| Course Unit Code | 470-4407/03 |
|---|
| Number of ECTS Credits Allocated | 4 ECTS credits |
|---|
| Type of Course Unit * | Compulsory |
|---|
| Level of Course Unit * | Second Cycle |
|---|
| Year of Study * | First Year |
|---|
| Semester when the Course Unit is delivered | Summer Semester |
|---|
| Mode of Delivery | Face-to-face |
|---|
| Language of Instruction | Czech |
|---|
| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
|---|
| Name of Lecturer(s) | Personal ID | Name |
|---|
| BRI10 | prof. Ing. Radim Briš, CSc. |
| 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. |
| Learning Outcomes of the Course Unit |
|---|
| Graduate of the subject will be know basic mathematics which is necessary for reliability estimation and quantification. |
| Course Contents |
|---|
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.
|
| Recommended or Required Reading |
|---|
| Required Reading: |
|---|
Barlow,R.E.- Proschan,F.: Mathematical Theory of Reliability, SIAM 1996,
ISBN 0-89871-369-2.
|
Briš, R.: Inovační metody pro ocenění spolehlivosti prvků a systémů. 1.vyd. Ostrava:VŠB-Technická univerzita Ostrava, 2007, ISBN 978-80-248-1596-1. Monografie.
Hurt J.: Teorie spolehlivosti, MFF UK Praha 1984.
Barlow,R.E.- Proschan,F.: Mathematical Theory of Reliability, SIAM 1996,
ISBN 0-89871-369-2.
|
| Recommended Reading: |
|---|
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.
|
Briš, R.: Inovační metody pro ocenění spolehlivosti prvků a systémů. 1.vyd. Ostrava:VŠB-Technická univerzita Ostrava, 2007, ISBN 978-80-248-1596-1. Monografie.
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.
|
| Planned learning activities and teaching methods |
|---|
| Lectures, Tutorials, Project work |
| Assesment methods and criteria |
|---|
| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
|---|
| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 40 | 18 |
| Examination | Examination | 60 | 18 |