Analysis of Engineering Experiment (FSI-TAI)

Academic year 2025/2026
Supervisor: Ing. Pavel Hrabec, Ph.D.  
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.

 

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.
Learning outcomes and competences:
 
Prerequisites:

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

The course is aimed at the selected parts of mathematical statistics for stochastic modeling of the engineering experiments: regression models, regression diagnostics, multivariate methodsand design iof experiment. Computations are carried out using the software Minitab.
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:

Course-unit credit requirements: active participation in seminars.
Exam: Presenting a assigned project.

 

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

  1. Principal components

  2. Factor analysis.

  3. Cluster analysis.

  4. ANOVA.

  5. Linear regression.

  6. Identification of regression model, regularized regression.

  7. Factorial design of experiment.

  8. Central point, blocks, replications and randomization in DoE.

  9. Fractional factorial DoE.

  10. Response surface DoE.

  11. Mixture DoE.

  12. Logistic regression.

  13. Nonparametric hypotheses testing.
    Computer-assisted exercise

  1. Principal components

  2. Factor analysis.

  3. Cluster analysis.

  4. ANOVA.

  5. Linear regression.

  6. Identification of regression model, regularized regression.

  7. Factorial design of experiment.

  8. Central point, blocks, replications and randomization in DoE.

  9. Fractional factorial DoE.

  10. Response surface DoE.

  11. Mixture DoE.

  12. Logistic regression.

  13. Nonparametric hypotheses testing.
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.
5.

Montgomery, D. C. (c2013). Design and analysis of experiments (8th ed). Wiley.
6.

Agresti, A. (c2013). Categorical data analysis (3rd ed). Wiley-Interscience.
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-FIN-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory 2 1 S
N-MAI-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory 2 2 S
N-PMO-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory-optional 2 1 S