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Slide 1
Measurement data analysis in quality management systems.
Application to fuel test methods.
PhD Thesis
of
Dimitrios G. Theodorou
October 2015
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
School οf Chemical Engineering
Department οf Synthesis and
Development οf Industrial Processes
Slide 2PhD Thesis – D. Theodorou
Presentation Outline
Introduction and motivation
Statistical and numerical methods overview
Measurement uncertainty arising from sampling
Measurement uncertainty estimation of an analytical procedure
Estimation of the standard uncertainty of a calibration curve
The use of measurement uncertainty and precision data in conformity assessment
Conclusions
Slide 3PhD Thesis – D. Theodorou
Introduction and motivation
Fuels produced and placed on market should comply withstrict requirements introduced by relevant legislation
Directive 98/70/EC
Directive 2003/17/EC
Several laboratory test methods are used for theevaluation and assessment of fuel properties
The social and economic impact of the laboratory gettinga wrong result and the customer consequentlyreaching a false conclusion can be enormous.
The laboratory should provide a high quality service toits customers
Slide 4PhD Thesis – D. Theodorou
Introduction and motivation
Quality = Fitness for purpose (i.e. intended use)
The quality of a result and its fitness for purpose isdirectly related to the estimation of measurementuncertainty
Measurement uncertainty – A key requirement foraccreditation according to international standards:
ISO/IEC 17025, for testing and calibration laboratories
ISO 15189, for medical laboratories
ISO/IEC 17043, for proficiency testing providers
ISO Guide 34, for reference material producers
Slide 5PhD Thesis – D. Theodorou
Introduction and motivation
Slide 6PhD Thesis – D. Theodorou
Statistical and numerical methods overview
Measurement Uncertainty (MU) = nonnegativeparameter characterizing the dispersion of the quantityvalues being attributed to a measurand, based on theinformation used.
International Vocabulary of Metrology (VIM)
Slide 7PhD Thesis – D. Theodorou
Statistical and numerical methods overview
Master document on MU estimation
Guide to the Expression of Uncertainty in Measurement,
GUM
All MU estimation methodologies should give
results consistent with GUM
Slide 8PhD Thesis – D. Theodorou
Statistical and numerical methods overview
Modelling approach – GUM uncertainty framework
Slide 9PhD Thesis – D. Theodorou
Statistical and numerical methods overview
Modelling approach – GUM uncertainty framework
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Slide 10PhD Thesis – D. Theodorou
Statistical and numerical methods overview
Modelling approach – Kragten approximation
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Slide 11PhD Thesis – D. Theodorou
Statistical and numerical methods overview
Modelling approach – Monte Carlo Method
Slide 12PhD Thesis – D. Theodorou
Statistical and numerical methods overview
Empirical approaches
Data produced by single laboratory validation approach and analyzed by
ANOVA
Robust ANOVA
Range statistics
Data obtained by proficiency testing schemes
Standard uncertainty estimated as pooled reproducibility limit
Bayesian uncertainty analysis
Type A uncertainty evaluated through a Bayesianapproach
Slide 13PhD Thesis – D. Theodorou
Statistical and numerical methods overview
Measurement uncertainty and precision data are used in conformity assessment
Slide 14PhD Thesis – D. Theodorou
Statistical and numerical methods overview
SAMPLINGMEASUREMENT
PROCEDURE
REPORTING RESULTS AND
ASSESSING CONFORMITY
Chapter 3 Estimation of sampling uncertainty
Chapter 4Estimation of the uncertainty of a typical measurement procedure
Chapter 5Estimation of the uncertainty of a measurement procedure involving the construction of a calibration curve
Chapter 6Use of measurement uncertainty in conformity assessment
Slide 15PhD Thesis – D. Theodorou
Measurement uncertainty arising from sampling
Sampling uncertainty is defined as the part of the total measurement uncertainty attributable to sampling
Empirical approach
Statistical model
analysissamplingtrue Xx2
analysis
2
sampling
2
tmeasuremen
2
analysis
2
sampling
2
tmeasuremen sss
sU 2
Slide 16PhD Thesis – D. Theodorou
Measurement uncertainty arising from sampling
Experimental protocol and experimental design
Balanced nested
experimental design
Duplicate diesel samples
were taken from 104
petroleum retail stations
The sampling protocol used was consistent with the standard method ASTM D 4057
The duplicated samples were analyzed in duplicate under repeatability conditions for sulful mass content determination. (ANTEK 9000S sulfur analyzer  ASTM D 5453 /ISO 20846)
Sampling
target
Sample B
Sample A
Analysis A2
Analysis A1
Analysis B2
Analysis B1
Slide 17PhD Thesis – D. Theodorou
Measurement uncertainty arising from sampling
Data analysis methods
1. Classical Analysis of Variance (ANOVA)
Variations associated with different sources (analysis and sampling) can be isolated and estimated
Slide 18PhD Thesis – D. Theodorou
Measurement uncertainty arising from sampling
Data analysis methods (continued)
2. Robust Analysis of Variance
Particularly appropriate for providing estimated of variances, in cases where the validity of classical ANOVA is doubtful It is insensitive to distributional assumptions (such as normality)
It can tolerate a certain amount of unusual observations (outliers)
It uses robust estimates of the mean and standard deviation calculated by aniterative process (Huber’s method). Extreme values that exceed a certaindistance from the sample mean are downweighted or brought in.
Slide 19PhD Thesis – D. Theodorou
Measurement uncertainty arising from sampling
Data analysis methods (continued)3. Range Statistics
The variance of sampling is calculated indirectly as the difference of the variances of measurement and analysis.
2
analysis2
tmeasuremen
2
sampling2
sss
128.1
analysis
analysis
Ds 128.1
tmeasuremen
tmeasuremen
Ds
Sampling
target
Sample B
Sample A
Analysis A2
Analysis A1
Analysis B2
Analysis B1
Slide 20PhD Thesis – D. Theodorou
Measurement uncertainty arising from sampling
Results
•Robust ANOVA leads to statistically significantly different results (Ftest) compared to the other two methodologies.
•Robust ANOVA, which is not influenced by less than 10% outliers, is considered as the method providing the most reliable estimates
Slide 21PhD Thesis – D. Theodorou
Measurement uncertainty arising from sampling
Discussion
Different results is an indication that the assumptions of classical ANOVA and range statistics are not justified
Classical ANOVA and range statistics are strongly affected by the presence of outlying values (9 out of 104 datasets  8.7 %).
Slide 22PhD Thesis – D. Theodorou
Measurement uncertainty arising from sampling
Discussion (continued) The measurement uncertainty of manual sampling of fuels is
dominated by the analytical variance (accounts for the 71 % of the measurement uncertainty)
This leaves “room” for an effective reduction e.g. by making more measurements and calculating their average, instead of making a single measurement.
Then the standard deviation of the mean gets smaller as the number of data increases leading to smaller random error uncertainty contributions.
2
analysiss 20 % Expanded uncertainty of measurement
Slide 23PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
Test method studied
Gross Heat of Combustion (GHC) (or Higher Calorific Value) determination of a diesel fuel using a bomb calorimeter and following the standard method ASTM D240
Measurement principle
Heat of combustion is determined in this test method by burning a weighed sample in an oxygen bomb calorimeter under controlled conditions. The heat of combustion is computed from temperature observations before, during and after combustion, with proper allowance for thermochemical and heat transfer corrections.
Slide 24PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
Equipment used – Parr Instruments
Parr 6200 calorimeter
Parr 1108 oxygen bomb
Parr 6510 water handing system
Reference material
Benzoic acid traceable to NIST SRM 39j
Slide 25PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
Measurement system modeling
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Slide 26PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
Uncertainty estimation methods
GUM uncertainty framework Assumed normal distribution
Assumed tStudent distribution (use of effective degrees of freedom)
Monte Carlo Method (MCM) Fixed number of trials
Adaptive MCM
GUM with Bayesian statistics
Empirical method using interlaboratory study (Proficiency Testing Scheme) data
Slide 27PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
GUM uncertainty framework vs Monte Carlo Method (MCM)
Formulation Definition of the output quantity (measurand)
 Determination of the input quantities (sources of
uncertainty)
 Development of a model relating the output quantity
with the input quantities
 Assignment of PDFs to the input quantities on the
basis of available knowledge
Propagation Propagation of the PDFs of the input quantities through
the model to obtain the PDF for the output quantity
Summarizing Use of the PDF of the output quantity to obtain the
expectation (measurement result) of the output quantity
 Use of the PDF of the output quantity to obtain the
standard uncertainty associated with expectation
 Use of the PDF of the output quantity to obtain a
coverage interval containing the output quantity with a
specified probability
PDF: Probability Density Function
No difference
Slide 28PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
GUM uncertainty framework vs Monte Carlo Method (MCM)
Formulation Definition of the output quantity (measurand)
 Determination of the input quantities (sources of
uncertainty)
 Development of a model relating the output quantity
with the input quantities
 Assignment of PDFs to the input quantities on the
basis of available knowledge
Propagation Propagation of the PDFs of the input quantities through
the model to obtain the PDF for the output quantity
Summarizing Use of the PDF of the output quantity to obtain the
expectation (measurement result) of the output quantity
 Use of the PDF of the output quantity to obtain the
standard uncertainty associated with expectation
 Use of the PDF of the output quantity to obtain a
coverage interval containing the output quantity with a
specified probability
PDF: Probability Density Function
x1, u(x1)
Y = f (X1,X2,X3) y, u(y)x2, u(x2)
x3, u(x3)
Assumed PDF for Y
GUM
MCM
PDF for X1
PDF for X2
PDF for X3
Y = f (X1,X2,X3)
PDF for Y
Propagation of uncertainties
Propagation of distributions
Slide 29PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
GUM uncertainty framework vs Monte Carlo Method (MCM)
Formulation Definition of the output quantity (measurand)
 Determination of the input quantities (sources of
uncertainty)
 Development of a model relating the output quantity
with the input quantities
 Assignment of PDFs to the input quantities on the
basis of available knowledge
Propagation Propagation of the PDFs of the input quantities through
the model to obtain the PDF for the output quantity
Summarizing Use of the PDF of the output quantity to obtain the
expectation (measurement result) of the output quantity
 Use of the PDF of the output quantity to obtain the
standard uncertainty associated with expectation
 Use of the PDF of the output quantity to obtain a
coverage interval containing the output quantity with a
specified probability
PDF: Probability Density Function
GUM
MCM
U = k u(y)
Slide 30PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
GUM uncertainty framework – Uncertainty budget
Slide 31PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
GUM uncertainty framework – Uncertainty contributions
Slide 32PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
GUM uncertainty framework – Expanded uncertainty /
Coverage interval estimation
Assumed probability distribution
Standard uncertainty u(Qg) =141.7 J g1 (33.84 cal g1)
Normal (Gaussian) distribution
t distribution
Expanded uncertainty U(Qg)=k . u(Qg)
k=1.96
k=2.08
22 effective degreesof freedom
U(Qg)=277.7 J g1 (66.3 cal g1)
U(Qg)=294.6 J g1 (70.4 cal g1)
Welch–Satterthwaite formula
Slide 33PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
Monte Carlo Method (MCM)– Development
The algorithm of MCM was developed in MATLAB®
1
2
…
n
Number of trials
o Fixed (106)
o Increasing number of trials until the results have stabilized in a statistical sense (Adaptive MCM)
Slide 34PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
Monte Carlo Method (MCM)– MATLAB code flow diagram
Establishment of the process parameters and the
default values of the control variables
Creation of M size row vectors for each of the input
variables
Evaluation of the model. M size file vector
Calculation of the average, standard deviation and
symmetrical interval of the M value sequence
Shortest interval?
Calculation of the shortest coverage interval of the M
value sequence
Value matrices and parameter vectors are formed
First sequence?
Add row to value matrices and parameter vectors
Calculation of the standard deviation of the
parameters
Calculation of the total standard deviation
Calculation of the numerical tolerance related to the
standard deviation
Stabilization?
Calculation of the average and the symmetrical
coverage interval of all the values
Shortest interval?
Calculation of the shortest coverage interval of all the
values
Show results
YES: Interval=1
YES: h=1
YES: Interval=1
YES: comp=1
NO
NO
NO
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Slide 35PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
Monte Carlo Method (MCM)– MATLAB code Flow diagram
Slide 36PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
Monte Carlo Method (MCM)–– Expanded uncertainty /
Coverage interval estimation
1 using a PC equipped with Intel® Core™ i3 M330, 2.13GHz, 4GB RAM
Slide 37PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
MCM results vs GUM results (95% coverage intervals)
12% underestimation
7% underestimation
Slide 38PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
GUM with Bayesian treatment of Type A uncertainties
)(3
1)( iiBayes xs
m
mxu
Standard uncertainty, u(Qg) = 160.7 Jg1 (38 cal g1)
95% coverage interval [44.88 – 45.51] MJ kg1
or [10719 – 10870] cal g1
Comparable to MCM results !!!
Slide 39PhD Thesis – D. Theodorou
Measurement uncertainty estimation of an analytical procedure
Uncertainty evaluated from proficiency testing data
zl
sl
sz
i
i
z
i
i
Ripooled
R
1
1
2)()1(
• The PTS provider is accredited according to ISO/IEC 17043
• Most of the participants used the standard method ASTM D240 for the measurement
li :number of participating laboratories in round i, z: number of rounds
95% expanded uncertainty 0.30 MJ kg1 (71 cal g1)
pooled
Rg sQU 96.1)(
6,3 % compared to MCM
Slide 40PhD Thesis – D. Theodorou
Estimation of the standard uncertainty of a calibration curve
Calibration often comprises an important uncertainty component of the uncertainty of the whole analytical procedure
The slope and the intercept of a linear calibration model are only estimates based on a finite number of measurements
Therefore their values are associated with uncertainties
Slide 41PhD Thesis – D. Theodorou
Estimation of the standard uncertainty of a calibration curve
2 stage  measurement model
xbbY 10
1
00pred
b
byx
calibration data (pairs of xi yi)
0y
correlated
Slide 42PhD Thesis – D. Theodorou
Estimation of the standard uncertainty of a calibration curve
The standard uncertainty of a calibration curve used for the determination of sulfur mass concentration in fuels has been estimated using 4 methodologies:
GUM uncertainty framework
Kragten numerical method
Monte Carlo method (MCM)
Approximate equation calculating the standard error of prediction
n
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yy
Nnb
SExs
1
22
1
2
0
1
regression
pred
11)(
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predb
byx
Slide 43PhD Thesis – D. Theodorou
Estimation of the standard uncertainty of a calibration curve
Results
Mean value (ng μL1)
Standard uncertainty
(ng μL1)
GUM (correlation included) 8.000 0.175
Kragten method (correlation included) 8.000 0.172
MCM (correlation included) 8.003 0.175
Standard error of prediction equation
(including response uncertainty) 8.000 0.175
Standard error of prediction equation
(no response uncertainty included) 8.000 0.137
GUM (no correlation included) 8.000 0.283
Kragten method (no correlation
included) 8.000 0.279
MCM (no correlation included) 8.005 0.284
n
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yy
Nnb
SExs
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22
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2
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1
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pred
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n
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SExs
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pred
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Overestimation of uncertainty by 62%
Slide 44PhD Thesis – D. Theodorou
Estimation of the standard uncertainty of a calibration curve
Bivariate (or joint) Gaussian distribution N(E,V) characterized by the expectation and the covariance (or uncertainty) matrices, E and V
1b
bE
o
)(),(
),()(
1
2
10
100
2
bubbu
bbubuV
A coverage region can be determinedTwo types:•rectangle centered coverage region (separatelydetermined coverage intervals for b1 and b0).•ellipse centered coverage region
specifies a region in 2dimensional space that contains E with
probability p
Treating calibration curve as a bivariate measurement model
Slide 45PhD Thesis – D. Theodorou
Estimation of the standard uncertainty of a calibration curve
(η – E)T V1 (η – E) = kp2
2
11
00
1
1
2
10
100
2
1100)(),(
),()(pk
bn
bn
bubbu
bbububnbn
Rectangular and elliptical coverage regions (p=0.95)
p=0.95
Slide 47PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
Certain approaches should be used to support reliable decisions in conformity assessment of fuels (EN 228, EN 590)
It is necessary to take into account thedispersion of the values that can beattributed to the measurand.
