Binary Decision Diagrams and Extensions for System Reliability Analysis.
Xing, Liudong.
Binary Decision Diagrams and Extensions for System Reliability Analysis. - 1st ed. - 1 online resource (238 pages) - Performability Engineering Series . - Performability Engineering Series .
Cover -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Nomenclature -- 1 Introduction -- 1.1 Historical Developments -- 1.2 Reliability and Safety Applications -- 2 Basic Reliability Theory and Models -- 2.1 Probabiltiy Concepts -- 2.1.1 Axioms of Probability -- 2.1.2 Total Probability Law -- 2.1.3 Random Variables -- 2.1.4 Parameters of Random Variables -- 2.1.5 Lifetime Distributions -- 2.2 Reliability Measures -- 2.2.1 Time-to-Failure and Failure Function -- 2.2.2 Reliability Function -- 2.2.3 Failure Rate Function -- 2.2.4 Mean Time to Failure -- 2.2.5 Mean Residual Life -- 2.3 Fault Tree Analysis -- 2.3.1 Overview -- 2.3.2 Fault Tree Construction -- 2.3.3 Different Forms of Fault Trees -- 2.3.3.1 Static Fault Trees -- 2.3.3.2 Dynamic Fault Trees (DFTs) -- 2.3.3.3 Noncoherent Fault Trees -- 2.3.4 Types of Fault Tree Analysis -- 2.3.4.1 Qualitative Analysis -- 2.3.4.2 Quantitative Analysis -- 2.3.5 Fault Tree Analysis Techniques -- 2.3.5.1 Inclusion-Exclusion (I-E) -- 2.3.5.2 Sum of Disjoint Products (SDPs) -- 3 Fundamentals of Binary Decision Diagrams -- 3.1 Preliminaries -- 3.2 Basic Concepts -- 3.3 BDD Construction -- 3.3.1 Input Variable Ordering -- 3.3.2 OBDD Generation -- 3.3.3 ROBDD Generation -- 3.3.4 Example Illustrations -- 3.4 BDD Evaluation -- 3.5 BDD-Based Software Package -- 4 Application of BDD to Binary-State Systems -- 4.1 Network Reliability Analysis -- 4.2 Event Tree Analysis -- 4.3 Failure Frequency Analysis -- 4.3.1 Steady-State System Failure Frequency -- 4.3.2 Time-Dependent System Failure and Success Frequencies -- 4.4 Importance Measures and Analysis -- 4.4.1 Deterministic Importance Measures -- 4.4.2 Probabilistic Importance Measures -- 4.4.2.1 Birnbaum's Measure -- 4.4.2.2 Criticality Importance Factor -- 4.4.2.3 Fussell-Vesely Measure -- 4.5 Modularization Methods -- 4.6 Non-Coherent Systems. 4.6.1 Prime Implicants Based Method -- 4.6.2 BDD Based Method -- 4.7 Disjoint Failures -- 4.8 Dependent Failures -- 4.8.1 Common-Cause Failures (CCFs) -- 4.8.2 Functional Dependent Failures -- 5 Phased-Mission Systems -- 5.1 System Description -- 5.2 Rules of Phase Algebra -- 5.3 BDD-Based Method for PMS Analysis -- 5.3.1 Input Variable Ordering -- 5.3.2 Single-Phase BDD Generation -- 5.3.3 PMS BDD Generation -- 5.3.4 PMS BDD Evaluation -- 5.4 Mission Performance Analysis -- 6 Multi-State Systems -- 6.1 Assumptions -- 6.2 An Illustrative Example -- 6.3 MSS Representation -- 6.3.1 MSS Representation Using MFT -- 6.3.2 MSS Representation Using MRBD -- 6.3.3 Equivalency of MRBD and MFT Representations -- 6.4 Multi-State BDD (MBDD) -- 6.4.1 Step 1 - State Variable Encoding -- 6.4.2 Step 2 - Generating MBDD from MFT -- 6.4.3 Step 3 - MBDD Evaluation -- 6.4.4 Example Illustration -- 6.5 Logarithmically-Encoded BDD (LBDD) -- 6.5.1 Step 1 - Variable Encoding -- 6.5.2 Step 2 - Generating LBDD from MFT -- 6.5.3 Step 3 - LBDD Evaluation -- 6.5.4 Example Illustration -- 6.6 Multi-State Multi-Valued Decision Diagrams (MMDD) -- 6.6.1 Step 1 - Variable Encoding -- 6.6.2 Step 2 - Generating MMDD from MFT -- 6.6.3 Step 3 - MMDD Evaluation -- 6.6.4 Example Illustration -- 6.7 Performance Evaluation and Benchmarks -- 6.7.1 Example Analyses -- 6.7.2 Benchmark Studies -- 6.7.3 Performance Comparison and Discussions -- 6.7.3.1 Comparing Model Size -- 6.7.3.2 Comparing Runtime Complexity of Model Construction -- 6.7.3.3 Comparing Runtime Complexity of Model Evaluation -- 6.8 Summary -- 7 Fault Tolerant Systems and Coverage Models -- 7.1 Basic Types -- 7.2 Imperfect Coverage Model -- 7.3 Applications to Binary-State Systems -- 7.3.1 BDD Expansion Method -- 7.3.2 Simple and Efficient Algorithm -- 7.4 Applications to Multi-State Systems. 