1. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material Calibration and Detection Limits Rüdiger Kaus Thomas Nagel

2. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material Contents 1Introduction 2Basics of Calibration 3Excel-charts for calibration 4Limits of detection, determination

3. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 1 Introduction Calibration is an important process in  establishing traceability  method validation to get the performance characteristics  the routine use of modern analytical equipment

4. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 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.

5. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 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

6. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material Calibration Concepts  External standard  Internal standard  Standard addition  Definitive calibration methods

7. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 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

8. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 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

9. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 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

10. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 2 Basics of Calibration Mathematical Functions  simple linear function with intercept in zero origin y = m x  linear function with intercept a and slope b y = ax + b  quadratic function y = ax 2 + bx + c  cubic function y = ax 3 + bx 2 + ax + d  exponential function y = a e bx

11. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material Principle of Linear Regression

12. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material Simple Example of Linear Regression No.xyx2x2 y2y2 yx 10,50,470,250,2210,2350,491 21,01,011,001,0201,0100,997 31,51,542,252,3722,3101,503 42,01,984,003,9203,9602,009 X m =1,25y m =1,25Σ=7,5Σ=7,533Σ=7,515 a = 1,012b = -0,015

13. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material Simple Example of Linear Regression No.x mg/L y 11,037 22,0120 33,0170 44,0205 X m =2,50y m =133

14. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 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”

15. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 3 Excel-charts for Calibration

16. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 3 Excel-charts for Calibration

17. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 3 Excel-charts for Calibration

18. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 3Excel-charts for calibration 3.1Insert Data part from sheet: Insert data & presenting result

19. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 3Excel-charts for calibration 3.2Linear regression and performance characteristics

20. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 3Excel-charts for Calibration 3.2Linear Regression and Performance Characteristics slopeb ==SLOPE(C4:C13;B4:B13) intercepta ==INTERCEPT(C4:C13;B4:B13) residual standard deviations(y) ==STEYX(C4:C13;B4:B13) process standard deviations(x0) ==s_y/b process variation coefficientV(x0) ==s_x0/x_m Q==SUMQUADABW(B4:B12) auxillary value for the determination of x_Py_P ==a+t*s_y*SQRT(1+1/N+x_m^2/Q) testing value to secure the lower range limitx_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) yast N x xx xst N yy bxx PY i Pxo P i        1 1 21 1 2 2 2 22 () () ()

21. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material part from sheet: Insert data & presenting result Do we need tables of statistics? No, in EXCEL are a lot of functions integrated Example:=TINV(0,1;N-2) = 1,86 3Excel-charts for Calibration 3.2Linear Regression and Performance Characteristics

22. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 3Excel-charts for Calibration 3.3Variance Homogeneity (Heteroscedasticity) from sheet: Calibration (10 values) with test for homogeneity of the variances

23. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material part from sheet: Insert data & presenting result 3Excel-charts for calibration 3.4 Comparing function of 1. order with function of 2. order

24. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material Calibration function: y = a+ b *x (+ c* x 2 ) 3Excel-charts for calibration 3.5 Calculating the function part from sheet: Insert data & presenting result

25. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 3Excel-charts for calibration 3.6 Graphically representation the data part from sheet: Insert data & presenting result

26. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material part from sheet: Outlier 3Excel-charts for calibration 3.7 Calculating outliers 3.8 Graphically representation the outliers

27. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material part from sheet: Outlier 3Excel-charts for calibration 3.7 Calculating outliers 3.8 Graphically representation the outliers

28. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material The analytical results will be calculated by the inverse of the calibration function: x = (y-a)/b 3Excel-charts for calibration 3.9 Calculating analytical results part from sheet: Insert data & presenting result

29. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material part from sheet: Insert data & presenting result 3Excel-charts for calibration 3.10 Estimating the uncertainty Standard uncertainty e.g. double measurement M =2 Standard-relative expanded uncertaintyS.U. 0,01274,8%0,025

30. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 4Limits of Detection, Determination 4.1Limit of Detection 4.2Limit of Determination (Quantitation)

31. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 4.Limits of Detection, Determination 4.1 Limit of Detection Detection limit DIN 32645 from blanks from calibration data Funk dynamic model IUPAC Coleman recursive formula explicit formula

32. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 4.Limits of Detection, Determination 4.1 Limit of Detection 4.2 Limit of Determination (Quantitation) A) DIN 32645 Detection limit by fast estimation: Capability limit Determination limit by fast estimation Factor for fast estimation

33. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 4.Limits of Detection, Determination 4.1 Limit of Detection 4.2 Limit of Determination (Quantitation) B) Funk Detection limitdynamic model Determination limitdynamic model

34. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 4.Limits of Detection, Determination 4.1 Limit of Detection 4.2 Limit of Determination (Quantitation) C) IUPAC Detection limit

35. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 4.Limits of Detection, Determination 4.1 Limit of Detection 4.2 Limit of Determination (Quantitation) D) Coleman/HUBAUX-VOS model Detection limitrecursive formula explicit formula

36. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 4Limits of Detection, Determination 4.3 Critical Discussion The values are calculated with the formulas from Funks book in an EXCEL sheet The values are calculated with the formulas from DIN 32645 in an EXCEL sheet

37. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 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% 4Limits of Detection, Determination 4.3 Critical Discussion

38. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 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 4Limits of Detection, Determination 4.3 Critical Discussion

39. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 4Limits of Detection, Determination 4.3 Critical Discussion

40. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 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? 4Limits of Detection, Determination 4.3 Critical Discussion

41. 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 TeachingIn: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material 4Limits of Detection, Determination 4.3 Critical Discussion