Design of Experiments

Course guarantor:

Jiří Franc

Lecturer:

Jiří Franc

Tutor:

Jiří Franc

Supervisor:

Department of Mathematics

Synopsis:

1.Introduction to the design of experiments and data analysis.

2.Completely randomized one-factor experiment: introduction of a fixed-effect model, tests of equality of mean values, choice of number of observations.

3.Methods of multiple comparison: Bonferroni method, Scheffy method, Tukey method

4.Randomized complete block design: model definition, equality effects tests, power of test, determining sample size.

5.Latin and Greco-Latin squares, balanced incomplete block design, model adequacy checking, residuals, multiple comparisons.

6.Two factor factorial design: statistical models and their properties for designs 2^2, 2^3 and 2^k, fractional factorial design, resolutions.

7.3^k factorial designs, confounding in 3^k factorial design.

8.Models with random effects, factorials with mixed levels.

Requirements:

Prerequisites: Knowledge corresponding to the basic courses in probability, statistics, and linear regression taught at KM, FNSPE.

Conditions for successful completion of the course:

Credit requirements:

Active participation in at least 10 lectures (can be substituted by completing and submitting the assignments given in those lectures).

Active participation in two team assignments consisting of designing an experiment, collecting data, and analyzing it.

Exam:

An individual project involving the design of an experiment, data collection, data analysis, and discussion of the analysis.

Syllabus of lectures:

1.5. Introduction to the design of experiments and their evaluation, Completely randomized one-factor experiment: introduction of the fixed effects model, tests of equality of means, choice of sample size, Multiple comparison methods: Bonferroni method, Scheffé method, Tukey method, Randomized block experiment: model definition, tests of equality of effects, test power, choice of sample size, estimation of missing values, Designs using Latin and Graeco-Latin squares: tests of equality of effects, verification of model adequacy, residuals, multiple comparisons

6.10. Two-level factorial experiments: statistical models and their properties for designs 2², 2³, and 2, Three-level factorial experiments 3, Response Surface Methods and Designs

11.12. Models with random effects, use of mixed linear models, Nested and Split-Plot models

Syllabus of tutorials:

1.5. Introduction to the design of experiments and their evaluation, Completely randomized one-factor experiment: introduction of the fixed effects model, tests of equality of means, choice of sample size, Multiple comparison methods: Bonferroni method, Scheffé method, Tukey method, Randomized block experiment: model definition, tests of equality of effects, test power, choice of sample size, estimation of missing values, Designs using Latin and Graeco-Latin squares: tests of equality of effects, verification of model adequacy, residuals, multiple comparisons

6.10. Two-level factorial experiments: statistical models and their properties for designs 2², 2³, and 2, Three-level factorial experiments 3, Response Surface Methods and Designs

11.12. Models with random effects, use of mixed linear models, Nested and Split-Plot models

Study Objective:

Knowledge:

Basic notions and principles of design and analysis of experiments.

Skills:

Application to solution of practical problems, i.e. ability to design an experiment for a concrete problem and to do its statistical evaluation.

Study materials:

Key references:

[1] Design and Analysis of Experiments, 10th Edition, Wiley 2019

Recommended references:

[2] J. Antony: Design of Experiments for Engineers and Scientists, Butterworth-Heinemann, 2003

[3] R. H. Myers: D. C. Montgomery: Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley 2016

Note:

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Aplikované matematicko-stochastické metody (compulsory course in the program)