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Reliability and availability engineering : modeling, analysis, and applications / Kishor S. Trivedi, Duke University, North Carolina, Andrea Bobbio, Universitá degli Studi del Piemonte Orientale

Author
Trivedi, Kishor Shridharbhai, 1946-
Published
Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2017.
Copyright Date
©2017
Physical Description
1 online resource (730 pages)
Additional Creators
Bobbio, Andrea
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Contents
Machine generated contents note: 1.Dependability -- 1.1.Definition -- 1.2.Dependability Measures and Metrics -- 1.3.Examples of System Dependability Evaluation -- 1.3.1.Pure Reliability Evaluation -- 1.3.2.Safety Analysis of Critical Systems -- 1.3.3.Availability and Maintainability Evaluation -- 1.3.4.Software Dependability -- 1.3.5.Service-Oriented Dependability -- 1.3.6.Task-Oriented Dependability -- 1.4.Predictive Dependability Assessment -- 1.5.Further Reading -- References -- 2.Dependability Evaluation -- 2.1.Quantitative Evaluation of Dependability -- 2.1.1.Measurement-Based Evaluation -- 2.1.2.Model-Based Evaluation -- 2.1.3.Interplay between Measurement and Modeling -- 2.2.The Modeling Process -- 2.2.1.Studying/Understanding the System Being Modeled -- 2.2.2.Development of a Conceptual Model -- 2.2.3.Translation into an Operational Computerized Model -- 2.2.4.Parametrization of the Operational Model -- 2.2.5.Solution of the Operational Model and Presentation of the Results -- 2.2.6.Verification, Validation and Improvement of the Model -- 2.2.7.Use of the Model -- 2.3.Modeling Formalisms -- 2.4.Model Verification and Validation -- 2.4.1.Model Verification -- 2.4.2.Model Validation -- 2.5.Errors in Models -- 2.5.1.Errors in the Construction of the Conceptual Model -- 2.5.2.Errors in the Construction of the Operational Computerized Model -- 2.5.3.Errors in Model Solution -- 2.6.The Probabilistic Approach -- 2.7.Statistical Dependence -- 2.8.Further Reading -- References -- 3.Dependability Metrics Defined on a Single Unit -- 3.1.Non-Repairable Unit -- 3.2.Common Probability Distribution Functions -- 3.2.1.Exponential Distribution -- 3.2.2.Shifted Exponential Distribution -- 3.2.3.Weibull Distribution -- 3.2.4.Normal and Lognormal Distributions -- 3.2.5.Phase-Type Distribution -- 3.2.6.Gamma Distribution -- 3.2.7.Log-Logistic Distribution -- 3.2.8.Bernoulli Distribution -- 3.2.9.Poisson Distribution -- 3.2.10.Mass at Origin -- 3.2.11.Defective Distribution -- 3.3.Minimum and Maximum of Random Variables -- 3.3.1.The Cdf of the Minimum of Random Variables -- 3.3.2.The Cdf of the Maximum of Random Variables -- 3.4.Epistemic Uncertainty Propagation -- 3.4.1.Distribution for Rate Parameter of an Exponential Distribution -- 3.4.2.Reliability Distribution -- 3.5.Repairable Unit -- 3.5.1.Measures for Repairable Systems -- 3.5.2.Renewal Processes -- 3.5.3.The Exponential Case: Poisson Process -- 3.5.4.Modified Renewal Process -- 3.5.5.Availability Analysis: Alternating Renewal Process -- 3.5.6.Availability Analysis: State Transition Diagram -- 3.5.7.Sensitivity of Steady-State Availability -- 3.5.8.Scaled Sensitivity of Steady-State Availability -- 3.5.9.Cumulative Downtime Distribution -- 3.6.Interval Reliability -- 3.7.Task-Oriented Measures -- 3.7.1.No Failure and No Repair -- 3.7.2.Failure and Repair -- 3.7.3.Failure and Constrained Repair -- 3.8.Improving Dependability -- 3.9.Further Reading -- References -- 4.Reliability Block Diagram -- 4.1.Series Systems -- 4.1.1.Reliability of Series Systems -- 4.1.2.Importance (Sensitivity) Analysis of Series Systems -- 4.1.3.The Parts Count Method -- 4.1.4.Other Measures for Series Systems -- 4.2.Systems with Redundancy -- 4.2.1.Parallel Redundancy -- 4.2.2.Reliability of a Parallel System -- 4.2.3.Parallel System: The Exponential Case -- 4.2.4.Importance (Sensitivity) Analysis of Parallel Systems -- 4.2.5.Parallel Systems: Availability -- 4.2.6.Series-Parallel Systems -- 4.2.7.Importance (Sensitivity) Analysis of Series-Parallel Systems -- 4.2.8.System Redundancy vs. Component Redundancy -- 4.2.9.Is Redundancy Always Useful? -- 4.3.k-out-of-n Majority Voting Systems -- 4.3.1.The Exponential Case -- 4.3.2.Application of k-out-of-n Redundancy -- 4.3.3.The Consecutive k-out-of-n System -- 4.4.Factoring for Non-Series-Parallel Systems -- 4.5.Non-Identical k-out-of-n System -- 4.5.1.k-out-of-n System with Two Groups of Components -- 4.6.Further Reading -- References -- 5.Network Reliability -- 5.1.Networks and Graphs -- 5.2.Binary Probabilistic Networks -- 5.2.1.Basic Properties of a Binary Decision Diagram -- 5.2.2.Network Reliability Based on Minpath Analysis -- 5.2.3.Network Reliability Based on Mincut Analysis -- 5.2.4.Network Reliability Based on Factoring -- 5.2.5.Graph-Visiting Algorithm -- 5.2.6.Deriving Minpaths and Mincuts from BDD -- 5.3.Binary Probabilistic Weighted Networks -- 5.3.1.Definition of BPWN -- 5.3.2.Weight as Cost -- 5.3.3.Weight as Capacity -- 5.4.Multi-State Networks -- 5.4.1.Weighted Multi-State Networks -- 5.4.2.Multi-Valued Decision Diagrams -- 5.4.3.Basic Operations for MDD Manipulation -- 5.4.4.Algorithmic Implementation and Probability Evaluation -- 5.5.Limitation of the Exact Algorithm -- 5.6.Computing Upper and Lower Bounds of Reliability -- 5.7.Further Reading -- References -- 6.Fault Tree Analysis -- 6.1.Motivation for and Application of FTA -- 6.2.Construction of the Fault Tree -- 6.2.1.The OR Logic Gate -- 6.2.2.The AND Logic Gate -- 6.2.3.Fault Trees with OR and AND Gates -- 6.2.4.Fault Trees with Repeated Events -- 6.2.5.The k-out-of-n Node -- 6.3.Qualitative Analysis of a Fault Tree -- 6.3.1.Logical Expression through Minimal Cut Sets -- 6.3.2.Logical Expression through Graph-Visiting Algorithm -- 6.3.3.Qualitative Analysis of FTRE -- 6.3.4.Fault Tree and Success Tree -- 6.3.5.Structural Importance -- 6.4.Quantitative Analysis -- 6.4.1.Probability of Basic Events -- 6.4.2.Quantitative Analysis of an FT without Repeated Events -- 6.4.3.Quantitative Analysis of an FT with Repeated Events -- 6.5.Modularization -- 6.6.Importance Measures -- 6.6.1.Birnbaum Importance Index -- 6.6.2.Criticality Importance Index -- 6.6.3.Vesely-Fussell Importance Index -- 6.7.Case Studies -- 6.8.Attack and Defense Tree -- 6.8.1.Countermeasures -- 6.8.2.Weighted Attack Tree (WAT) -- 6.9.Multi-State Fault Tree -- 6.10.Mapping Fault Trees into Bayesian Networks -- 6.10.1.Bayesian Network Definition -- 6.10.2.Mapping an Algorithm from FT to BN -- 6.10.3.Probabilistic Gates: Common Cause Failures -- 6.10.4.Noisy Gates -- 6.10.5.Multi-State Variables -- 6.10.6.Sequentially Dependent Failures -- 6.10.7.Dependability Analysis through BN Inference -- 6.11.Further Reading -- 6.12.Useful Properties of Boolean Algebra -- References -- 7.State Enumeration -- 7.1.The State Space -- 7.1.1.Characterization of System States: Truth Table and Structure Function -- 7.1.2.Structural Importance and Frontier States -- 7.1.3.Boolean Expression of the Structure Function -- 7.2.The Failure Process Defined on the State Space -- 7.2.1.Dependability Measures Defined on the State Space -- 7.3.System Reliability with Independent Components -- 7.4.Repairable Systems with Independent Components -- References -- 8.Dynamic Redundancy -- 8.1.Cold Standby Case -- 8.2.Warm Standby -- 8.3.Hot Standby and k-out-of-n -- 8.4.Imperfect Fault Coverage -- 8.5.Epistemic Uncertainty Propagation -- 8.5.1.Cold Standby with Identical Components -- 8.5.2.Warm Standby -- 8.5.3.Hot Standby and k-out-of-n -- References -- 9.Continuous-Time Markov Chain: Availability Models -- 9.1.Introduction -- 9.1.1.Chapman-Kolmogorov Equations -- 9.1.2.The Infinitesimal Generator Matrix -- 9.1.3.Kolmogorov Differential Equation -- 9.1.4.Distribution of the Sojourn Time in a Given State -- 9.2.Classification of States and Stationary Distribution -- 9.2.1.Irreducible Markov Chain -- 9.2.2.Expected State Occupancy -- 9.3.Dependability Models Defined on a CTMC -- 9.3.1.Expected Uptime and Expected Downtime -- 9.4.Markov Reward Models -- 9.4.1.MRM with Reward Rates -- 9.4.2.MRM with Impulse Reward -- 9.5.Availability Measures Defined on an MRM -- 9.5.1.Instantaneous, Steady-State, and Interval Availability -- 9.5.2.Expected Uptime and Expected Downtime -- 9.5.3.Expected Number of Transitions -- 9.5.4.Expected Number of Visits -- 9.5.5.Expected Number of System Failures/Repairs -- 9.5.6.Equivalent Failure and Repair Rate -- 9.5.7.Defects per Million -- 9.6.Case Study: IBM Blade Server System -- 9.7.Parametric Sensitivity Analysis -- 9.7.1.Parametric Sensitivity Analysis for a CTMC -- 9.8.Numerical Methods for Steady-State Analysis of Markov Models -- 9.8.1.Power Method -- 9.8.2.Successive Over-Relaxation -- 9.9.Further Reading -- References -- 10.Continuous-Time Markov Chain: Reliability Models -- 10.1.Continuous-Time Markov Chain Reliability Models -- 10.1.1.Convolution Integration Method for Transient Probabilities -- 10.1.2.Solution with Laplace Transforms -- 10.1.3.Other Dependability Measures Defined on a CTMC -- 10.2.Continuous-Time Markov Chains with Absorbing States -- 10.2.1.Single Absorbing State: Cdf of Time to Absorption -- 10.2.2.Single Absorbing State: Expected Time to Absorption -- 10.2.3.Single Absorbing State: Moments of Time to Absorption -- 10.2.4.Multiple Absorbing States -- 10.2.5.Expected First-Passage Time -- 10.3.Continuous-Time Markov Chains with Self-Loops -- 10.3.1.Uniformization of a CTMC -- 10.4.Transient Solution Methods -- 10.4.1.Fully Symbolic and Semi-Symbolic Methods -- 10.4.2.Transient Solution via Series Expansion -- 10.4.3.Transient Solution via Uniformization (Jensen's method) -- 10.4.4.ODE-Based Solution Methods -- 10.5.Further Reading -- References -- 11.Continuous-Time Markov Chain: Queuing Systems -- 11.1.Continuous-Time Markov Chain Performance Models -- 11.2.The Birth-Death Process -- 11.3.The Single Queue -- 11.3.1.M/M/1 Queue -- 11.4.M/M/m: Single Queue with m Servers -- 11.4.1.M/M/infinity: An Infinite Number of Servers -- 11.5.M/M/1/K: Finite Storage -- 11.5.1.M/M/m/m Queue -- 11.6.Closed M/M/1 Queue -- 11.7.Queues with Breakdown -- 11.8.Further Reading -- References -- 12.Petri Nets -- 12.1.Introduction -- 12.2.From Petri Nets to Stochastic Reward Nets -- 12.2.1.Petri Nets -- 12.2.2.Structural Extensions to Petri Nets -- 12.2.3.Stochastic Petri Nets -- 12.2.4.Generalized Stochastic Petri Nets -- 12.3.Stochastic Reward Nets -- and Contents note continued: 