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Calibration and Detection Limits

Calibration and Detection Limits. Rüdiger Kaus Thomas Nagel. Contents. 1 Introduction 2 Basics of Calibration 3 Excel-charts for calibration 4 Limits of detection, determination. establishing traceability method validation to get the performance characteristics

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Calibration and Detection Limits

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

  2. 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

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

  4. 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. What is Calibration? In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  5. 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 Calibration has Two Major Aims: In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

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

  7. “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 Goals of Calibration In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  8. 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 First Steps to the Goal: In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  9. 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 Next Steps to the Goal: In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  10. simple linear function with intercept in zero originy = m x • linear function with intercept a and slope b y = ax + b • quadratic functiony = ax2 + bx + c • cubic functiony = ax3 + bx2 + ax + d • exponential functiony = a ebx 2 Basics of Calibration Mathematical Functions In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

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

  12. Simple Example of Linear Regression a = 1,012 b = -0,015 In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  13. Simple Example of Linear Regression In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

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

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

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

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

  18. part from sheet:Insert data & presenting result 3Excel-charts for calibration3.1 Insert Data In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  19. 3Excel-charts for calibration3.2Linear regression and performance characteristics In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  20. Performance characteristics of the calibration function (DIN 38402 Teil 51) 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) XN = detection limit (DIN 32645) =s_x0*t99e*SQRT(1+1/N+x_m^2/Q) XB = quantiation limit (DIN 32645) =k*s_x0*t99z*SQRT(1+1/N+(k*NG-x_m)^2/Q) k = 3 2 1 x ? ? ? ? ? ? 1 y a s t ? P Y ? 2 N ( ) x x i ? 2 ( ) y y 1 ? ? ? ? ? ? P 2 1 x s t ? P xo ? ? 2 2 N ( ) b x x i 3Excel-charts for Calibration3.2Linear Regression and Performance Characteristics In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  21. part from sheet:Insert data & presenting result 3Excel-charts for Calibration3.2Linear Regression and Performance Characteristics Do we need tables of statistics? No, in EXCEL are a lot of functions integrated Example: =TINV(0,1;N-2) = 1,86 In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  22. from sheet:Calibration (10 values) with test for homogeneity of the variances 3 Excel-charts for Calibration3.3 Variance Homogeneity (Heteroscedasticity) In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  23. 3 Excel-charts for calibration3.4Comparing function of 1. order with function of 2. order part from sheet:Insert data & presenting result In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  24. 3 Excel-charts for calibration3.5Calculating the function part from sheet:Insert data & presenting result Calibration function: y = a+ b *x (+ c* x2) In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  25. 3 Excel-charts for calibration3.6 Graphically representation the data part from sheet:Insert data & presenting result In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  26. 3 Excel-charts for calibration3.7 Calculating outliers 3.8   Graphically representation the outliers part from sheet:Outlier In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  27. 3 Excel-charts for calibration3.7 Calculating outliers 3.8   Graphically representation the outliers part from sheet:Outlier In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  28. 3 Excel-charts for calibration3.9Calculating analytical results part from sheet:Insert data & presenting result The analytical results will be calculated by the inverse of the calibration function: x = (y-a)/b In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  29. Standard uncertainty e.g. double measurement M = 2 Standard- relative expanded uncertainty S.U. S.U. 0,0127 4,8% 0,025 3 Excel-charts for calibration3.10 Estimating the uncertainty part from sheet:Insert data & presenting result In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

  30. 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

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

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

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

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

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

  36. 4 Limits 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 In:Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Laboratories – Teaching Material

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

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

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

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

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

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