470-4407/03 – Mathematical Theory of Reliability (MTS)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantorprof. Ing. Radim Briš, CSc.Subject version guarantorprof. Ing. Radim Briš, CSc.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEIIntended for study typesMaster, Follow-up Master
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 Credit and Examination 2+2
Combined Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

Graduate of the subject will be know basic mathematics which is necessary for reliability estimation and quantification.

Teaching methods

Lectures
Tutorials
Project work

Summary

The subject is focused on reliability prognosis, estimation and optimisation of complex systems and its elements. Basic methods of reliabilioty growth are presented. Basic statistics for reliability quantification is introduced.

Compulsory literature:

Barlow,R.E.- Proschan,F.: Mathematical Theory of Reliability, SIAM 1996, ISBN 0-89871-369-2.

Recommended literature:

Aven T., Jensen U.: Stochastic Models in Reliability, 1999 Springer-Verlag New York,Inc., ISBN 0-387-98633-2. Fleming T.R., Harrington D.P.: Counting Processes and Survival Analysis, Wiley 1991, ISBN 0-471-52218-X.

Way of continuous check of knowledge in the course of semester

Test for maximum 20 points, semestral project with maximum 20 point. Written and oral exam.

E-learning

Další požadavky na studenta

Semestral project under leadership of responsible teachers.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Introduction to Mathematical Theory of Reliability- definitions of reliability, hazard function, reliability function, MTTF. Typical Hazard Models-constant hazard, increasing/decreasing hazard, bathtub hazard. Monotone Failure Rate-important inequalities. Renewal Theory-renewal equation and generalizations,limit theorems,models with renewal,alternating renewal processes. System Reliability Analysis-Boolean algebra theorems, Boolean function, models for system reliability, coherent systems and structure function, series,paralel and k out of n systems, representation of coherent systems by minimal path and minimal cuts,inclusion-exclusion formula, reliability estimation of the coherent systems. Maintenance Policies-replacement based on age, random replacement. Statistical Analysis of Censored Reliability Data, type I censoring, type II and III censoring, general censoring, Kaplan-Meier PL estimate.

Conditions for subject completion

Full-time form (validity from: 2016/2017 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 40  18
        Examination Examination 60  18
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2019/2020 (N2661) Designing of Electrical Systems and Technologies P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2661) Designing of Electrical Systems and Technologies K Czech Ostrava 1 Compulsory study plan
2018/2019 (N2661) Designing of Electrical Systems and Technologies P Czech Ostrava 1 Compulsory study plan
2018/2019 (N2661) Designing of Electrical Systems and Technologies K Czech Ostrava 1 Compulsory study plan
2017/2018 (N2661) Designing of Electrical Systems and Technologies P Czech Ostrava 1 Compulsory study plan
2017/2018 (N2661) Designing of Electrical Systems and Technologies K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner