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Binary Decision Diagrams and Extensions for System Reliability Analysis

By Liudong Xing and Suprasad V. Amari
Series: Performability Engineering Series
Copyright: 2015   |   Status: Published
ISBN: 9781118549377  |  Hardcover  |  
236 pages | 117 illustrations
Price: $175 USD
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One Line Description
The very first book that provides detailed coverage of binary decision diagrams and their extensions in solving complex reliability problems in an efficient and exact manner.

Audience
The core interest groups are research scientists and engineers (e.g. reliability engineering, electrical engineering, mechanical engineering, power engineering, nuclear engineering, computer scientists) working on algorithms and data structures. The book will also be very valuable to those working in companies that purchase reliability, safety, and dependability standards including IEC standards, SAE standards, ISO standards, MIL standards, and aerospace standards. The book can also be used as a textbook on system reliability analysis courses at the graduate and undergraduate levels.

Description
Recent advances in science and technology have made modern computing and engineering systems more powerful and sophisticated than ever. The increasing complexity and scale imply that system reliability problems not only continue to be a challenge but also require more efficient models and solutions. This is the first book systematically covering the state-of-the-art binary decision diagrams and their extended models, which can provide efficient and exact solutions to reliability analysis of large and complex systems.
The book provides both basic concepts and detailed algorithms for modeling and evaluating reliability of a wide range of complex systems, such as multi-state systems, phased-mission systems, fault-tolerant systems with imperfect fault coverage, systems with common-cause failures, systems with disjoint failures, and systems with functional dependent failures. These types of systems abound in safety-critical or mission-critical applications such as aerospace, circuits, power systems, medical systems, telecommunication systems, transmission systems, traffic light systems, data storage systems, etc.
The book provides both small-scale illustrative examples and large-scale benchmark examples to demonstrate broad applications and advantages of different decision diagrams based methods for complex system reliability analysis. Other measures including component importance and failure frequency are also covered. A rich set of references is cited in the book, providing helpful resources for readers to pursue further research and study of the topics.

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Author / Editor Details
Liudong Xing is a professor in the Department of Electrical and Computer Engineering at the University of Massachusetts (UMass), Dartmouth. She received her PhD degree in Electrical Engineering from the University of Virginia, Charlottesville in 2002 and has authored or co-authored more than 200 technical papers. She is the recipient of the Leo M. Sullivan Teacher of the Year Award (2014), Scholar of the Year Award (2010), Outstanding Women Award (2011) of UMass Dartmouth, as well as the IEEE Region 1 Technological Innovation (Academic) Award (2007).

Suprasad V. Amari received the MS and PhD degrees in Reliability Engineering from the Indian Institute of Technology, Kharagpur, India. He is a senior technical staff member at Relyence Corporation. Prior to joining Relyence, he served as a Technical Fellow at Parametric Technology Corporation (PTC) for 14 years, where he was responsible for research, design, and development of PTC’s reliability modeling and analysis software products. He has authored or co-authored 6 book chapters in handbooks and about 90 technical papers in the area of reliability engineering. He has been actively involved with the Annual Reliability and Maintainability Symposium (RAMS) and currently serves as the Vice General Chair.

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Table of 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



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