470-6401/02 – Mathematical Methods and Tools for Reliability and Risk Analysis (MTSAR)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantorprof. Ing. Radim Briš, CSc.Subject version guarantorprof. Ing. Radim Briš, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFS, USP, FEI, HGF, FMT, FBI, FASTIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
BRI10 prof. Ing. Radim Briš, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+0
Part-time Examination 28+0

Subject aims expressed by acquired skills and competences

Mastering of the basic methodology to PRA.

Teaching methods

Individual consultations
Project work

Summary

Basic methodology for probabilistic risk assessment. Topics: * Introduction to reliability mathematics. * Models for system reliability, coherent systems and structure function; * Boolean modelling, series, parallel and k out of n systems; * Probability calculations for coherent systems; * Representation of coherent systems by minimal paths and minimal cuts; * Inclusion - exclusion formula, Estimation of reliability. * Multi-state reliability theory, General Markov model for non maintained systems. * Maintainability analysis. * Fault Tree Analysis, Probabilistic risk assessment * Monte Carlo Methods in Reliability.

Compulsory literature:

E. Zio: An Introduction to the Basics of Reliability and Risk Analysis, World Scientific 2007. ISBN 978-981-270-639-3. E. Zio: Computational Methods for Reliability and Risk Analysis, World Scientific 2009, ISBN 978-981-283-901-5. Nozer D. Singpurwalla, Reliability and Risk, A Bayesian Perspective. Wiley 2006, ISBN 978-0-470-85502-7.

Recommended literature:

Modarres M., Kaminskiy M.P., Krivtsov V.: Reliability Engineering and Risk Analysis: A Practical Guide, 3rd Edition, CRC Press 2016, ISBN 978-1498745871.

Way of continuous check of knowledge in the course of semester

Consultancy to semestral project. Oral exam.

E-learning

Other requirements

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: - Introduction to reliability mathematics. Models for system reliability, coherent systems and structure function; Boolean modelling, series, parallel and k out of n systems; Probability calculations for coherent systems; - Representation of coherent systems by minimal paths and minimal cuts; - Inclusion - exclusion formula, Estimation of reliability. Multi-state reliability theory, General Markov model for non maintained systems. - Maintainability analysis. Fault Tree Analysis, Probabilistic risk assessment - Monte Carlo Methods in Reliability.

Conditions for subject completion

Part-time form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Examination Examination   3
Mandatory attendence participation:

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