RELIABILITY ENGINEERING
Course objective:
To strengthen the knowledge of probability theory by introducing the concept of reliability engineering applicable to the physical systems especially at different level of electric power systems.
- Review of probability theory (4 hours)
- Probability concepts, permutation and combination, practical engineering concepts, Venn diagrams
- Rules for combining probabilities, independent, mutually exclusive, complimentary, conditional events, application of conditional probability
- Probability distributions: random variables, density distribution functions, mathematical expectation, variance and standard deviation.
- Binomial distribution and its Applications (4 hours)
- Binomial distribution: concepts, properties, general characteristics, binomial coefficients, expected value and standard deviation
- Applications in engineering system evaluation, economic implications, identical and non‐identical units, COPT
- Network modeling and analysis of simple systems (4 hours)
- Modeling concepts for reliability evaluations
- Series, parallel and series‐parallel systems
- Redundancy: standby redundancy, impact of redundancy, perfect and imperfect switching
- Modeling and analysis of complex systems (8 hours)
- Modeling and evaluation concepts for complex systems
- Conditional probability approach, cut set and tie set methods, connection matrix techniques, event tree and fault tree methods
- Probability distribution in reliability evaluation (4 hours)
- Distribution concepts, terminology, general reliability functions, evaluation techniques, shapes
- Poisson distribution, relationship with binomial distribution
- Normal and exponential distributions, probability density functions, a priori and a posterior probability, normal distribution and probability density function, mean value and mean time to failure.
- Other distributions: Weibull, Gamma, Rayleigh and Log Normal distribution and their application in electric power change.
- System reliability evaluation using probability distribution (4 hours)
- Series, parallel and partially redundant systems, mean time to failure
- Standby systems: perfect and imperfect switching, effect of spare components, failure in standby mode
- Discrete Markov chains (4 hours)
- General modeling concept, STPM, time dependent probability evaluation
- Limiting state probability, absorbing states, applications of discrete Markov techniques in system reliability evaluation
- Continuous Markov processes (4 hours)
- General modeling concepts, transition rates, time dependent and limiting state probabilities, STTP
- State space diagram: single, two and three components repairable systems, mission oriented systems
- Evaluation of time dependent state probabilities by differential equations method and matrix multiplication methods
- Reliability evaluation of repairable systems, MTTF, application in complex system
- Frequency and duration techniques for reliability evaluation (8 hours)
- Basic concepts of F&D techniques, application in multi‐state problems, frequency of encountering individual states, mean duration of individual states, frequency of encountering cumulated states, frequency balance approach
- Approximate reliability evaluation: series and parallel systems, network reduction techniques, minimum cut set method
Practical:
- Evaluate the reliability of simple and complex systems using various techniques like series/parallel, cut set and tie set methods
- Application of discrete Markov chain and continuous Markov process, F&D techniques, approximate reliability evaluation for complex engineering system
References:
- Roy Billinton and Ronald Allan, “Reliability Evaluation of Engineering Systems: Concepts and Techniques”, Plenum Publishers, New York, 1992.
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