Slide 48PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
The comparison of the result with the specified requirements should be based on predefined decision rules, which are of key importance when the result is close to the tolerance limit
Use of guard bands to determine acceptance or rejection zones taking into account measurement variability
Guarded acceptance
Guarded rejection (Relaxed acceptance)
No rule
Slide 49PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
Guard bands minimize the probability of incorrect decisions (risks)
Guarded acceptance decision rules for upperand lower specification limits (TU, TL) andmaximum probability of falseacceptance (Type II error) when guardbands of width w are used
Guarded rejection (relaxed acceptance)decision rules for upper and lowerspecification limits (TU, TL) and maximumprobability of false rejection (Type Ierror) when guard bands of width w areused
Slide 50PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
Approaches for defining guard bands
The between laboratory precision data approach (ISO 4259 approach)
The intermediate precision (or uncertainty estimate) approach
ISO 4259:2006 Petroleum products  Determination and application of precision data in relation to methods of test
Widely used in fuel market for resolution of disputes
Slide 51PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
The between laboratory precision data approach (ISO 4259 approach)
Sulphur content test method limits
Product Automotive diesel
Specification 10 mg/kg
Dispute Sulphur content off specification
Test method ISO 20846
Reproducibility value R = 0.112*x + 1.12x = sample resultFor x=10, R = 2.24
Upper limit of guard band = TU+0.59*R=10+0.59*2.24=11.3 mg/kg
The product can be considered as FAILING the specification when a single test results falls above 11.3 mg/kg (for 95% confidence level)
Slide 52PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
The between laboratory precision data approach (ISO 4259 approach)
krRR
1122
1
For multiple (k) test results
The expressions have been applied for all the parameters related toautomotive fuel quality referred in EN 590:2009 and EN 228:2008 andthe acceptance limits were calculated using the precision data of therelevant test methods
Slide 53PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
The between laboratory precision data approach (ISO 4259)
unleaded petrol (gasoline) EN228
automotive diesel EN 590
Slide 54PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
The intermediate precision (or uncertainty estimate) approach
Sulphur content test method limits
Product Automotive diesel
Specification 10 mg/kg
Dispute Sulphur content off specification
Test method ISO 20846
Standard uncertainty value u = 0.31
Upper limit of guard band = TU+1.64*u=10+1.64*0.31=10.5 mg/kg
The product can be considered as FAILING the specification when a single test results falls above 10.5 mg/kg (for 95% confidence level)
Slide 55PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
The intermediate precision (or uncertainty estimate) approach
2
analysis2
sampling
k
uuu
For multiple (k) test results
Slide 56PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
Automotive diesel fuel samples were taken from 769 petroleum retail stations and their sulfur mass content was determined in order to assess their compliance with the EU regulatory limit of 10 mg kg1
Slide 57PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
The effect of different approaches for defining guard bands, different levelsof confidence or different number of replicate measurements isinvestigated
ISO 4259 approach
Slide 58PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
Intermediate precision approach
Slide 59PhD Thesis – D. Theodorou
Measurement uncertainty and precision data inconformity assessment
General remarks
The larger the width of the guard band used, the larger the proportion ofsamples that will be judged incorrectly
The differences in the calculations of the two approaches reflect a possiblenumber of samples judged incorrectly when using the ISO 4259 approach(uncertainty estimates represent more precisely the dispersion of the values ofthe measurand)
Minimizing the guard band width by reducing the measurement uncertainty(more replicates, more accurate measurement method) leads to fewer casesof false acceptance or false rejection decisions, reducing as well thecosts associated with these decisions.
At the same time the cost of analysis becomes higher, there is a need that these two costs are balanced against each other in order to find an optimum (target) measurement uncertainty
Slide 60PhD Thesis – D. Theodorou
Conclusions
SAMPLINGMEASUREMENT
PROCEDURE
REPORTING RESULTS AND
ASSESSING CONFORMITY
Statistical and numerical methods have been developed and/or applied concerning the estimation and use of the measurement uncertainty in all parts of the measurement process.
Slide 61PhD Thesis – D. Theodorou
Conclusions
SAMPLINGMEASUREMENT
PROCEDURE
REPORTING RESULTS AND
ASSESSING CONFORMITY
Manual sampling from petroleum retail stations for sulphur determination
Three alternative empirical statistical approaches
Expanded uncertainty of sampling estimated in the range of 0.34 – 0.40 mg kg1.
The estimation of robust ANOVA (0.40 mg kg1) is considered more reliable, because of the presence of outliers
Slide 62PhD Thesis – D. Theodorou
Conclusions
SAMPLINGMEASUREMENT
PROCEDURE
REPORTING RESULTS AND
ASSESSING CONFORMITY
Gross Heat of Combustion of diesel fuel
Two alternative modelling approaches (GUM and Monte Carlo Method)
GUM approaches (Gaussian or tdistribution) underestimate measurement uncertainty
Overall Monte Carlo Method is a more reliable tool (subject to fewer assumptions) (0.32 MJ kg1)
Bayesian treatment of Type A uncertainties “corrects” GUM estimates
Slide 63PhD Thesis – D. Theodorou
Conclusions
SAMPLINGMEASUREMENT
PROCEDURE
REPORTING RESULTS AND
ASSESSING CONFORMITY
Calibration curve construction (Sulphur content determination)
Four alternative approaches (GUM, Monte Carlo Method, Kragten, standard error equation)
All approaches agree well (std uncertainty 0.172 – 0.175 ng μL1)
Importance of correlation – correct use of standard error equation
Slide 64PhD Thesis – D. Theodorou
Conclusions
SAMPLINGMEASUREMENT
PROCEDURE
REPORTING RESULTS AND
ASSESSING CONFORMITY
Conformity assessment of automotive fuel products (EN 590, EN 228)
Acceptance limits for guarded acceptance and guarded rejection for 95% and 99% confidence levels
Significant differences in the resulting number of nonconforming results when using different approaches for defining guard bands, different levels of confidence or different number of replicate measurements
Slide 65PhD Thesis – D. Theodorou
Applications
The program codes developed in MATLAB in order to apply the Monte Carlo method (adaptive and fixed trials) may be used in any type of measurement
Decision Support System for the Evaluation of Conformity of Fuel Products (key features defined)
Slide 66PhD Thesis – D. Theodorou
Future Work
Bayesian uncertainty analysis – Development of numerical techniques
Conformity assessment – Take into account the variability of both the measuring system and the process (production system)
Sampling  Development of methods for the estimation and the inclusion of sampling bias
Slide 67PhD Thesis – D. Theodorou
List of publications  Conferences
PUBLICATIONS
1. D. Theodorou, Y. Zannikou, G. Anastopoulos, F. Zannikos. Coverage interval estimation of the measurement of Gross Heat of Combustion of fuel by bomb calorimetry: Comparison of ISO GUM and
adaptive Monte Carlo method. Thermochimica Acta (2011) 526: 122– 129
2. D. Theodorou, Y. Zannikou, F. Zannikos. Estimation of the standard uncertainty of a calibration curve:
application to sulfur mass concentration determination in fuels. Accreditation and Quality Assurance (2012) 17: 275–281
3. D. Theodorou, N. Liapis, F. Zannikos. Estimation of measurement uncertainty arising from manual
sampling of fuels. Talanta (2013) 105: 360365
4. D. Theodorou, F. Zannikos. The use of measurement uncertainty and precision data in conformity
assessment of automotive fuel products. Measurement (2014) 50: 141151
5. D. Theodorou, Y. Zannikou, F. Zannikos. Components of measurement uncertainty from a measurement
model with two stages involving two output quantities. Chemometrics and Intelligent Laboratory Systems (2015) 146: 305–312
CONFERENCES
5th National Congress on Metrology "Metrologia 2014”
EuroAnalysis 2013  XVII European Conference on Analytical Chemistry
4th National Congress on Metrology "Metrologia 2012”
Slide 68PhD Thesis – D. Theodorou
Acknowledgments
Advisory Committee
F. Zannikos –Professor – School of Chemical Engineering, NTUA (Supervisor)
K. Tzia  Professor – School of Chemical Engineering, NTUA
D. Karonis – Associate Professor  School of Chemical Engineering, NTUA
Fuels and Lubricants Technology Laboratory
Staff
Partners
Graduate / Post graduate students
Slide 69PhD Thesis – D. Theodorou
ΤΗΑΝΚ YOU FOR YOUR ATTENTION !
ΕΥΧΑΡΙΣΤΩ ΓΙΑ ΤΗΝ ΠΡΟΣΟΧΗ ΣΑΣ !