470-4407/03 – Mathematical Theory of Reliability (MTS)
| Gurantor department | Department of Applied Mathematics | Credits | 4 |
| Subject guarantor | prof. Ing. Radim Briš, CSc. | Subject version guarantor | prof. Ing. Radim Briš, CSc. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2010/2011 | Year of cancellation | |
| Intended for the faculties | FEI | Intended for study types | Follow-up Master, Master |
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:
Recommended literature:
Additional study materials
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
Basic materials are available on the educator's website:
http://homel.vsb.cz/~bri10,
Teaching,
MTS pro PES.zip
Other requirements
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction