**Evaluation of Inter-laboratory Comparisons**

**Adriana Horníková**

**div. 898 (SED), ITL**

***Abstract:*** Under evaluation of inter-laboratory comparisons (ILC)
is understood the statistical determination of estimates of the mean
value (value of the true measured quantity in specific cases referred to
as reference value), variance components (which are within-laboratory
and between-laboratory variances) and their confidence intervals. The
model for evaluation of inter-laboratory comparison in this study (my
PhD thesis) coincides with the mixed linear model with one factor
$\alpha$ („laboratory"):

$Y = 1\mu + \alpha + e$.

$Y$ represents measurement series vector of the true value of the
measured quantity $\mu$ in individual laboratories. $e$ stands for
random quantity of errors.

The factor $\alpha$ can be understood either as a fixed effect or a
random effect (random effect model). If we suppose $\alpha$ to be random
and the measurements are normally distributed with mean $\mu$ (the true
measured value) and dispersion
$\sigma_{L}^{2} + \sigma_{\text{ei}}^{2}$, where $\sigma_{L}^{2}$ being
the inter-laboratory variance and $\sigma_{\text{ei}}^{2}$ the
within-laboratory variance of i^th^ laboratory. In model with one random
effect we try to estimate the variability of random effect, so of
inter-laboratory variance $\sigma_{L}^{2}$. If $\sigma_{L}^{2} = 0$, the
random effect „laboratory" does not have any influence on results.

In the first step of ILC evaluation we test the requirement of normal
probability distribution of measurements and the homoscedasticity of
measurements that is the achievement of comparable within-laboratory
variances (repeatability) of measurements in individual laboratories.

PhD-thesis allows to determine the consensus value for a large class of
ILC models also for heteroscedastic measurements when introducing
uncertainty evaluated by means of method type B.

Based on a study of simulated experiments with heteroscedastic
measurements it can be shown that the use of either one of the three
following methods: maximum likelihood, Mandel-Paule and modified
Mandel-Paule's method to evaluate ILC is appropriate.

The influences of variance components (between laboratory variance based
on the Burdick-Eickman estimate) on the consensus value for
heteroscedastics measurements has been also studied.

Presenting Author\'s information

Name: Adriana Horníková

Division: 898

Laboratory:ITL

Room and Building address: 820 W. Diamond Avenue, 820/381 (NIST North)

Mail Stop: 8980 Telephone: (301) 975-8118 FAX: (301) 990-4127

Email: Adriana.hornikova@nist.gov

Sigma Xi member - no

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**Curriculum Vitae**

**of Adriana Horníková**

-   1973: Born in Bratislava, Slovak Republic

**Education and Long Term Employment**

-   1980 - 88: Elementary/primary school in Bratislava

-   1988 -- 92: Grammar school in Bratislava

-   1992 -- 97: Slovak Technical University in Bratislava Faculty of
    Mechanical Engineering, studying later at Department for Measurement
    and Automation

-   1992-2000: Comenius University in Bratislava, Faculty of Natural
    Sciences studying chemistry and biochemistry

-   1997-2002: Slovak Technical University in Bratislava Faculty of
    Mechanical Engineering in Metrology

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-   Since 2001- : I work as a university teacher at the Dept. of
    Statistics at the Faculty of Economics Informatics at University of
    Economy in Bratislava

-   2003: Education to certified Quality Auditor at TU Wien (the
    University of Technology in Wien, Austria at the Faculty of
    Mechanical Engineering dep. for interchangeable manufacturing and
    metrology (Prof. P. H. Osanna)).

# Studies abroad and visiting posts:

-   1991: Grammar school in Wien, Austria

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-   1995-96: University of Technology in Wien, Austria at the Faculty of
    Mechanical Engineering in an interdisciplinary area of Biomedical
    Engineering (tutor: Prof. H.P. Troger).

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-   1998-1999: student exchange stay at Swiss Federal Institute of
    Technology ETH in Zurich, Switzerland (tutor: Doc. Dipl.
    Ing.-ETH K. H. Ruhm), project on dynamical force calibration.

-   2002-2003: several distinguished visits at the University of
    Technology in Wien, Austria at the Faculty of Mechanical Engineering
    dep. for interchangeable manufacturing and metrology (Prof. P. H.
    Osanna)

-   2003-2004: foreign guest researcher at NIST (Statistical Engineering
    Division) in Gaithersburg, MD, USA.

# Academic Titles

-   1997: Ing (Engineer of Mechanical Engineering)-eq. to Master of
    Engineering

-   2000: Mgr (Magister in Natural Sciences)-eq. to Master of Natural
    Sciences

-   2002: PhD (Philosophiae doctor).

# Teaching Experience

-   Since 1998 at the Faculty of Mechanical Engineering, Slovak
    Technical University in Bratislava in:

-   Design and Evaluation of Measurement,

-   Quality Assurance of Measuring and Information System,

-   Measurement Theory, Experiment and Signal Processing,

-   Measurement and Automatic Control,

-   Informatics,

-   Programming Languages (Turbo Pascal),

-   Since 2001 at the Faculty of Economics Informatics at University of
    Economy in Bratislava in:

-   Statistics (fundamentals).