7.5 Applications to Phased-Mission Systems -- 7.5.1 Mini-Component Concept -- 7.5.2 Extended SEA Method for PMS -- 7.5.3 An Illustrative Example -- 7.6 Summary -- 8 Shared Decision Diagrams -- 8.1 Multi-Rooted Decision Diagrams -- 8.2 Multi-Terminal Decision Diagrams -- 8.3 Performance Study on Multi-State Systems -- 8.3.1 Example Analyses -- 8.3.2 Benchmark Studies -- 8.4 Application to Phased-Mission Systems -- 8.4.1 PMS Analysis Using MDDs -- 8.4.1.1 Step 1-Variable Encoding -- 8.4.1.2 Step 2-Input Variable Ordering -- 8.4.1.3 Step 3-PMS MDD Generation -- 8.4.1.4 Step 4-PMS MDD Evaluation -- 8.4.2 An Illustrative Example -- 8.5 Application to Multi-State k-out-of-n Systems -- 8.5.1 Multi-State k-out-of-n System Analysis Using MDDs -- 8.5.1.1 Step 1- BDDkl Generation -- 8.5.1.2 Step 2- MDDkl Generation -- 8.5.1.3 Step 3- MDDSj Generation -- 8.5.1.4 Step 4-System MDDSj Evaluation -- 8.5.2 An Illustrative Example -- 8.6 Importance Measures -- 8.6.1 Capacity Networks and Reliability Modeling -- 8.6.2 Composite Importance Measures (Type 1) -- 8.6.2.1 General CIMs -- 8.6.2.2 Alternative CIMs -- 8.6.3 Computing CIMs Using MDD -- 8.6.4 An Illustrative Example -- 8.7 Failure Frequency Based Measures -- 8.8 Summary -- Conclusions -- References -- Index -- EULA.
9781119178002
Reliability (Engineering)-Graphic methods.
Electronic books.
TA169.X55 2015
Binary Decision Diagrams and Extensions for System Reliability Analysis. - 1st ed. - 1 online resource (238 pages) - Performability Engineering Series . - Performability Engineering Series .
Cover -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Nomenclature -- 1 Introduction -- 1.1 Historical Developments -- 1.2 Reliability and Safety Applications -- 2 Basic Reliability Theory and Models -- 2.1 Probabiltiy Concepts -- 2.1.1 Axioms of Probability -- 2.1.2 Total Probability Law -- 2.1.3 Random Variables -- 2.1.4 Parameters of Random Variables -- 2.1.5 Lifetime Distributions -- 2.2 Reliability Measures -- 2.2.1 Time-to-Failure and Failure Function -- 2.2.2 Reliability Function -- 2.2.3 Failure Rate Function -- 2.2.4 Mean Time to Failure -- 2.2.5 Mean Residual Life -- 2.3 Fault Tree Analysis -- 2.3.1 Overview -- 2.3.2 Fault Tree Construction -- 2.3.3 Different Forms of Fault Trees -- 2.3.3.1 Static Fault Trees -- 2.3.3.2 Dynamic Fault Trees (DFTs) -- 2.3.3.3 Noncoherent Fault Trees -- 2.3.4 Types of Fault Tree Analysis -- 2.3.4.1 Qualitative Analysis -- 2.3.4.2 Quantitative Analysis -- 2.3.5 Fault Tree Analysis Techniques -- 2.3.5.1 Inclusion-Exclusion (I-E) -- 2.3.5.2 Sum of Disjoint Products (SDPs) -- 3 Fundamentals of Binary Decision Diagrams -- 3.1 Preliminaries -- 3.2 Basic Concepts -- 3.3 BDD Construction -- 3.3.1 Input Variable Ordering -- 3.3.2 OBDD Generation -- 3.3.3 ROBDD Generation -- 3.3.4 Example Illustrations -- 3.4 BDD Evaluation -- 3.5 BDD-Based Software Package -- 4 Application of BDD to Binary-State Systems -- 4.1 Network Reliability Analysis -- 4.2 Event Tree Analysis -- 4.3 Failure Frequency Analysis -- 4.3.1 Steady-State System Failure Frequency -- 4.3.2 Time-Dependent System Failure and Success Frequencies -- 4.4 Importance Measures and Analysis -- 4.4.1 Deterministic Importance Measures -- 4.4.2 Probabilistic Importance Measures -- 4.4.2.1 Birnbaum's Measure -- 4.4.2.2 Criticality Importance Factor -- 4.4.2.3 Fussell-Vesely Measure -- 4.5 Modularization Methods -- 4.6 Non-Coherent Systems. 