470-6401/01 – 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 languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFMT, FS, FBI, FEI, USP, FAST, HGFIntended 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

Full-time form (validity from: 2013/2014 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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2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2649) Electrical Engineering (3907V001) Electric Power Engineering P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2649) Electrical Engineering (3907V001) Electric Power Engineering K Czech Ostrava Choice-compulsory study plan
2015/2016 (P3655) Civil Engineering (3607V012) Municipal Engineering and Construction K Czech Ostrava Optional study plan
2015/2016 (P3655) Civil Engineering (3607V012) Municipal Engineering and Construction P Czech Ostrava Optional study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2649) Electrical Engineering (3907V001) Electric Power Engineering P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2649) Electrical Engineering (3907V001) Electric Power Engineering K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K English Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K English Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2649) Electrical Engineering (3907V001) Electric Power Engineering P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2649) Electrical Engineering (3907V001) Electric Power Engineering K Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2649) Electrical Engineering (3907V001) Electric Power Engineering P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2649) Electrical Engineering (3907V001) Electric Power Engineering K Czech Ostrava Choice-compulsory study plan
2012/2013 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2011/2012 (P2649) Electrical Engineering (3907V001) Electric Power Engineering P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2649) Electrical Engineering (3907V001) Electric Power Engineering K Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2649) Electrical Engineering (3907V001) Electric Power Engineering P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2649) Electrical Engineering (3907V001) Electric Power Engineering K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P2649) Electrical Engineering (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2649) Electrical Engineering (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (2601V018) Communication Technology K Czech Ostrava Choice-compulsory study plan

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