Theory of Reliability

Course guarantor:

Michal Šejnoha

Lecturer:

Tomáš Janda, Michal Šejnoha

Tutor:

Supervisor:

Department of Mechanics

Synopsis:

The covered material splits into three blocks: (i) Important relations and theorems necessary in the area of the theory of reliability and mathematical statistics, (ii) Analytical and simulation methods to analyze reliability of structures, (iii) Advanced methods of reliability analysis exploiting the Bayesian inference in conjunction with MCMC simulation.

List of lectures:

1. Basic relations, definitions and notation, 2. Selected probability distributions and important inequalities, 3. Transformation of probability density function (one and more variables), 4. Reliability of simple structures, 5. Evolution of reliability in time, 6. Reliability and solution methods, 7. Renewable systems, 8. Reflection of the theory in EC standards, 9. Analytical methods to address reliability, 10. Simulation methods, 11. Monte Carlo type simulation, 12. MCMC sampling (Markov chain-Monte Carlo, Bayesian statistical method).

Requirements:

No particular prerequisites are necessary for this course. Basic knowledge of differential and integral calculus is welcomed as it will help the students to understand the methods in greater detail. Elementary knowledge of programming (e.g. Python, Matlab) is also welcomed as it will allow the students to modify the presented methods and algorithms to their own applications.

Syllabus of lectures:

1. Basic relations and terminology

2. Common probability distributions and useful inequalities

3. Transformation of random variables

4. Reliability of simple structures

5. Evolution of reliability in time

6. Solution methods and models

7. Markov chains and Kolmogorov equations

8. Reliability in design codes

9. First order reliability methods Transformation

10. Monte Carlo method, Latin Hypercube sampling

11. Advanced methods: Subset simulation, MCMC sampling

12. Bayesian inference, Metropolis Hastings algorithm

Syllabus of tutorials:

Hands-on exercise on how to do the actual computations is a part of each lecture.

Study Objective:

The goal of the course is to introduce the students to the foundations of reliability theory and to show them the tools for practical calculations.

Study materials:

S. S. Rao: Reliability-Based Design, McGraw Hill, Inc. New York, 1992

I. Elishakoff: Probability Theory of Structures, Dover Publication , New. York, 1999

O. Ditlevsen, H. O. Madsen: Structural Reliability Methods, John Wiley & Sons, Chichester, 1996

D. Blockley: The nature of structural design and safety, Ellis Horwood Limited, Chichester, John Willey&Sons, New York, 1980

J. Kruschke, Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, 2nd edition. Boston: Academic Press, 2014

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: