uncertainty e stimation of a nalytical r esults in forensic analysis
DESCRIPTION
Uncertainty E stimation of A nalytical R esults in Forensic Analysis. Ing. Ján Hrouzek, Ph.D. * Ing. Svetlana Hrouzkov á , Ph.D. Hermes Labsystems, Púchovská 12, SK-831 06 Bratislava - PowerPoint PPT PresentationTRANSCRIPT
Uncertainty Uncertainty EEstimation of stimation of AAnalytical nalytical RResultsesults
ininForensic AnalysisForensic 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
f o r
f o rISO 17025
f o r
EN45001
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 ux
Quantify ux components
Calculate Combined uc
The Uncertainty Estimation Process
Specify Measurand
Identify Sources of ux
Quantify ux
Calculate uc and U
Simplify, Group by existing data
Quantify Group of ux
Quantify remaining ux
Convert to SD
Calculate uc
Re-evaluatelarge components
Calculate U
Normal distribution
k p % (µ±kσ)
1 68.27
1.645 90
1.960 95
2 95.45
2.576 99
3 99.73
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. 3 101-105 (1998)
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 ux
– estimated from repeatability experiments
– estimated by other means
• Combined standard uncertainty uc(y)
• Expanded uncertainty U
U = k · uc coverage factor k = 2, level of confidence α = 95%
• Result = x ± U (units) e.g.: nitrates = 7,25 ± 0,06 % (weight)
n
ki ki
n
ii
iji ikx
x
y
x
yx
x
yxy
1,
2
1
2
...,C ,suu
Standard uncertainty ux• 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 onexperience or informed bymodelling of assumptions
1
s 1
2
n
xxn
ii
x
Combined standard uncertainty uc(y)
• In general
• Assumption: y = f(x) is linear OR u(xi) << xi
n
ki ki
n
ii
iji ikx
x
y
x
yx
x
yxy
1,
2
1
2
...,C ,suu
i
iii
i x
xyxxy
x
y
u
u
reduce by u(xi)
Combined standard uncertainty uc(y)
• In general
• Assumption: y = (x1+x2+...+x3)
• Assumption: y = (x1 · x2 · ... · x3)
n
ki ki
n
ii
iji ikx
x
y
x
yx
x
yxy
1,
2
1
2
...,C ,suu
222
21...,C uuuu nji xxxxy
2
3
3
2
2
2
2
1
1...,C
uuuu
x
x
x
x
x
xyxy ji x
Uncertainty – numerical calculation
x
xy
xux
xuxy
xyxuxyyu
yu
12
12
xx
yyGradient
yu
xu1x 2x
1y
2y
Terms
n
xx
n
ii
1
11
2
n
xxs
n
ii
x
sRSD
Arithmetic mean
Standard deviation
Relative standard deviation
Uncertainty y = f (p, q, r, s)
A B C D E
1 u(p) u(q) u(r) u(s)
2
3 p p + u(p) p p p
4 q q q + u(q) q q
5 r r r r + u(r) r
6 s s s s s + u(s)
7
8 y=f(p,q,...) y=f(p’, ...) y=f(..,q’,..) y=f(..,r’,..) y=f(..,s’,..)
9 u(y,p) u(y,q) u(y,r) u(y,s)
10 u(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%; 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
ux = s
ux = 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
ux = s
ux = sux = x.(s/x)ux = CV/100.x
ux = I/2confidence level for I = 95%
Uncertainies from linear calibration
bxay
bayx obspred /
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 xpred due to variability in y for n pairs of values (xi, yi) and p meassurements
iiiii
pred
i
iii
predwxwxw
xx
wbn
bxayw
yxu 22
2
2
2
12,
nxx
xx
npbn
bxay
yxuii
pred
ii
pred 22
2
2
2
112,
Uncertainty Uncertainty EEstimation of stimation of AAnalytical nalytical RResultsesults
ininForensic AnalysisForensic 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