12.4.Computing the Dependability and Performance Measures -- 12.5.Further Reading -- References -- 13.Non-Homogeneous Continuous-Time Markov Chains -- 13.1.Introduction -- 13.1.1.Kolmogorov Differential Equation -- 13.2.Illustrative Examples -- 13.3.Piecewise Constant Approximation -- 13.4.Queuing Examples -- 13.5.Reliability Growth Examples -- 13.6.Numerical Solution Methods for NHCTMCs -- 13.6.1.Ordinary Differential Equation Method -- 13.6.2.Uniformization Method -- 13.7.Further Reading -- References -- 14.Semi-Markov and Markov Regenerative Models -- 14.1.Introduction -- 14.2.Steady-State Solution -- 14.3.Semi-Markov Processes with Absorbing States -- 14.3.1.Mean Time to Absorption -- 14.3.2.Variance of the Time to Absorption -- 14.3.3.Probability of Absorption in SMPs with Multiple Absorbing States -- 14.4.Transient Solution -- 14.5.Markov Regenerative Process -- 14.5.1.Transient and Steady-State Analysis of an MRGP -- 14.6.Further Reading -- References -- 15.Phase-Type Expansion -- 15.1.Introduction -- 15.1.1.Definition -- 15.2.Properties of the PH Distribution -- 15.3.Phase-Type Distributions in System Modeling -- 15.4.Task Completion Time under a PH Work Requirement -- 15.5.Phase-Type Distribution in Queuing Models -- 15.6.Comparison of the Modeling Power of Different Model Types -- 15.7.Further Reading -- References -- 16.Hierarchical Models -- 16.1.Introduction -- 16.2.Hierarchical Modeling -- 16.2.1.Import Graph -- 16.3.Availability Models -- 16.4.Reliability Models -- 16.4.1.Phased Mission Systems -- 16.4.2.Behavioral Decomposition -- 16.5.Dynamic Fault Tree -- 16.6.Performance Models -- 16.7.Performability Models -- 16.8.Survivability Models -- 16.9.Further Reading -- References -- 17.Fixed-Point Iteration -- 17.1.Introduction -- 17.1.1.Revisiting the Import Graph -- 17.2.Availability Models -- 17.3.Reliability Models -- 17.4.Performance Models -- 17.5.Further Reading -- References -- 18.Modeling Real-Life Systems -- 18.1.Availability Models -- 18.2.Reliability Models -- 18.3.Combined Performance and Reliability Models -- 18.4.Further Reading -- References.
Summary
Do you need to know what technique to use to evaluate the reliability of an engineered system? This self-contained guide provides comprehensive coverage of all the analytical and modeling techniques currently in use, from classical non-state and state space approaches, to newer and more advanced methods such as binary decision diagrams, dynamic fault trees, Bayesian belief networks, stochastic Petri nets, non-homogeneous Markov chains, semi-Markov processes, and phase type expansions. Readers will quickly understand the relative pros and cons of each technique, as well as how to combine different models together to address complex, real-world modeling scenarios. Numerous examples, case studies and problems provided throughout help readers put knowledge into practice, and a solutions manual and Powerpoint slides for instructors accompany the book online. This is the ideal self-study guide for students, researchers and practitioners in engineering and computer science.
Subject(s)
ISBN
9781316163047 (electronic book)
1316163040 (electronic book)
Bibliography Note
Includes bibliographical references and index.
Source of Acquisition
Purchased with funds from the J. Harvey Fahnestock Endowment for Scientific, Engineering and Rare Books; 2017
Endowment Note
J. Harvey Fahnestock Endowment for Scientific, Engineering and Rare Books
View MARC record | catkey: 22088621