**Research Interests:**

-   uncertainty evaluation on hydraulic elements

-   quality assurance and measurement process control

-   dynamic calibration of force sensor

-   statistical analysis, testing and design

-   inter-laboratory comparison, consensus value, repeatability and
    reproducibility

**International Co-operation:**

-   International Project within the framework of grant of European
    Training Foundation (ETF), namely Tempus Institution Building
    Project IB-JEP-13 250/98 *Education and Training in Accreditation
    and Certification (EDUTRAC)*.

**Institutional Projects of the Slovak Research Agency VEGA:**

-   01/4157/97 Testing and Calibration of Multicomponent Sensors;

-   1/7077/20 Verification and Calibration of Sensors;

-   1/8084/01 Statistical Measurement Processes Control;

-   Chajdiak at University of Economics

**Address:**

Statistical Engineering Division

US Department of Commerce, NIST

820 W. Diamond Avenue, 820/381

Gaithersburg, MD 20899-8980

Tel: (301) 975-8118

Fax: (301) 990-4127

E-mail: adriana.hornikova@nist.gov

Web-side:

Home Address: 18831 Nathans Place, Gaithersburg, MD 20 879, USA

Home Phone: 301 977 8044

***In Slovakia***

Home Address: Palisády 25, 811 06 Bratislava, Slovak Republic

Home Phone: 00421/2/544 11 258

**Selected Publications:**

**Books** (1): Palenčár, R., Ruiz, J. M., Janiga, I., Horníková, A. to
the topic "Statistical Methods in Metrological and Testing
Laboratories", Graphic studio Ing. P. Juriga, 2001 Bratislava (ISBN
80-968449-3-8).

**Evaluation Guide**: Palenčár, R., Horníková, A.: (Inter-laboratory
comparison of transformation oils testing / Statistical Evaluation)
1999, SjF STU Bratislava.

**Workshops contributions** (17):

-   Horníková, A., Palenčár, R., Wimmer, G.: Mathematical Models for
    Inter-laboratory Comparison. Workshop on Advanced Robot Systems and
    Virtual Reality, ISMCR´2000, 28-30 September 2000, Vienna-Austria.
    XVI IMEKO WORLD CONGRESS IMEKO 2000, PROCEEDINGS Vol. XI: p. 133-138

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-   Horníková, A.: Mathematical Model for Inter-Laboratory Comparison.
    2^nd^ Proceedings, April 26-29, 1999 Smolenice SR. (eng.)

-   Horníková, A.: Evaluation of Consensus Values, In: Strojné
    inžinierstvo '98, p. 505-508.

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-   Horníková, A., Palenčár, R., Wimmer, G.: Inter-laboratory Comparison
    Methods In: Strojné inžinierstvo ´2000.

-   Palenčár, R., Chudý, V., Horníková, A.: Further Dissemination of the
    EDUTRAC Project Results (Training Activities of Slovak Technical
    University Faculty of Mechanical Engineering Dep. of Automation and
    Measurement for the year 2001 as the Output of International TEMPUS
    Project).

## M.N.Durakbasa: Developments of surface measurement and evaluation of biomedical structures, Trendy Rozvoja Biomedicínskeho Inžinierstva Konferencia s medzinárodnou účasťou poriadaná pri príležitosti osláv 50. výročia založenia Strojníckej fakulty TU v Košiciach a 15. výročia zriadenia študijného odboru \"Biomedicínske inžinierstvo\", Hotel SLOVAN, Tatranská Lomnica, Máj 22 -- 23, 2002.

-   Ing., Mgr. Adriana Horníková: International Standards (CEN and ISO)
    and their Transfer into Slovakian Norms, International Quality Days
    Pristina, Kosova 27-29 September 2002.

-   P. Herbert Osanna, Peter Kopacek, Adriana Hornikova: Automation
    Education in the EC from the Viewpoint of SME\`s, Co-ma-tech 2002,
    24-25 October 2002.

-   Ing., Mgr. Adriana Horníková: International Standards (CEN and ISO)
    and their Transfer into Slovakian Norms, Co-ma-tech 2002, 24-25
    October.

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-   Horníková: Analysis of Measurement of Inter-Laboratory Comparison
    through Confidence intervals, XVII IMEKO World Congress, June 22-27,
    2003 Dubrovnik Croatia, pp. 1284-1288.

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-   A. Horníková: Evaluation of Inter-laboratory Comparison, Proceedings
    of the 4^th^ International Conference on Measurement, June 15-19,
    2003 Smolenice SR, pp. 51-54.

-   M. Numan Durakbasa, P. Herbert Osanna, Adriana Hornikova: Biomedical
    Application of Form Measurement and Coordinate Metrology, 2003 (in
    preparation)

-   P. H. Osanna, A. Janac, M. N. Durakbasa, A. Hornikova: Modern Design
    and Manufacturing on the Basis of Developments in Nanotechnology,
    2003 (in preparation)