Uncertainty E stimation of A nalytical R esults in Forensic Analysis

1. Uncertainty Estimation of Analytical Results in Forensic Analysis Ing. Ján Hrouzek, Ph.D. *Ing. Svetlana Hrouzková, Ph.D. Hermes Labsystems, Púchovská 12, SK-831 06 Bratislava *Department of Analytical Chemistry, FChFT, Slovak University of Technology in Bratislava, Radlinského 9, SK-812 37 Bratislava 7th. International Symposium on Forensic Sciences, Papiernička, Slovakia, September 30, 2005

2. Uncertainty Estimation

3. Quality • method validation • am I measuring what I set out to measure? • uncertainty • how well do I know the result of what I’ve measured? • traceability of result • can I compare this result with other results?

4. Quality vs. Time SHALL I RUSH YOUR RUSH JOB BEFORE I START THE RUSH JOB I WAS RUSHING WHEN YOU RUSHED IN ?

5. Quality Uncertainty • how well do you know the result? • essential part of being able to compare! • are these two results the same??? • are these results good enough? • fit-for-purpose result = value ± uncertainty

6. Specify Measurand Identify all Sources of ux Quantify ux components Calculate Combined uc Uncertainty Estimation

7. Specify Measurand Simplify, Group by existing data Identify Sources of ux Quantify Group of ux Calculate uc Quantify remaining ux Quantify ux Convert to SD Re-evaluate large components Calculate uc and U Calculate U The Uncertainty Estimation Process

9. Normal distribution σ µ -3σ -2σ -1σ +1σ +2σ +3σ

10. Specify Measurand • Write down a clear statement of what is being measured, including the relationship between the measurand and the input quantities (e.g. measured quantities, constants, calibration standard values etc.) upon which it depends. • Where possible, include corrections for known systematic effects. • The specification information should be given in the relevant Standard Operating Procedure (SOP) or other method description.

11. Identify Uncertainty Sources • List the possible sources of uncertainty. This will include sources that contribute to the uncertainty on the parameters in the relationship specified in Step 1, but may include other sources and must include sources arising from chemical assumptions. • Tool for forming a structured list is the Cause and Effect diagram. • Appendix D. Analysing Uncertainty Sources based on S. L. R. Ellison, V. J. Barwick; Accred. Qual. Assur. 3 101-105 (1998)

12. Formula

13. Cause and effect diagram

14. Cause and effect diagram - rearrangement

15. Quantify Uncertainty Components • Measure or estimate the size of the uncertainty component associated with each potential source of uncertainty identified. • It is often possible to estimate or determine a single contribution to uncertainty associated with a number of separate sources. • It is also important to consider whether available data accounts sufficiently for all sources of uncertainty. If necessary plan additional experiments and studies carefully to ensure that all sources of uncertainty are adequately accounted for.

16. How to quantify grouped components • Uncertainty estimation using prior collaborative method development and validation study data • Uncertainty estimation using in-house development and validation studies • Evaluation of uncertainty for empirical methods • Evaluation of uncertainty for ad-hoc methods

17. Uncertainty components • Standard uncertainty ux • estimated from repeatability experiments • estimated by other means • Combined standard uncertainty uc(y) • Expanded uncertainty U U = k·uccoverage factork = 2, level of confidenceα=95% • Result = x±U (units) e.g.: nitrates = 7,25 ± 0,06 % (weight)

18. Standard uncertainty ux • Experimental variation of input variables • often measured fromrepeatability experiments and is quantified interms of the standard deviation • study of the effect of a variation of a single parameter on the result • robustness studies • systematic multifactor experimental designs • From standing data such as measurement andcalibration certificates • Proficiency Testing (PT) schemes • Quality Assurance (QA) data • suppliers' information • By modelling from theoretical principles • Using judgement based onexperience orinformed bymodelling of assumptions

19. Combined standard uncertainty uc(y) • In general • Assumption:y = f(x) is linearORu(xi) << xi reduce by u(xi)

20. Combined standard uncertainty uc(y) • In general • Assumption:y = (x1+x2+...+x3) • Assumption:y = (x1 · x2 · ...· x3)

21. Uncertainty – numerical calculation

22. Terms Arithmetic mean Relative standard deviation Standard deviation

23. Uncertainty y = f (p, q, r, s) Eurachem

24. Uncertainty component was evaluated experimentally u(x)=s limits of ±a are given with confidence level – assume rectangular distribution(e.g. ±0.2 mg 95%;ux = 0.2/1.96 = 0.1 mg) limits of ±a are given without confidence level – assume rectangular distribution(e.g. 1000 ± 2 mg.l-1 ux = 2/3 = 1,2 mg.l-1) limits of ±a are given without confidence level and extreme values are unlikely (volumetric glassware) ux = a/3 ux = a/6 Standard uncertainty estimationrectangular 3/triangular 6distribution ux = s ux = a/(tabelated value)

25. evaluated experimentally from the dispersion of repeated measurements uncertainty given as sORσ, RSD, CV%, without information about distribution uncertainty given as 95% (OR other) confidence bandIwithout information about distribution ux = s ux = sux = x.(s/x)ux = CV/100.xux = I/2 confidence level for I = 95% Standard uncertainty estimationnormal9distribution

26. Uncertainies from linear calibration calibration of the responses yto different level of analytes x to obtain predicted concentration xfrom a sample giving observed response y uncertainty in xpred due to variability in y for n pairs of values (xi, yi) and p meassurements

27. Uncertainty Estimation of Analytical Results in Forensic Analysis Ing. Ján Hrouzek, Ph.D. *Ing. Svetlana Hrouzková, Ph.D. Hermes Labsystems, Púchovská 12, SK-831 06 Bratislava *Department of Analytical Chemistry, FChFT, Slovak University of Technology in Bratislava, Radlinského 9, SK-812 37 Bratislava 7th. International Symposium on Forensic Sciences, Papiernička, Slovakia, September 30, 2005