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
Web linkStudy languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEI, USP, HGF, FMMI, FS, 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
Combined 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:

Barlow R.E., Proschan F.; Mathematical Theory of Reliability, SIAM 1996, ISBN 0-89871-369-2 Misra K.B.; Reliability Analysis and Prediction, Elsevier 1992, ISBN 0-444-89606-6. Fleming T.R., Harrington D.P.: Counting Processes and Survival Analysis, Wiley 1991, ISBN 0-471-52218-X. Modares M.; What Every Engineer Should Know About Reliability and Risk Analysis, Dekker 1993 ISBN 0-8247-8958-X. Crowder M.J., Kimber A.C., Smith R.L., Sweeting T.J.; Statistical Analysis of Reliability Data; Chapman and Hall 1991, ISBN 0-412-30560-7

Recommended literature:

Fleming T.R., Harrington D.P.: Counting Processes and Survival Analysis, Wiley 1991, ISBN 0-471-52218-X Modares M.; What Every Engineer Should Know About Reliability and Risk Analysis, Dekker 1993 ISBN 0-8247-8958-X.

Way of continuous check of knowledge in the course of semester

Consultancy to semestral project.

E-learning

Další požadavky na studenta

There are not defined other requirements for student.

Minimum knowledge requirements

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

Combined form (validity from: 2013/2014 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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