Reliability (0365.4221)
Professor Uri Yechiali
Department
of Statistics and Operations Research
School of Mathematical Sciences
Tel-Aviv University
uriy@tauex.tau.ac.il
Office Hours: Monday 15:00 - 16:00 Schreiber 325
+972-3-640-9637.
Class Days and Hours:
Spring semester 2022
Monday 16:00 - 19:00, Room 008, Schreiber Building
Prerequisites
Probability Theory, Operations Research 1, Introd. to Stochastic Processes
(desired)
Course Content:
Reliability of a system is its probability of functioning
properly for a given period of time.
The course deals with the probabilistic analysis of multi-component
complex systems where the life-time of each component is random. Characterizations
of such systems, their properties, along with their design and optimization
are the focus of this course.
Topics:
- Introduction
- Reliability of systems of components; Systems in Series, Parallel,
k out of n, or general configuration; Presentation of Coherent systems
in terms of paths and cuts
- Families of probability distributions useful in describing life-times
of components
- The hazard function; IFR, DFR, IFRA and DFRA properties
- Maintenance policies; NBU, NWU, NBUE and NWUE characterizations; Shock
models
- Replacement models
- Optimization and design of reliability systems
Helpful Reference Books
- Barlow, R.E. and Proschan, F., Statistical Theory of Reliability and
Life Testing, Holt,Rinehart and Winston, 1975.
- Kenett, R.S. and Zacks, S., Modern Industrial Statistics, Duxbury press,
1998.
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Articles
- Gottlieb. G. and Yechiali, U., "Damage Models for Multi-Component Systems",
European Journal of Operational Research 5(3), 193-197 (1980).
- Verd, G. and yechiali, U., "Optimal Structures and Maintenance Policies
for PABX Power Systems", Operations Research 27(1), 37-47 (1979).
- Douer, N. and Yechiali, U., "Optimal Repair and Replacement
in Markovian Systems", Stochastic Models 10(1), 253-270 (1994).
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Last update: January 2022