Analysis of Engineering Experiment (FSI-TAI)

Academic year 2023/2024
Supervisor: doc. RNDr. Zdeněk Karpíšek, CSc.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:

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.
Learning outcomes and competences:

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.
Course contents:

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..
Teaching methods and criteria:

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.
Controlled participation in lessons:

Attendance at seminars is controlled and the teacher decides on the compensation for absences.
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 1 hrs. compulsory                  
Course curriculum:
    Lecture

  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

  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.
Literature - fundamental:
1. Ryan, T. P.: Modern Regression Methods. New York : John Wiley, 2004.
2. Montgomery, D. C., Renger, G.: Applied Statistics and Probability for Engineers. New York: John Wiley & Sons, 2010.
3. Anděl, J.: Základy matematické statistiky. Praha: Matfyzpress, 2011.
4. Hebák, P., Hustopecký, J., Jarošová, E., Pecáková, I.: Vícerozměrné statistické metody 1, 2, 3, Praha: INFORMATORIUM, 2004.
Literature - recommended:
1.

Davison, A. C., Hinkley, D. V.: Bootstrap Methods and their Applications. Cambridge: Cambridge University Press, 2006.
2.

Moor, R. E., Kearfott, R. B., Clood, M. J.: Introduction to Interval Analysis. Philadelphia: SIAM 2009.
3.

Klir, G. J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. New Jersey: Prentice Hall 1995.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
N-MAI-P full-time study --- no specialisation -- GCr 5 Compulsory 2 2 S
N-PMO-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory-optional 2 1 S
N-FIN-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory 2 1 S