Fundamentals of Reliability Engineering – Applications in Multistage Interconnection Networks

<p>Preface ix<br /><br />1 Introduction to Reliability Engineering 1<br /><br />1.1 The Logic of Certainty 1<br /><br />1.2 Union (OR) operation 2<br /><br />1.3 Intersection (AND) operation 3<br /><br />1.4 Series systems 4<br /><br />1.5 Parallel systems 5<br /><br />1.6 General Series–Parallel System 6<br /><br />1.7 Active Redundancy 6<br /><br />1.8 Standby Redundancy 7<br /><br />1.9 Fault Tree Analysis 7<br /><br />1.10 Minimum Cut Sets and Path Sets 9<br /><br />References 10<br /><br />2 Elements of Probability Theory 11<br /><br />2.1 Basic Rules of Probability 11<br /><br />2.2 Cumulative Distribution Function 12<br /><br />2.3 Probability Mass Function 12<br /><br />2.4 Probability Density Function 12<br /><br />2.5 Moments 13<br /><br />2.6 Percentiles 13<br /><br />References 14<br /><br />3 Probability Distributions 15<br /><br />3.1 Binomial 16<br /><br />3.2 Poisson 17<br /><br />3.3 Exponential 18<br /><br />3.4 Weibull 19<br /><br />3.5 Normal 19<br /><br />3.6 Lognormal 20<br /><br />3.7 Mean Time To Failure (MTTF) 22<br /><br />References 23<br /><br />4 Availability 25<br /><br />4.1 Definition 25<br /><br />4.2 Summary 27<br /><br />4.3 Availability of Systems with Repair 28<br /><br />References 29<br /><br />5 Data Analysis 31<br /><br />5.1 Theoretical Model and Evidence 31<br /><br />5.2 Censored Samples 32<br /><br />5.3 Bayesian Theorem 33<br /><br />References 35<br /><br />6 Introduction to Network Systems 37<br /><br />6.1 Parallel Computing and Networks 38<br /><br />6.2 Network Design Considerations 41 <br /><br />6.3 Classification of Interconnection Networks 45<br /><br />References 56<br /><br />7 Classification of Multistage Interconnection Networks 57<br /><br />7.1 Background 57<br /><br />7.2 Multistage Cube Network 67<br /><br />7.3 Extra–Stage Cube Network 70<br /><br />7.4 Shuffle–Exchange Network 72<br /><br />7.5 Shuffle–Exchange Network with an Additional Stage 73<br /><br />7.6 Gamma Network 75<br /><br />7.7 Extra–Stage Gamma Network 77<br /><br />7.8 Dynamic Redundancy Network 78<br /><br />7.9 Improved Enhanced Augmented Data Manipulator Network 79<br /><br />7.10 Improved Logical Neighborhood Network 80<br /><br />7.11 Comparison 81<br /><br />References 84<br /><br />8 Network Reliability Evaluation Methods 87<br /><br />8.1 Overview of Network Reliability 87<br /><br />8.2 Network Model 88<br /><br />8.3 Network Operations 89<br /><br />8.4 Approaches for Calculating Network Reliability 89<br /><br />8.5 Summary 99<br /><br />References 100<br /><br />9 Reliability Analysis of Multistage Interconnection Networks 101<br /><br />9.1 Reliability Analysis of Shuffle–Exchange Network with Minimal Extra Stages 101<br /><br />9.2 Terminal Reliability Improvement in Modified Shuffle–Exchange Network 115<br /><br />9.3 Reliability Bounds for Large MINs 121<br /><br />References 132<br /><br />10 Terminal Reliability Assessment of Gamma and Extra–Stage Gamma Networks 133<br /><br />10.1 Introduction 133<br /><br />10.2 Gamma Network 135<br /><br />10.3 Terminal Reliability of Gamma Network 139<br /><br />10.4 Extra–Stage Gamma Network 140<br /><br />10.5 Comparison 146<br /><br />10.6 Conclusions 146<br /><br />References 147<br /><br />11 Reliability Prediction of Distributed Systems Using Monte Carlo Method 149<br /><br />11.1 Introduction 149<br /><br />11.2 Reliability Parameters 152<br /><br />11.3 Monte Carlo Method 153<br /><br />11.4 Confidence Interval for Monte Carlo Point Estimate 155<br /><br />11.5 Numerical Results 157<br /><br />11.6 Conclusion 163<br /><br />References 164<br /><br />Index 167</p>