Experiments in Engineering
Code  Completion  Credits  Range  Language 

2362701  KZ  3  1P+2L  Czech 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Instrumentation and Control Engineering
 Synopsis:

The course provides an introduction to Design of Experiments in the field of engineering. The concept of measurement is presented as a key method for information acquisition which together with correct interpretation allow understanding of not only engineering phenomena. Provided is an introduction to applied mathematical statistic and uptodate data analysis with computer support. During exercises students master design of effective experiments and get skilled with MATLAB environment especialy with tools for data analysis.
 Requirements:
 Syllabus of lectures:

1. Research project. Population and sample, Deduction and induction, A Characteristic, Design of a research project, Data acquisition, Interpretation of the results
2. Probability theory  an introduction. Rules of probability, Bayes theorem, ROC curve, Odds, probability, likelihood
3. Probability distribution. Discrete and continuous random variable, Probability and relative frequency, Normal distribution, Binomial distribution, Poisson distribution, Sample and descriptive statistics, Measures of central tendency, Mean, modus, median, Measures of variation, Range, Variation, Standard deviation, Quantiles
4. Estimates of probability, Distribution of a sample mean, Interval estimate of a mean, Sample size
5. Hypothesis testing. Null and alternative hypothesis, The type I. and II. errors
6. Two samples comparison. Mean comparison, Pair comparison
7. Nonparametric methods. Quantile, median and sign tests, Wilcoxon's pair test, MannWhitney's test
8. Nominal data. Chisquare test, Contingency tables
9. Linear regression and correlation
10. Analysis of variance. Mean comparison for 3+ groups, Model condition verification, Multiple comparison
 Syllabus of tutorials:

1. Visualising a random process . Random numbers generation, Creating a plot, Computation of the probability of random processes, Conditional probability computation, Testing the dependence of random processes, Calculating probabilities using Bayes' theorem (Matlab)
2. Calculation of the sensitivity and selectivity of a test. Construction of the ROC curve (Matlab)
3. Calculation of odds, probabilities and likelihoods
4. Construction of the probability distribution function and the distribution function for discrete and continuous random variable (Matlab)
5. Visualising the probability density. Calculating probabilities (Matlab)
6. Calculation of the descriptive characteristics. Plotting the histogram, the percentile plot, box plot, normal plot (Matlab)
7. Visualising the probability distribution of the sample mean (Matlab)
8. Hypothesis testing. Carrying out one sample ttest, two sample ttest, comparison of the population probabilities, Evaluation of the pair measurement, Carrying out nonparametric tests, quantile test, median test, sign test, Wilcoxon's test, MannWhitney's test
9. Categorial data. Carrying out chisquare test, Evaluation of the contingency table (Matlab)
10. Carrying out linear regression and correlation (Matlab)
11. Carrying out analysis of variance
12. Execution of an experiment
13. Presentation of the results of the experiment
 Study Objective:

1. Ability to design and execute an experiment in engineering
2. Ability to formulate an experimental problem
3. Ability to analyze the object under investigation
4. Ability to analyze available means for execution of an experiment
5. Ability to desing the ideal model of an experiment
6. Ability to design the experimental model of an experiment
7. Ability to design and solve the analytical model of an experiment
8. Ability to acquire the data
9. Ability to infer conclusions for the model of a system
10. Ability to infere conclusions for the behavior of the real system
11. Ability to analyze data in the Matlab environment
12. Ability to present the results of an experiment
 Study materials:

1. Experiments in Engineering subject web, http://pmo.fs.cvut.cz/tex
2. Bernard, J., Technický experiment, ČVUT Praha 1999
3. Novovičová, J., Pravděpodobnost a matematická statistika, ČVUT Praha 1999
4. Beneš, V., Pravděpodobnost a matematická statistika, ČVUT Praha 1995
5. Zvárová, J., Introduction to Statistics for Biomedical Domains, Karolinum Praha 1998, http://pmo.fs.cvut.cz/biostaten
6. MATLAB Statistics Toolbox, http://www.mathworks.com/help/toolbox/stats
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: