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Statistics in Metrology
Abbreviation: STATUMJLoad: 30(L) + 0(E) + 15(LE) + 0(CE) + 0(PEE) + 0(FE) + 0(S) + 0(DE) + 0(P) + 0(FLE) + 0()
Lecturers in charge: prof. dr. sc. Biserka Runje
Lecturers: dr. sc. Amalija Horvatić Novak ( Laboratory exercises )
doc. dr. sc. Marko Katić ( Laboratory exercises )
doc. dr. sc. Vedran Šimunović ( Laboratory exercises )
Course description: Course objectives:
The course objective is to acquire theoretical and practical knowledge in the application of statistics in metrology.

Enrolment requirements and required entry competences for the course:
No prerequisites.

Student responsibilities:
Attending of laboratory exercises (it is possible to abstain from participating in two lab exercises however this abstention must be compensated for) Attending the lectures (three abstentions are permitted) Passing the practical part of the examination. Passing the theoretical part of the examination.

Grading and evaluation of student work over the course of instruction and at a final exam:
Successfully complete the practical part of the examination: 70% Successfully complete the theoretical part of the examination: 30%

Methods of monitoring quality that ensure acquisition of exit competences:
In order to have continuous monitoring of quality performance of the Course an anonymous, simple and quick questionnaires of student"s opinion will be preformed by use of module Moodle application Question. The readiness of students to other forms of engagement will be analyzed (research, discussion, development projects, etc.) At the end, the quality of Course will be assessed through University questionnaire that student fulfills online, through the ISVU system, in order to evaluate work of teachers and the attractiveness of topics.

Upon successful completion of the course, students will be able to (learning outcomes):
Interprete the basic measurement terms with statistical quantities. Use statistical tools and methods for the analysis, comparison and validation of measurement results. Conduct a statistical analysis of the quality of the measurement system. Use statistical tools in the estimation of the process capability. Determine the influence of the measurement system on process capability assessment.

1. Statistical thought and the need for the application of statistics in measurement
2. Statistics in the function of measurement and ofbasic measurement terms.
3. Application of simulation in metrology. Theoretical basis of the simulations. Data distributions.
4. Analysis of the measurement system. Assessment of the quality of the measurement system (GR&R).
5. The theory of intercomparison measurements according to standards ISO 5725.
6. Exam 1.
7. Measurement uncertainty. Theory. Methods of estimation of measurement uncertainty. GUM method, MCS method.
8. The steps to be followed for evaluating and expressing the uncertainty of the result of a measurement according to GUM method.
9. The steps to be followed for evaluating and expressing the uncertainty of the result of a measurement according to the MCS method.
10. Uncertainty budgets. Choosing a coverage factor. Coverage interval. Reporting uncertainty.
11. Validation of the GUM uncertainty framework using a Monte Carlo method.
12. Intercomparison measurements. International intercomarison measurements. Key comparison. Bayesian approach to key comparisons.
13. Statistical Tolerancing. Worst Case analysis, Root Sum of Squares (RSS) analysis.
14. Six Sigma Tolerance Analysis.
15. Exam 2.

1. Practical problems examples
2. Numerical and graphical description of measurement terms. Correcting errors.
3. Using random numbers to generate probability distributions: normal, uniform, triangular, U shaped, Weibull, exponential.
4. X bar and R method. ANOVA method.
5. Accuracy and precision of measurement results. Precision in terms of reproducibility, precision in terms of reproducibility.
6. Analysis of the first test results.
7. Modelling the measurement Evaluating standard uncertainty
8. Type A evaluation of standard uncertainty Type B evaluation of standard uncertainty
9. Determining combined standard uncertainty according to the GUM and MCS methods. Uncorrelated input quantities Correlated input quantities. Determining expanded uncertainty according to the GUM and MCS methods.
10. GUM method, MCS method. Examples.
11. Expression of measurement results. Validation of the results. Rule of compliance.
12. Examples Analysis of Intercomparison mesaurements. En ratio, Birg"s ratio. Application of chisquared test in key comparisons.
13. WCS and RSS methods. Examples.
14. SSTA method. Examples.
15. Course evaluation and final discussion.
Lecture languages: hr
Compulsory literature:
1. JCGM 100: 2008 Vrednovanje mjernih podataka Uputa za iskazivanje mjerne nesigurnosti,
2. Državni zavod za mjeriteljstvo 2008.
3. JCGM 101: 2008 Vrednovanje mjernih podataka Dopuna 1. Uputama za iskazivanje mjerne nesigurnosti
4. Prijenos razdioba upotrebom metode Monte Carlo, Državni zavod za mjeriteljstvo 2008.
5. A Bayesian approach to the linking of key comparisons, M Krystek, H Bosse 2015.
6. Douglas C. Montgomery, Statistical Quality Control, 2012
Recommended literature: - - -
L - Lectures
FLE - Practical foreign language exercises
E - Exercises
LE - Laboratory exercises
CE - Project laboratory
PEE - Physical education excercises
FE - Field exercises
S - Seminar
DE - Design exercises
P - Practicum
* - Not graded
Copyright (c) 2006. Ministarstva znanosti, obrazovanja i športa. Sva prava zadržana.
Programska podrška (c) 2006. Fakultet elektrotehnike i računarstva.
Oblikovanje(c) 2006. Listopad Web Studio.
Posljednja izmjena 2019-06-07