4.6.1 Prime Implicants Based Method -- 4.6.2 BDD Based Method -- 4.7 Disjoint Failures -- 4.8 Dependent Failures -- 4.8.1 Common-Cause Failures (CCFs) -- 4.8.2 Functional Dependent Failures -- 5 Phased-Mission Systems -- 5.1 System Description -- 5.2 Rules of Phase Algebra -- 5.3 BDD-Based Method for PMS Analysis -- 5.3.1 Input Variable Ordering -- 5.3.2 Single-Phase BDD Generation -- 5.3.3 PMS BDD Generation -- 5.3.4 PMS BDD Evaluation -- 5.4 Mission Performance Analysis -- 6 Multi-State Systems -- 6.1 Assumptions -- 6.2 An Illustrative Example -- 6.3 MSS Representation -- 6.3.1 MSS Representation Using MFT -- 6.3.2 MSS Representation Using MRBD -- 6.3.3 Equivalency of MRBD and MFT Representations -- 6.4 Multi-State BDD (MBDD) -- 6.4.1 Step 1 - State Variable Encoding -- 6.4.2 Step 2 - Generating MBDD from MFT -- 6.4.3 Step 3 - MBDD Evaluation -- 6.4.4 Example Illustration -- 6.5 Logarithmically-Encoded BDD (LBDD) -- 6.5.1 Step 1 - Variable Encoding -- 6.5.2 Step 2 - Generating LBDD from MFT -- 6.5.3 Step 3 - LBDD Evaluation -- 6.5.4 Example Illustration -- 6.6 Multi-State Multi-Valued Decision Diagrams (MMDD) -- 6.6.1 Step 1 - Variable Encoding -- 6.6.2 Step 2 - Generating MMDD from MFT -- 6.6.3 Step 3 - MMDD Evaluation -- 6.6.4 Example Illustration -- 6.7 Performance Evaluation and Benchmarks -- 6.7.1 Example Analyses -- 6.7.2 Benchmark Studies -- 6.7.3 Performance Comparison and Discussions -- 6.7.3.1 Comparing Model Size -- 6.7.3.2 Comparing Runtime Complexity of Model Construction -- 6.7.3.3 Comparing Runtime Complexity of Model Evaluation -- 6.8 Summary -- 7 Fault Tolerant Systems and Coverage Models -- 7.1 Basic Types -- 7.2 Imperfect Coverage Model -- 7.3 Applications to Binary-State Systems -- 7.3.1 BDD Expansion Method -- 7.3.2 Simple and Efficient Algorithm -- 7.4 Applications to Multi-State Systems. 7.5 Applications to Phased-Mission Systems -- 7.5.1 Mini-Component Concept -- 7.5.2 Extended SEA Method for PMS -- 7.5.3 An Illustrative Example -- 7.6 Summary -- 8 Shared Decision Diagrams -- 8.1 Multi-Rooted Decision Diagrams -- 8.2 Multi-Terminal Decision Diagrams -- 8.3 Performance Study on Multi-State Systems -- 8.3.1 Example Analyses -- 8.3.2 Benchmark Studies -- 8.4 Application to Phased-Mission Systems -- 8.4.1 PMS Analysis Using MDDs -- 8.4.1.1 Step 1-Variable Encoding -- 8.4.1.2 Step 2-Input Variable Ordering -- 8.4.1.3 Step 3-PMS MDD Generation -- 8.4.1.4 Step 4-PMS MDD Evaluation -- 8.4.2 An Illustrative Example -- 8.5 Application to Multi-State k-out-of-n Systems -- 8.5.1 Multi-State k-out-of-n System Analysis Using MDDs -- 8.5.1.1 Step 1- BDDkl Generation -- 8.5.1.2 Step 2- MDDkl Generation -- 8.5.1.3 Step 3- MDDSj Generation -- 8.5.1.4 Step 4-System MDDSj Evaluation -- 8.5.2 An Illustrative Example -- 8.6 Importance Measures -- 8.6.1 Capacity Networks and Reliability Modeling -- 8.6.2 Composite Importance Measures (Type 1) -- 8.6.2.1 General CIMs -- 8.6.2.2 Alternative CIMs -- 8.6.3 Computing CIMs Using MDD -- 8.6.4 An Illustrative Example -- 8.7 Failure Frequency Based Measures -- 8.8 Summary -- Conclusions -- References -- Index -- EULA.
9781119178002
Reliability (Engineering)-Graphic methods.
Electronic books.
TA169.X55 2015