ISBN-10:
1849964130
ISBN-13:
9781849964135
Pub. Date:
09/23/2010
Publisher:
Springer London
Complex System Reliability: Multichannel Systems with Imperfect Fault Coverage / Edition 2

Complex System Reliability: Multichannel Systems with Imperfect Fault Coverage / Edition 2

by Albert Myers

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Product Details

ISBN-13: 9781849964135
Publisher: Springer London
Publication date: 09/23/2010
Series: Springer Series in Reliability Engineering
Edition description: 2nd ed. 2010
Pages: 238
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

About the Author

Albert Myers retired as Chief Technology Officer for the Northrop Grumman Corporation and is an elected member of the National Academy of Engineering. During his career he has had extensive experience in the development and qualification of digital flight control systems - including the N.A.S.A. F-8 Digital Fly-by-Wire Program, the world’s first digital fly-by-wire aircraft - and was the chief architect of the flight control system for the B-2 Stealth Bomber.

Table of Contents

1 Introduction 1

1.1 Imperfect Fault Coverage 1

1.2 Computational Complexity 2

1.3 Symbolic Algebra 3

1.4 Binary Decision Diagrams 4

References 4

2 Basic Elements of System Reliability 7

2.1 The Reliability Function 7

2.2 Reliability Functional Block Diagrams 9

2.3 Elements in Series 10

2.4 Elements in Parallel 12

2.5 Combined Series/Parallel Systems 13

2.6 Parallel System Arrangements 15

2.7 Redundancy and System Reliability 16

2.8 k-out-of-n:G Systems 21

2.8.1 At Least k-out-of-n:G Systems 21

2.8.2 Exactly k-out-of-n:G Systems 23

2.8.3 Mathematica k-out-of-n:G Reliability 23

References 26

3 Complex System Reliability 27

3.1 Systems with Complex Interconnections 27

3.2 Sum over States and Truth Tables 28

3.3 Bernoulli State Variables (BSV) 31

3.4 BernoulliRule and the &$$$; and &$$$; Operators 32

3.5 BSV Operations Using &$$$; and &$$$; 34

4 Imperfect Fault Coverage 39

4.1 Background 39

4.2 Imperfect Fault Coverage Models 41

4.2.1 ELC Systems 41

4.2.2 FLC Systems 42

4.2.3 OLC Systems 43

4.3 IFC Sum-over-States Models 43

4.4 IFC Combinatorial Functions 45

4.4.1 ELC Functions 45

4.4.2 FLC Functions 47

4.4.3 OLC Functions 48

4.5 Combinatorial Functions for i.i.d. Systems 49

4.6 Recursive k-out-of-n:G Functions 51

4.6.1 PFC Recursive Functions 51

4.6.2 ELC Recursive Functions 52

4.6.3 FLC Recursive Functions 52

4.6.4 OLC Recursive Functions 53

4.7 PFC and IFC Table-Based Algorithms 54

4.7.1 PFC Table-Based Algorithms 54

4.7.2 ELC Table-Based Algorithms 55

4.7.3 FLC Table-Based Algorithms 56

4.7.4 OLC Table-Based Algorithms 57

4.8 Estimation of FLC Coverage 57

4.9 Comparison of PFC and IFC Systems 60

References 64

5 Complex Systems Modeling Using BSV 65

5.1 Background 65

5.2 Blocks of Redundant Components in Series 66

5.2.1 Configuration 1 68

5.2.2 Configuration 2 70

5.2.3 Comparison of Configurations 1 and 2 71

5.3 Quadruplex Computer Control System 74

5.3.1 FLC Quadruplex Computer System 76

5.3.2 Quadruplex Computer System Results 80

5.4 Actuation Subsystem 81

5.4.1 Mathematica Code for Actuation Subsystem 83

5.4.2 Actuation Subsystem Analysis 87

5.5 Combined Computer and Actuation Systems 87

References 89

6 CPM using BSV 91

6.1 Background 91

6.2 Combined System CPM 92

6.3 Combined System CPM Results 97

6.4 CPM: System A 98

6.5 CPM: System B 108

6.6 Comparison of System A and System B 113

6.7 Comments on CPM 116

7 Binary Decision Diagrams 117

7.1 Overview 117

7.1.1 Shannon Decomposition Theorem 118

7.1.2 Example 118

7.1.3 Reduction Rules 119

7.1.4 if-then-else (ite) Function 120

7.1.5 BDD-Based k-out-of-n:G for PFC and IFC Systems 120

7.2 BDDs for k-out-of-n:G Systems 123

7.3 BDD Comments and Observations 126

References 126

8 FCASE Introduction 127

8.1 Background 127

8.2 Simple System Example 128

8.2.1 FCASE Input File Description 129

8.2.2 FCASE Output File Description 135

8.3 FCASE 1-out-of-4:G PFC and IFC Examples 140

8.3.1 Simple 1-out-of-4:G System FCASE Code and Results 140

8.4 FCASE Fly-by-Wire Systems A and B 144

8.4.1 FCASE Results for System A 145

8.4.2 FCASE Results for System B 146

8.5 System B with Actuators in Series 148

References 150

9 Digital Fly-by-Wire System 151

9.1 Quad-Channel DFBW System Description 151

9.2 FCASE Output File for Quad DFBW System 156

9.3 Results for Quad DFBW System 165

9.4 FCASE Output File for Triplex System 166

10 Limits on Achievable Reliability 177

10.1 Introduction 177

10.2 IFC Models for i.i.d. k-out-out-of-n:G Systems 178

10.3 Optimum Reliability for IFC 1-out-of-n:G Systems 179

10.3.1 Optimum ELC 1-out-of-n:G Systems 179

10.3.2 Optimum FLC 1-out-of-n:G Systems 179

10.4 Comparison of Optimum ELC and FLC Systems 182

References 182

11 Architectural Considerations 183

11.1 Background 183

11.2 Redundancy Level 184

11.2.1 Variations in Actuator Redundancy 184

11.2.2 Variations in Hydraulic System Redundancy 185

11.3 Variations in Redundancy Level 187

11.4 The Value of Cross-Strapping Power 190

11.5 Component Reliability Uncertainty 192

A Mathematica Combinatorial k-out-of-n:G Functions 195

A.1 Combinatorial k-out-of-n:G PFC Functions 196

A.2 Combinatorial k-out-of-n:G ELC Functions 197

A.3 Combinatorial k-out-of-n:G FLC Functions 198

A.4 Combinatorial k-out-of-n:G OLC Functions 199

B Mathematica Recursive k-out-of-n:G Functions 201

B.1 Recursive k-out-of-n:G PFC Functions 202

B.2 Recursive k-out-of-n:G ELC Functions 203

B.3 Recursive k-out-of-n:G FLC Functions 204

B.4 Recursive k-out-of-n:G OLC Functions 205

C Mathematica Table-Based k-out-of-n:G Functions 207

C.1 Table-Based k-out-of-n:G PFC Functions 208

C.2 Table-Based k-out-of-n:G ELC Functions 209

C.3 Table-Based k-out-of-n:G FLC Functions 210

C.4 Table-Based k-out-of-n:G OLC Functions 211

D FCASE System A and System B 213

D.1 FCASE System A 213

D.2 FCASE System B 220

E FCASE Input File Syntax 227

E.1 FCASE start VarDef Section 227

E.2 FCASE start System Section 229

E.3 FCASE start Results Section 231

E.4 Comments on FCASE Numerical Precision 232

Index 235

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