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To all the students, collaborators and colleagues, to whom we are forever indebted for all the enriching experience and knowledge that they have shared with us and that have made us grow professionally and personally.
Contents
1 Cover
7 Preface
10 Notations
11 Part I The Fundamentals1 Reliability Assessment1.1 Definitions of Reliability1.1.1 Probability of Survival1.2 Component Reliability Modeling1.2.1 Discrete Probability Distributions1.2.2 Continuous Probability Distributions1.2.3 Physics-of-Failure Equations1.3 System Reliability Modeling1.3.1 Series System1.3.2 Parallel System1.3.3 Series-parallel System1.3.4 K-out-of-n System1.3.5 Network System1.4 System Reliability Assessment Methods1.4.1 Path-set and Cut-set Method1.4.2 Decomposition and Factorization1.4.3 Binary Decision Diagram1.5 ExercisesReferences2 Optimization 2.1 Optimization Problems2.1.1 Component Reliability Enhancement2.1.2 Redundancy Allocation2.1.3 Component Assignment2.1.4 Maintenance and Testing2.2 Optimization Methods2.2.1 Mathematical Programming2.2.2 Meta-heuristics2.3 ExercisesReferences
12 Part II Reliability Techniques3 Multi-State Systems (MSSs)3.1 Classical Multi-state Models3.2 Generalized Multi-state Models3.3 Time-dependent Multi-State Models3.4 Methods to Evaluate Multi-state System Reliability3.4.1 Methods Based on MPVs or MCVs3.4.2 Methods Derived from Binary State Reliability Assessment3.4.3 Universal Generating Function Approach3.4.4 Monte Carlo Simulation3.5 ExercisesReferences4 Markov Processes4.1 Continuous Time Markov Chain (CMTC)4.2 In homogeneous Continuous Time Markov Chain4.3 Semi-Markov Process (SMP)4.4 Piecewise Deterministic Markov Process (PDMP)4.5 ExercisesReferences5 Monte Carlo Simulation (MCS) for Reliability and Availability Assessment5.1 Introduction5.2 Random Variable Generation5.2.1 Random Number Generation5.2.2 Random Variable Generation5.3 Random Process Generation5.3.1 Markov Chains5.3.2 Markov Jump Processes5.4 Markov Chain Monte Carlo (MCMC)5.4.1 Metropolis-Hastings (M-H) Algorithm5.4.2 Gibbs Sampler5.4.3 Multiple-try Metropolis-Hastings (M-H) Method5.5 Rare-Event Simulation5.5.1 Importance Sampling5.5.2 Repetitive Simulation Trials after Reaching Thresholds (RESTART)5.6 ExercisesAppendixReferences6 Uncertainty Treatment under Imprecise or Incomplete Knowledge6.1 Interval Number and Interval of Confidence6.1.1 Definition and Basic Arithmetic Operations6.1.2 Algebraic Properties6.1.3 Order Relations6.1.4 Interval Functions6.1.5 Interval of Confidence6.2 Fuzzy Number6.3 Possibility Theory6.3.1 Possibility Propagation6.4 Evidence Theory6.4.1 Data Fusion6.5 Random-fuzzy Numbers (RFNs)6.5.1 Universal Generating Function (UGF) Representation of Random-fuzzy Numbers6.5.2 Hybrid UGF (HUGF) Composition Operator6.6 ExercisesReferences7 Applications7.1 Distributed Power Generation System Reliability Assessment7.1.1 Reliability of Power Distributed Generation (DG) System7.1.2 Energy Source Models and Uncertainties7.1.3 Algorithm for the Joint Propagation of Probabilistic and Possibilistic Uncertainties7.1.4 Case Study7.2 Nuclear Power Plant Components Degradation7.2.1 Dissimilar Metal Weld Degradation7.2.2 MCS Method7.2.3 Numerical ResultsReferences
13 Part III Optimization Methods and Applications8 Mathematical Programming8.1 Linear Programming (LP)8.1.1 Standard Form and Duality8.2 Integer Programming (IP)8.3 ExercisesReferences9 Evolutionary Algorithms (EAs)9.1 Evolutionary Search9.2 Genetic Algorithm (GA)9.2.1 Encoding and Initialization9.2.2 Evaluation9.2.3 Selection9.2.4 Mutation9.2.5 Crossover9.2.6 Elitism9.2.7 Termination Condition and Convergence9.3 Other Popular EAs9.4 ExercisesReferences10 Multi-Objective Optimization (MOO)10.1 Multi-objective Problem Formulation10.2 MOO-to-SOO Problem Conversion Methods10.2.1 Weighted-sum Approach10.2.2 ε-constraint Approach10.3 Multi-objective Evolutionary Algorithms10.3.1 Fast Non-dominated Sorting Genetic Algorithm (NSGA-II)10.3.2 Improved Strength Pareto Evolutionary Algorithm (SPEA 2)10.4 Performance Measures10.5 Selection of Preferred Solutions10.5.1 “Min-max” Method10.5.2 Compromise Programming Approach10.6 Guidelines for Solving RAMS+C Optimization Problems10.7 ExercisesReferences11 Optimization under Uncertainty11.1 Stochastic Programming (SP)11.1.1 Two-stage Stochastic Linear Programs with Fixed Recourse11.1.2 Multi-stage Stochastic Programs with Recourse11.2 Chance-Constrained Programming11.2.1 Model and Properties11.2.2 Example11.3 Robust Optimization (RO)11.3.1 Uncertain Linear Optimization (LO) and its Robust Counterparts11.3.2 Tractability of Robust Counterparts11.3.3 Robust Optimization (RO) with Cardinality Constrained Uncertainty Set11.3.4 Example11.4 ExercisesReferences12 Applications12.1 Multi-objective Optimization (MOO) Framework for the Integration of Distributed Renewable Generation and Storage12.1.1 Description of Distributed Generation (DG) System12.1.2 Optimal Power Flow (OPF)12.1.3 Performance Indicators12.1.4 MOO Problem Formulation12.1.5 Solution Approach and Case Study Results12.2 Redundancy Allocation for Binary-State Series-Parallel Systems (BSSPSs) under Epistemic Uncertainty12.2.1 Problem Description12.2.2 Robust Model12.2.3 ExperimentReferences
14 Index