New calibration procedure in analytical chemistry in agreement to VIM 3

1. New calibration procedure in analytical chemistry in agreement to VIM 3 Miloslav Suchanek ICT Prague and EURACHEM Czech Republic

2. T&M Conference 2010, SA

3. Prague castle and Vltava river T&M Conference 2010, SA

4. Overview • New definition of calibration • Theoretical backround of various calibration methods • Practial calculation with MS Excel • Do we need measurement uncertainty? T&M Conference 2010, SA

5. Terminology x, independent variable  c, concentration, content y, dependent variable  y, Y, indication, signal Measurement in chemistry: calibration of a measurement procedure not calibration of an instrument Result : quantity value ± expanded measurement uncertainty T&M Conference 2010, SA

6. ISO/IEC Guide 99:2008 • International vocabulary of metrology (VIM 3) • 2.39 calibration • operation that, under specified conditions, in a first step, • established a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties and, in a second step, • uses this information to establish a relation for obtaining a measurement result from an indication T&M Conference 2010, SA

7. Calibration models x – concentration, content; y – indication, signal T&M Conference 2010, SA

8. Ordinary regression cannot be used! underestimation of measurement uncertainty T&M Conference 2010, SA

9. Solution: • Least square analysis with uncertainties in both variables - bivariate (bilinear) regression • Monte Carlo simulation (regression) (MCS) • Bracketing calibration T&M Conference 2010, SA

10. Bivariate (bilinear) regression – theory (J.M. Lisy et.all: Computers Chem. 14, 189, 1990) Task: Estimate the parameters of linear equation y = b1 + b2.x providing that experimental data have a structure: xi u(xi) and yi u(yi) (u(xi) and u(yi)are standard uncertainties) T&M Conference 2010, SA

11. Solution: j = 1,2; N is the number of experimental points See EXCEL calculations Parameters of linear model are estimated iteratively T&M Conference 2010, SA

12. The Monte Carlo steps • Each calibration point is characterised by {xi u(xi), yi u(yi)} assumed to be normally distributed {N(xi, u2(xi)), N(yi, u2(yi)} • Replace eachcalibration point by a randomly selected point (j) {xi(j), yi(j)} • Perform a (simple) Linear Regression using the « new » calibration dataset (j) • Derive the slope and intercept of calibration (j): b2(j), b1(j) • Repeat the sequence (e.g. 1000 times) • Compute the average and standard deviation of all b2(j), b1(j)to obtain the slope b2 and intercept b1, respectively. T&M Conference 2010, SA

13. The Monte Carlo calculation • provides reliable results • compliant with GUM (ISO/IEC Guide 98-3:2008) • easy to implement in a spreadsheet See EXCEL calculations T&M Conference 2010, SA

14. Bracketing calibration Model equation See EXCEL calculations T&M Conference 2010, SA

15. T&M Conference 2010, SA

16. 5 points calibration T&M Conference 2010, SA

17. BIVARIATE REGRESSION GOTO EXCEL RESULT T&M Conference 2010, SA

18. Monte Carlo simulation GOTO EXCEL RESULT T&M Conference 2010, SA

19. The simulated dataset T&M Conference 2010, SA

20. Bracketing GOTO EXCEL RESULT T&M Conference 2010, SA

21. Conclusions Measurement uncertainty is the most important in decision making process! T&M Conference 2010, SA

22. L Measurement result with 95% probability below limit Measurement result with 95% probability over limit uis the procedure characterization! 5 % u u 5 % results L-1.64*u L+1.64*u acceptance area ¿ grey zone ? rejection area 3.28 * u T&M Conference 2010, SA 22

23. Thank you! miloslav.suchanek@vscht.cz T&M Conference 2010, SA