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

f o r f o r ISO f o r EN f o r Uncertainty Estimation

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?

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

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 Quality

Uncertainty Estimation Specify Measurand Identify all Sources of u x Quantify u x components Calculate Combined u c

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

Normal distribution kp % (µ±kσ) µ σ +1σ+2σ+3σ-3σ-2σ-1σ

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.

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 (1998)

Formula

Cause and effect diagram

Cause and effect diagram - rearrangement

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.

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

Uncertainty components Standard uncertainty u x –estimated from repeatability experiments –estimated by other means Combined standard uncertainty u c (y) Expanded uncertainty U U = k · u c coverage factor k = 2, level of confidence α = 95% Result = x ± U (units) e.g.: nitrates = 7,25 ± 0,06 % (weight)

Standard uncertainty u x Experimental variation of input variables –often measured from repeatability experiments and is quantified in terms 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 and calibration certificates –Proficiency Testing (PT) schemes –Quality Assurance (QA) data –suppliers' information By modelling from theoretical principles Using judgement based on experience or informed by modelling of assumptions

Combined standard uncertainty u c (y) In general Assumption: y = f( x ) is linear OR u(x i ) << x i reduce by u(x i )

Combined standard uncertainty u c (y) In general Assumption: y = ( x 1 +x x 3 ) Assumption: y = ( x 1 · x 2 ·... · x 3 )

Uncertainty – numerical calculation

Terms Arithmetic mean Standard deviation Relative standard deviation

Uncertainty y = f (p, q, r, s) ABCDE 1u(p)u(q)u(r)u(s) 2 3pp + u(p)ppp 4qqq + u(q)qq 5rrrr + u(r)r 6sssss + u(s) 7 8y=f(p,q,...)y=f(p’,...)y=f(..,q’,..)y=f(..,r’,..)y=f(..,s’,..) 9u(y,p)u(y,q)u(y,r)u(y,s) 10u(y)u(y,p) 2 u(y,q) 2 u(y,r) 2 u(y,s) 2 Eurachem

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

Standard uncertainty estimation normal  9 distribution evaluated experimentally from the dispersion of repeated measurements uncertainty given as s OR σ, RSD, CV%, without information about distribution uncertainty given as 95% (OR other) confidence band I without information about distribution u x = s u x = s u x = x.(s/x) u x = CV/100.x u x = I/2 confidence level for I = 95%

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

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