Course detail

Analysis of Engineering Experiment

FSI-TAIAcad. year: 2023/2024

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..

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Zdeněk Karpíšek, CSc.

Department

Institute of Mathematics (ÚM)

Entry knowledge

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

Rules for evaluation and completion of the course

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.


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

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.


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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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

Recommended reading

Davison, A. C., Hinkley, D. V.: Bootstrap Methods and their Applications. Cambridge: Cambridge University Press, 2006. (EN)
Klir, G. J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. New Jersey: Prentice Hall 1995. (EN)
Moor, R. E., Kearfott, R. B., Clood, M. J.: Introduction to Interval Analysis. Philadelphia: SIAM 2009. (EN)

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme N-FIN-P Master's 1 year of study, summer semester, compulsory
  • Programme N-MAI-P Master's 2 year of study, summer semester, compulsory
  • Programme N-PMO-P Master's 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

26 hod., 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 hod., 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.

Elearning

eLearning: currently opened course