### Measurement Theory

#### Course Description

Data Measurement. Fields: monitoring, research, development, measurement, control. DMS (Data Measurement System): definition, structure, outer and inner limits, classification according to the information and energy.Experiment. Fundamentals and terms (requirements, limits, repeatability). Carrying out of an experiment and records.Error analysis. Direct measurements and weighted factors. Quantities measured indirectly. Weighted regression functions, uncertainty of parameters. Application of matrix in the error analysis. Uncertainty of the predicted value. Conditional measurements and conditional equations. Calculation of corrections. Examples.Mathematical model of measurand. Parameters of real measurements (final resolution, hysteresis, arithmetic of final precision, non-corrected values). Correlated and non-correlated quantities. Effective level of freedom and level of confidence. Examples.Results of measurement. Rejection of result according to Chauvenet criterion.

#### General Competencies

The course gives a deep understanding of the fundamentals of theory of measurements, as well as the theoretical approaches to the error analysis and the calculation of the values, parameters and predicted values according to the weighted functions. The students will have ability to analyse the results obtained in real measurement situations and practical skills to perform the necessary calculation for the determination of the most probable value and associated uncertainty.

#### Learning Outcomes

1. Recall diferent contributions to the uncertainty of measurement
2. Estimate uncertainty of measurement for uncorrelated quantities
3. Employ Gauss distribution for determination of expanded uncertainty
4. Analysis of indirect and conditional measurements
5. Create self-developed algorithms for regression functions
6. Assess different approaches in the estimation of measurement results

#### Forms of Teaching

Lectures

Lectures to the group of students.

Exams

Mid-term exam and final exam.

Exercises

The time-schedule for lectures will be used.

Consultations

Continuous Assessment Exam
Homeworks 0 % 10 % 0 % 10 %
Quizzes 0 % 10 % 0 % 0 %
Mid Term Exam: Written 40 % 25 % 0 %
Final Exam: Written 40 % 25 %
Final Exam: Oral 30 %
Exam: Written 40 % 50 %
Exam: Oral 40 %

#### Week by Week Schedule

1. Data Measurement. Fields: monitoring, research, development, measurement, control. Introduction to analysis of measurement data.
2. DMS (Data Measurement System): definition, structure, outer and inner limits, classification according to the information and energy. Experiment. Fundamentals and terms (requirements, limits, repeatability). Carrying out of an experiment and records.
3. Mathematical model of measurand. Uncertaint of measurement - concept and contributions.
4. Correlated and non-correlated quantities. Effective level of freedom and level of confidence.
5. Error analysis. Direct measurements and weighted factors.
6. Laboratory methods of measurements and examples of determination of uncertainty of measurement.
7. Interlaboratory comparisons and determination of reference value.
8. Mid-term exam.
9. Quantities measured indirectly. Weighted regression functions, uncertainty of parameters. Application of matrix in the error analysis. Uncertainty of the predicted value.
10. Conditional measurements and conditional equations. Calculation of corrections.
11. Statistical functions and computer programs.
12. Usporedba više mjernih nizova i analiza varijance (ANOVA metode).
13. Parameters of real measurements (final resolution, hysteresis, arithmetic of final precision, non-corrected values). Rejection of result according to Chauvenet criterion.
14. Advanced techniques for analysis of results of measurement.
15. Final exam

#### Study Programmes

[FER2-HR] Electrical Engineering Systems and Technologies - profile
Theoretical Course (2. semester)

#### Literature

D.C. Montgomery (2000.), Design and Analysis of Experiments (5th Edition), Wiley
J.R. Taylor (1997.), An introduction to error analysis, University Science Books, Sausalito, CA
B.E. Cooper (1975.), Statistics for experimentalists, Pergamon Press, Oxford
N. Čubranić (1967.), Teorija pogrešaka s računom izjednačenja, Tehnička knjiga
V. Bego (1966.), Mjerna tehnika (Pogreške električnih mjerenja), Sveučilište u Zagrebu

#### General

ID 86533
Summer semester
5 ECTS
L2 English Level
L1 e-Learning
40 Lectures
0 Seminar
5 Exercises
0 Laboratory exercises
0 Project laboratory