Theory of Measurement

Prerequisite:

Mathematics for cybernetics and measurement (X01MKM)
Mathematics 3C (X01M3C)
Electrical Measurements and Instrumentation C (X38EMC)

Lecturer:

Tutor:

Supervisor:

Department of Measurement

Synopsis:

After a brief introduction devoted to fundamentals of representation theory of measurement, explanation is focused on units of measurable quantities and possibilities of their definition, realisation, conservation and reproduction by means of measurement standards. Main attention is paid to measurement methods and to techniques of evaluating and increasing measurement accuracy. Fundamental problems of theory of measurement errors and uncertainties are outlined and basic principles of design of experiments are discussed.

Requirements:

Syllabus of lectures:

1. Introduction. Fundamental concepts of representation theory of measurement (uniqueness problem, scales).

2. Physical quantities and their units. International System of Units (SI). Standards of electrical quantities.

3. Quantum standards of voltage and resistance. Thompson-Lampard capacitance standard.

4. Secondary standards of electrical quantities. Hamon transfer standards.

5. Collective standards and optimum schemes of comparing their constituents.

6. Measurement principles, methods and procedures. Direct, indirect, absolute and comparative measurement methods.

7. Errors of direct measurements. Allan variance.

8. Procedures for eliminating systematic and random errors.

9. Errors of dynamic measurements and possibilities of their correction.

10. Fundamental concepts of information theory of measurement. Expected measurement information, entropy value of the measurement error.

11. Detecting outiers in a measurement data set. Normality tests.

12. Measurement uncertainties. Type A and Type B standard uncertainty, expanded uncertainty. Law of propagation of uncertainty.

13. Determination of the coverage factor for a given level of confidence. Effective degrees of freedom.

14. Basic principles of the theory of design of experiments. Full and fractional factorial designs.

Syllabus of tutorials:

1. Introduction.

2. Thompson-Lampard capacitance standard.

3. Measurement of characteristics of resistance standards.

4. Measurement of characteristics of capacitance standards.

5. Measurement of characteristics of standard self- and mutual inductors.

6. Thermoelectric transfer standard.

7. Hamon transfer standard.

8. Collective standard of DC voltage.

9. Statistical analysis of measurement data.

10. Examples of calculating measurement errors.

11. Examples of calculating measurement uncertainties.

12. Examples of calculating measurement uncertainties.

13. Examples of calculating measurement uncertainties.

14. Discussion of results, assessment.

Study Objective:

Study materials:

[1] Dietrich, C. F.: Uncertainty, Calibration and Probability. Adam Hilger, Bristol 1991

[2] The Expression of Uncertainty and Confidence in Measurement. M3003 Edition 2, UKAS 2007

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Cybernetics and Measurements - Measurement and Instrumentation Systems- structured studies (compulsory course)