Reliability of systems

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Inferential statistics. Theory of probability. Random variables and its characteristics. Basic methods of reliability theory.

Requirements:

Basic calculus.

Syllabus of lectures:

1.Statistical data processing in theory of reliability. Statistical inference.

2.Probability and conditional probability. Reliability of a system consisting of more components

(inclusion and exclusion principle).

3.The Law of Total probability and Bayes´ theorem.

4.Random variables.Expectation, standard deviation.

5.Continuous random variables. Expectation, standard deviation, quantiles.

6.Normal distribution. Log-normal distribution.

7.Estimation of expectation, stabdard deviation, quantiles fro data. Confidence interval for expectation of normal distribution.

8.Bivariate distribution. Independence of random variables.

9.Confidence interval for difference of expectations of two independent normally distributed random variables.

10.Correlation.

11.Distribution of a linear combination of normally distributed random variables.

12.Rezistence of the construction. Index of reliability. Degree of confidence.

13.Monte Carlo Methods.

Syllabus of tutorials:

Exercises follow lectures.

Study Objective:

Basic knowledge of reliability theory.

Study materials:

!Jarušková D. : Pravděpodobnost a matematická statistika, skripta nakladatelství ČVUT.

!Holický M., Marková J.: Základy teorie spolehlivosti a hodnocení rizik, skripta ČVUT.

!Hála M., Jarušková D.: Pravděpodobnost a matematická statistika - Tabulky.

?Rychlik I., Rydén J.: Probability and risk analysis, Springer 2006.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Stavební inženýrství, specializace Požární bezpečnost staveb (compulsory course)