### Reliability and Availability Assessment Methods

#### Course Description

Introduction: deterministic and probabilistic analyses. Fundamental postulates and concepts of reliability theory. Reliability, availability, safety, and risk. Mathematical models of component reliability. Reliability of a system with independent, nonrepairable and nonreplaceable components. Reliability of a system with dependent components. Complications due to standby operation, dependent failures, and repairs. Reliability of a system with standby operation. Markov models - general approach to the reliability and availability assessment. Mathematical model of component availability. Reliability and availability of a system with dependent, nonrepairable and nonreplaceable components. Reliability and availability of a system with repairable and replaceable components. Calculations of a steady-state availability of a system. Frequency and duration techniques. Reliability and availability assessment of a system using Monte Carlo simulation. Reliability and availability improvement.

#### General Competencies

Achieving a level of knowledge to master reliability and availability assessment methods.

#### Learning Outcomes

1. summarize the parts of probability theory and mathematical statistics essential to understanding the reliability and availability methods discussed
2. analyze basic field data to estimate component reliability, failure model, mean time to failure and exponential law of component reliability
3. combine general methods for reliability calculations of a system with independent, nonrepairable and nonreplaceable components: inspection methods, event-space method; path-tracing method, decomposition method, tie-set and cut-set methods in procedures for power system reliability evaluations
4. modify Markov models for general approach to the reliability and availability assessment of a system
5. rearrange methods for reliability and availability calculations of a system with dependent, nonrepairable and nonreplaceable components as well as a system with repairable and replaceable components
6. employ approximate reliability evaluation methods
7. identify of a steady-state availability of a system
8. appraise possibilities for system reliability and availability improvement

#### Forms of Teaching

Lectures

Teaching the course is organized in two teaching cycles. The first cycle contains seven weeks, mid-term exam, and the second cycle contains six weeks of classes and a final exam. Classes are conducted through a total of 15 weeks with weekly load of 2 hours.

Consultations

weekly

E-learning

homework assignments

Continuous Assessment Exam
Homeworks 0 % 1 % 0 % 0 %
Mid Term Exam: Written 0 % 40 % 0 %
Final Exam: Written 0 % 59 %
Exam: Written 0 % 100 %

#### Week by Week Schedule

1. Introduction: deterministic and probabilistic analyses. Fundamental postulates and concepts of reliability theory and reliability analysis. Reliability, availability, safety, and risk.
2. Review of probability and statistics essential to understanding the reliability and availability methods discussed.
3. Mathematical models of component reliability. Probability distribution function (failure distribution function), probability density function (failure density function), unreliability function, probability function, failure (hazard) rate and intensity functions, general reliability function. Choice of distribution.
4. Transformation of basic field data into estimates of component reliability. Failure models. Mean time to failure. Exponential law of component reliability.
5. Reliability of a system with independent, nonrepairable and nonreplaceable components. Reliability block-diagram (logic diagrams): functional logical structure of a system. Reliability analysis of a system with the series configuration, the parallel configuration, and an r-out-of-n structure. Mean times to failure.
6. General methods for reliability calculations of a system with independent, nonrepairable and nonreplaceable components: inspection method, event-space method; path-tracing method, decomposition method, tie-set and cut-set methods.
7. Approximate reliability evaluation methods. Parametric method.
8. Exams
9. Exams
10. Reliability of a system with dependent components. Complications due to standby operation, dependent failures, and repairs. Reliability of a system with standby operation: Poisson process.
11. Markov models - general approach to the reliability and availability assessment. Markov chain model. Markov process.
12. Reliability and availability of a system with dependent, nonrepairable and nonreplaceable components. Reliability and availability of a system with repairable and replaceable components. Mathematical model of component availability
13. Calculations of a steady-state availability of a system. The use of general methods for reliability calculations of a system with independent, nonrepairable and nonreplaceable components in system steady-state availability calculations.
14. Frequency and duration techniques. Reliability and availability assessment of a system using Monte Carlo methods.
15. Reliability and availability improvement.

#### Study Programmes

Electrical Power Engineering (profile)
Specialization Course (2. semester)

#### Literature

Mikuličić, V.; Šimić, Z. (2008.), Modeli pouzdanosti, raspoloživosti i rizika u elektroenergetsko sustavu, 1. dio Analitičke metode proračuna pouzdanosti i raspoloživosti, Kigen, Zagreb
Billinton, R.; Allan, R.N (1992.), Reliability Evaluation of Engineering Systems: Concepts and Techniques, Pitman Advanced Publishing Program
Endrenyi, J. (1978.), Reliability Modeling in Electric Power Systems, John Wiley & Sons

#### General

ID 34433
Summer semester
4 ECTS
L1 English Level
L1 e-Learning
30 Lectures
0 Exercises
0 Laboratory exercises
0 Project laboratory