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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

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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 f Chemical Engineering

    Department f Synthesis and

    Development f 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) = non-negativeparameter 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 (Hubers 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

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    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 (F-test) 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 t-Student 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 g-1 (33.84 cal g-1)

    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 g-1 (66.3 cal g-1)

    U(Qg)=294.6 J g-1 (70.4 cal g-1)

    WelchSatterthwaite 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

    Lines 3-7*

    Lines 8-49*

    Lines 50-53*

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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 Jg-1 (38 cal g-1)

    95% coverage interval [44.88 45.51] MJ kg-1

    or [10719 10870] cal g-1

    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 kg-1 (71 cal g-1)

    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

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    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

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    yy

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    22

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    regression

    pred

    11)(

    xbbY 10

    1

    00

    predb

    byx

  • Slide 43PhD Thesis D. Theodorou

    Estimation of the standard uncertainty of a calibration curve

    Results

    Mean value (ng L-1)

    Standard uncertainty

    (ng L-1)

    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

    i

    i xxb

    yy

    Nnb

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    1

    22

    1

    2

    0

    1

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    2022

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    n

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    yy

    nb

    SExs

    1

    22

    1

    2

    0

    1

    regression

    pred

    1)('

    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 2-dimensional 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

    ( E)T V-1 ( E) = kp2

    211

    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

    11221

    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 kg-1

  • 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 kg-1.

    The estimation of robust ANOVA (0.40 mg kg-1) 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 t-distribution) underestimate measurement uncertainty

    Overall Monte Carlo Method is a more reliable tool (subject to fewer assumptions) (0.32 MJ kg-1)

    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 L-1)

    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 non-conforming 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: 275281

    3. D. Theodorou, N. Liapis, F. Zannikos. Estimation of measurement uncertainty arising from manual

    sampling of fuels. Talanta (2013) 105: 360-365

    4. D. Theodorou, F. Zannikos. The use of measurement uncertainty and precision data in conformity

    assessment of automotive fuel products. Measurement (2014) 50: 141-151

    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: 305312

    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

    YOU FOR YOUR ATTENTION !

    !