Table of Contents

Preface ix

1 Introduction to Reliability Engineering 1

1.1 The Logic of Certainty 1

1.2 Union (OR) operation 2

1.3 Intersection (AND) operation 3

1.4 Series systems 4

1.5 Parallel systems 5

1.6 General Series-Parallel System 6

1.7 Active Redundancy 6

1.8 Standby Redundancy 7

1.9 Fault Tree Analysis 7

1.10 Minimum Cut Sets and Path Sets 9

References 10

2 Elements of Probability Theory 11

2.1 Basic Rules of Probability 11

2.2 Cumulative Distribution Function 12

2.3 Probability Mass Function 12

2.4 Probability Density Function 12

2.5 Moments 13

2.6 Percentiles 13

References 14

3 Probability Distributions 15

3.1 Binomial 16

3.2 Poisson 17

3.3 Exponential 18

3.4 Weibull 19

3.5 Normal 19

3.6 Lognormal 20

3.7 Mean Time To Failure (MTTF) 22

References 23

4 Availability 25

4.1 Definition 25

4.2 Summary 27

4.3 Availability of Systems with Repair 28

References 29

5 Data Analysis 31

5.1 Theoretical Model and Evidence 31

5.2 Censored Samples 32

5.3 Bayesian Theorem 33

References 35

6 Introduction to Network Systems 37

6.1 Parallel Computing and Networks 38

6.2 Network Design Considerations 41

6.3 Classification of Interconnection Networks 45

References 56

7 Classification of Multistage Interconnection Networks 57

7.1 Background 57

7.2 Multistage Cube Network 67

7.3 Extra-Stage Cube Network 70

7.4 Shuffle-Exchange Network 72

7.5 Shuffle-Exchange Network with an Additional Stage 73

7.6 Gamma Network 75

7.7 Extra-Stage Gamma Network 77

7.8 Dynamic Redundancy Network 78

7.9 Improved Enhanced Augmented Data Manipulator Network 79

7.10 Improved Logical Neighborhood Network 80

7.11 Comparison 81

References 84

8 Network Reliability Evaluation Methods 87

8.1 Overview of Network Reliability 87

8.2 Network Model 88

8.3 Network Operations 89

8.4 Approaches for Calculating Network Reliability 89

8.5 Summary 99

References 100

9 Reliability Analysis of Multistage Interconnection Networks 101

9.1 Reliability Analysis of Shuffle-Exchange Network with Minimal Extra Stages 101

9.2 Terminal Reliability Improvement in Modified Shuffle-Exchange Network 115

9.3 Reliability Bounds for Large MINs 121

References 132

10 Terminal Reliability Assessment of Gamma and Extra-Stage Gamma Networks 133

10.1 Introduction 133

10.2 Gamma Network 135

10.3 Terminal Reliability of Gamma Network 139

10.4 Extra-Stage Gamma Network 140

10.5 Comparison 146

10.6 Conclusions 146

References 147

11 Reliability Prediction of Distributed Systems Using Monte Carlo Method 149

11.1 Introduction 149

11.2 Reliability Parameters 152

11.3 Monte Carlo Method 153

11.4 Confidence Interval for Monte Carlo Point Estimate 155

11.5 Numerical Results 157

11.6 Conclusion 163

References 164

Index 167

About the Author

Indra Gunawan, PhD, is a Senior Lecturer and Coordinatorof Postgraduate Programs in Maintenance and Reliability Engineeringin the School of Applied Sciences and Engineering at the FederationUniversity, Australia. He completed his PhD degree in industrialengineering from Northeastern University, USA. Prior to joiningMonash University, he served as a faculty member in the Departmentof Mechanical and Manufacturing Engineering at Auckland Universityof Technology, New Zealand. His main areas of research aremaintenance and reliability engineering, project management,application of operations research, operations management, appliedstatistics, probability modeling, and engineering systems design.His work has appeared in many peer-reviewed journals and conferenceproceedings.