y_P = 2914 t( 95%, single-s ided) 1,86
testing value to secure the lower range limit x_P = 0,0862 t( 95%, single-s ided) 1,86
capability of detection (DIN 32465) XN = 0,070 t( 99%, single-s ided) 2,90
quantitation limit XB = 0,212 t(99%, double-s ided) 3,36
k = 3
Calibration
x_ P
XB(DIN)
__ XB(FUNK)
0
1 000
2 000
3 000
4 000
5 000
6 000
7 000
8 000
0 0,1 0,2 0,3 0,4 0,5 0,6mg/l
Are
a
regression curve confidence interval
4 Limits of Detection, Determination4.3 Critical Discussion