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Mathematical Theory of Reliability

Type of study MasterFollow-up Master
Language of instruction Czech
Code 470-4407/03
Abbreviation MTS
Course title Mathematical Theory of Reliability
Credits 4
Coordinating department Department of Applied Mathematics
Course coordinator prof. Ing. Radim Briš, CSc.

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.

E-learning

Basic materials are available on the educator's website:
http://homel.vsb.cz/~bri10,
Teaching,
MTS pro PES.zip

Literature

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

Advised 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.