System Reliability Assessment and Optimization: Methods and Applications

Reliability Analysis, Safety Assessment and Optimization
Contents
Series Editor’s Foreword by Dr. Andre V. Kleyner
Preface
Acknowledgments
List of Abbreviations
Notations
Part I The Fundamentals
	1 Reliability Assessment
		1.1 Definitions of Reliability
			1.1.1 Probability of Survival
			1.1.2 Probability of Time to Failure
		1.2 Component Reliability Modeling
			1.2.1 Discrete Probability Distributions
			1.2.2 Continuous Probability Distributions
			1.2.3 Physics-of-Failure Equations
		1.3 System Reliability Modeling
			1.3.1 Series System
			1.3.2 Parallel System
			1.3.3 Series-parallel System
			1.3.4 K-out-of-n System
			1.3.5 Network System
		1.4 System Reliability Assessment Methods
			1.4.1 Path-set and Cut-set Method
			1.4.2 Decomposition and Factorization
			1.4.3 Binary Decision Diagram
		1.5 Exercises
		References
	2 Optimization
		2.1 Optimization Problems
			2.1.1 Component Reliability Enhancement
			2.1.2 Redundancy Allocation
			2.1.3 Component Assignment
			2.1.4 Maintenance and Testing
		2.2 Optimization Methods
			2.2.1 Mathematical Programming
			2.2.2 Meta-heuristics
		2.3 Exercises
		References
Part II Reliability Techniques
	3 Multi-State Systems (MSSs)
		3.1 Classical Multi-state Models
		3.2 Generalized Multi-state Models
		3.3 Time-dependent Multi-State Models
		3.4 Methods to Evaluate Multi-state System Reliability
			3.4.1 Methods Based on MPVs or MCVs
			3.4.2 Methods Derived from Binary State Reliability Assessment
			3.4.3 Universal Generating Function Approach
			3.4.4 Monte Carlo Simulation
		3.5 Exercises
		References
	4 Markov Processes
		4.1 Continuous Time Markov Chain
		4.2 In homogeneous Continuous Time Markov Chain
		4.3 Semi-Markov Process (SMP)
			4.3.1 Markov Renewal Process
		4.4 Piecewise Deterministic Markov Process (PDMP)
		4.5 Exercises
		References
	5 Monte Carlo Simulation (MCS) for Reliability and Availability Assessment
		5.1 Introduction
		5.2 Random Variable Generation
			5.2.1 Random Number Generation
			5.2.2 Random Variable Generation
		5.3 Random Process Generation
			5.3.1 Markov Chains
			5.3.2 Markov Jump Processes
		5.4 Markov Chain Monte Carlo (MCMC)
			5.4.1 Metropolis-Hastings (M-H) Algorithm
			5.4.2 Gibbs Sampler
			5.4.3 Multiple-try Metropolis-Hastings (M-H) Method
		5.5 Rare-Event Simulation
			5.5.1 Importance Sampling
			5.5.2 Repetitive Simulation Trials after Reaching Thresholds (RESTART)
		5.6 Exercises
		Appendix
		References
	6 Uncertainty Treatment under Imprecise or Incomplete Knowledge
		6.1 Interval Number and Interval of Confidence
			6.1.1 Definition and Basic Arithmetic Operations
			6.1.2 Algebraic Properties
			6.1.3 Order Relations
			6.1.4 Interval Functions
			6.1.5 Interval of Confidence
		6.2 Fuzzy Number
		6.3 Possibility Theory
			6.3.1 Possibility Propagation
		6.4 Evidence Theory
			6.4.1 Data Fusion
		6.5 Random-fuzzy Numbers (RFNs)
			6.5.1 Universal Generating Function (UGF) Representation of Randomfuzzy Numbers
			6.5.2 Hybrid UGF (HUGF) Composition Operator
		6.6 Exercises
		References
	7 Applications
		7.1 Distributed Power Generation System Reliability Assessment
			7.1.1 Reliability of Power Distributed Generation (DG) System
			7.1.2 Energy Source Models and Uncertainties
			7.1.3 Algorithm for the Joint Propagation of Probabilistic and Possibilistic Uncertainties
			7.1.4 Case Study
		7.2 Nuclear Power Plant Components Degradation
			7.2.1 Dissimilar Metal Weld Degradation
			7.2.2 MCS Method
			7.2.3 Numerical Results
		References
Part III Optimization Methods and Applications
	8 Mathematical Programming
		8.1 Linear Programming (LP)
			8.1.1 Standard Form and Duality
		8.2 Integer Programming (IP)
		8.3 Exercises
		References
	9 Evolutionary Algorithms (EAs)
		9.1 Evolutionary Search
		9.2 Genetic Algorithm (GA)
			9.2.1 Encoding and Initialization
			9.2.2 Evaluation
			9.2.3 Selection
			9.2.4 Mutation
			9.2.5 Crossover
			9.2.6 Elitism
			9.2.7 Termination Condition and Convergence
		9.3 Other Popular EAs
		9.4 Exercises
		References
	10 Multi-Objective Optimization (MOO)
		10.1 Multi-objective Problem Formulation
		10.2 MOO-to-SOO Problem Conversion Methods
			10.2.1 Weighted-sum Approach
			10.2.2 ε-constraint Approach
			10.2.3 Goal Programming
		10.3 Multi-objective Evolutionary Algorithms
			10.3.1 Fast Non-dominated Sorting Genetic Algorithm (NSGA-II)
			10.3.2 Improved Strength Pareto Evolutionary Algorithm (SPEA 2)
		10.4 Performance Measures
		10.5 Selection of Preferred Solutions
			10.5.1 “Min-max” Method
			10.5.2 Compromise Programming Approach
		10.6 Guidelines for Solving RAMS+C Optimization Problems
		10.7 Exercises
		References
	11 Optimization under Uncertainty
		11.1 Stochastic Programming (SP)
			11.1.1 Two-stage Stochastic Linear Programs with Fixed Recourse
			11.1.2 Multi-stage Stochastic Programs with Recourse
		11.2 Chance-Constrained Programming
			11.2.1 Model and Properties
			11.2.2 Example
		11.3 Robust Optimization (RO)
			11.3.1 Uncertain Linear Optimization (LO) and its Robust Counterparts
			11.3.2 Tractability of Robust Counterparts
			11.3.3 Robust Optimization (RO) with Cardinality Constrained Uncertainty Set
			11.3.4 Example
		11.4 Exercises
		References
	12 Applications
		12.1 Multi-objective Optimization (MOO) Framework for the Integration of Distributed Renewable Generation and Storage
			12.1.1 Description of Distributed Generation (DG) System
			12.1.2 Optimal Power Flow (OPF)
			12.1.3 Performance Indicators
			12.1.4 MOO Problem Formulation
			12.1.5 Solution Approach and Case Study Results
		12.2 Redundancy Allocation for Binary-State SeriesParallel Systems (BSSPSs) under Epistemic Uncertainty
			12.2.1 Problem Description
			12.2.2 Robust Model
			12.2.3 Experiment
		References
Index
EULA