Course detail

Analysis of Engineering Experiment

FSI-TAI Acad. year: 2023/2024 Summer semester

The course is concerned with the selected parts of mathematical statistics for stochastic modeling of the engineering experiments: regression models, regression diagnostics, multivariate methods, probability distributions estimation, interval statistical analysis, and fuzzy statistics. Computations are carried out using the software as follows: Statistica, Minitab, and Excel..

Supervisor

doc. RNDr. Zdeněk Karpíšek, CSc.

Department

Institute of Mathematics

Learning outcomes of the course unit

Students acquire needed knowledge from the mathematical statistics, which will enable them to evaluate and develop stochastic and interval models of technical phenomena and processes based on these methods and realize them on PC.

Prerequisites

Descriptive statistics, probability, random variable, random vector, random sample, parameters estimation, hypotheses testing, and regression analysis.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Course-unit credit requirements: active participation in seminars, mastering the subject matter, and delivery of semester assignment. Examination (written form): a practical part (5 tasks), a theoretical part (5 tasks); ECTS evaluation used.

Language of instruction

Czech

Aims

The course objective is to make students majoring in Mathematical Engineering and Physical Engineering acquainted with important selected methods of mathematical statistics used for a technical problems solution.

Specification of controlled education, way of implementation and compensation for absences

Attendance at seminars is controlled and the teacher decides on the compensation for absences.

The study programmes with the given course

Programme N-FIN-P: Physical Engineering and Nanotechnology, Master's
branch ---: no specialisation, 5 credits, compulsory

Programme N-MAI-P: Mathematical Engineering, Master's
branch ---: no specialisation, 5 credits, compulsory

Programme N-PMO-P: Precise Mechanics and Optics, Master's
branch ---: no specialisation, 5 credits, compulsory-optional

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. RNDr. Zdeněk Karpíšek, CSc.

Syllabus


  1. Stochastic modeling of the engineering problems.

  2. Regression model identification.

  3. Linear regression models and diagnostic.

  4. Nonlinear regression analysis.

  5. Correlation analysis.

  6. Principle components and factor analysis.

  7. Cluster analysis.

  8. Bootstrap estimates.

  9. Continuous probability distributions estimation.

  10. Discrete probability distributions estimation.

  11. Interval analysis.

  12. Interval statistical models.

  13. Fuzzy statistics.

Computer-assisted exercise

13 hours, compulsory

Teacher / Lecturer

doc. RNDr. Zdeněk Karpíšek, CSc.

Syllabus


  1. PC statistical software.

  2. Regression model identification. Semester work assignment.

  3. Linear regression models and diagnostic.

  4. Nonlinear regression models.

  5. Correlation analysis.

  6. Principle components and factor analysis.

  7. Cluster analysis.

  8. Bootstrap estimates.

  9. Continuous probability distributions estimation.

  10. Discrete probability distributions estimation.

  11. Interval analysis.

  12. Interval statistical models.

  13. Fuzzy statistics.