| Introduction | p. 1 |
| Imperfect Fault Coverage | p. 1 |
| Computational Complexity | p. 2 |
| Symbolic Algebra | p. 3 |
| Binary Decision Diagrams | p. 4 |
| References | p. 4 |
| Basic Elements of System Reliability | p. 7 |
| The Reliability Function | p. 7 |
| Reliability Functional Block Diagrams | p. 9 |
| Elements in Series | p. 10 |
| Elements in Parallel | p. 12 |
| Combined Series/Parallel Systems | p. 13 |
| Parallel System Arrangements | p. 15 |
| Redundancy and System Reliability | p. 16 |
| k-out-of-n:G Systems | p. 21 |
| At Least k-out-of-n:G Systems | p. 21 |
| Exactly k-out-of-n:G Systems | p. 23 |
| Mathematica k-out-of-n:G Reliability | p. 23 |
| References | p. 26 |
| Complex System Reliability | p. 27 |
| Systems with Complex Interconnections | p. 27 |
| Sum over States and Truth Tables | p. 28 |
| Bernoulli State Variables (BSV) | p. 31 |
| BernoulliRule and the &$$$; and &$$$; Operators | p. 32 |
| BSV Operations Using &$$$; and &$$$; | p. 34 |
| Imperfect Fault Coverage | p. 39 |
| Background | p. 39 |
| Imperfect Fault Coverage Models | p. 41 |
| ELC Systems | p. 41 |
| FLC Systems | p. 42 |
| OLC Systems | p. 43 |
| IFC Sum-over-States Models | p. 43 |
| IFC Combinatorial Functions | p. 45 |
| ELC Functions | p. 45 |
| FLC Functions | p. 47 |
| OLC Functions | p. 48 |
| Combinatorial Functions for i.i.d. Systems | p. 49 |
| Recursive k-out-of-n:G Functions | p. 51 |
| PFC Recursive Functions | p. 51 |
| ELC Recursive Functions | p. 52 |
| FLC Recursive Functions | p. 52 |
| OLC Recursive Functions | p. 53 |
| PFC and IFC Table-Based Algorithms | p. 54 |
| PFC Table-Based Algorithms | p. 54 |
| ELC Table-Based Algorithms | p. 55 |
| FLC Table-Based Algorithms | p. 56 |
| OLC Table-Based Algorithms | p. 57 |
| Estimation of FLC Coverage | p. 57 |
| Comparison of PFC and IFC Systems | p. 60 |
| References | p. 64 |
| Complex Systems Modeling Using BSV | p. 65 |
| Background | p. 65 |
| Blocks of Redundant Components in Series | p. 66 |
| Configuration 1 | p. 68 |
| Configuration 2 | p. 70 |
| Comparison of Configurations 1 and 2 | p. 71 |
| Quadruplex Computer Control System | p. 74 |
| FLC Quadruplex Computer System | p. 76 |
| Quadruplex Computer System Results | p. 80 |
| Actuation Subsystem | p. 81 |
| Mathematica Code for Actuation Subsystem | p. 83 |
| Actuation Subsystem Analysis | p. 87 |
| Combined Computer and Actuation Systems | p. 87 |
| References | p. 89 |
| CPM using BSV | p. 91 |
| Background | p. 91 |
| Combined System CPM | p. 92 |
| Combined System CPM Results | p. 97 |
| CPM: System A | p. 98 |
| CPM: System B | p. 108 |
| Comparison of System A and System B | p. 113 |
| Comments on CPM | p. 116 |
| Binary Decision Diagrams | p. 117 |
| Overview | p. 117 |
| Shannon Decomposition Theorem | p. 118 |
| Example | p. 118 |
| Reduction Rules | p. 119 |
| if-then-else (ite) Function | p. 120 |
| BDD-Based k-out-of-n:G for PFC and IFC Systems | p. 120 |
| BDDs for k-out-of-n:G Systems | p. 123 |
| BDD Comments and Observations | p. 126 |
| References | p. 126 |
| FCASE Introduction | p. 127 |
| Background | p. 127 |
| Simple System Example | p. 128 |
| FCASE Input File Description | p. 129 |
| FCASE Output File Description | p. 135 |
| FCASE 1-out-of-4:G PFC and IFC Examples | p. 140 |
| Simple 1-out-of-4:G System FCASE Code and Results | p. 140 |
| FCASE Fly-by-Wire Systems A and B | p. 144 |
| FCASE Results for System A | p. 145 |
| FCASE Results for System B | p. 146 |
| System B with Actuators in Series | p. 148 |
| References | p. 150 |
| Digital Fly-by-Wire System | p. 151 |
| Quad-Channel DFBW System Description | p. 151 |
| FCASE Output File for Quad DFBW System | p. 156 |
| Results for Quad DFBW System | p. 165 |
| FCASE Output File for Triplex System | p. 166 |
| Limits on Achievable Reliability | p. 177 |
| Introduction | p. 177 |
| IFC Models for i.i.d. k-out-out-of-n:G Systems | p. 178 |
| Optimum Reliability for IFC 1-out-of-n:G Systems | p. 179 |
| Optimum ELC 1-out-of-n:G Systems | p. 179 |
| Optimum FLC 1-out-of-n:G Systems | p. 179 |
| Comparison of Optimum ELC and FLC Systems | p. 182 |
| References | p. 182 |
| Architectural Considerations | p. 183 |
| Background | p. 183 |
| Redundancy Level | p. 184 |
| Variations in Actuator Redundancy | p. 184 |
| Variations in Hydraulic System Redundancy | p. 185 |
| Variations in Redundancy Level | p. 187 |
| The Value of Cross-Strapping Power | p. 190 |
| Component Reliability Uncertainty | p. 192 |
| Mathematica Combinatorial k-out-of-n:G Functions | p. 195 |
| Combinatorial k-out-of-n:G PFC Functions | p. 196 |
| Combinatorial k-out-of-n:G ELC Functions | p. 197 |
| Combinatorial k-out-of-n:G FLC Functions | p. 198 |
| Combinatorial k-out-of-n:G OLC Functions | p. 199 |
| Mathematica Recursive k-out-of-n:G Functions | p. 201 |
| Recursive k-out-of-n:G PFC Functions | p. 202 |
| Recursive k-out-of-n:G ELC Functions | p. 203 |
| Recursive k-out-of-n:G FLC Functions | p. 204 |
| Recursive k-out-of-n:G OLC Functions | p. 205 |
| Mathematica Table-Based k-out-of-n:G Functions | p. 207 |
| Table-Based k-out-of-n:G PFC Functions | p. 208 |
| Table-Based k-out-of-n:G ELC Functions | p. 209 |
| Table-Based k-out-of-n:G FLC Functions | p. 210 |
| Table-Based k-out-of-n:G OLC Functions | p. 211 |
| FCASE System A and System B | p. 213 |
| FCASE System A | p. 213 |
| FCASE System B | p. 220 |
| FCASE Input File Syntax | p. 227 |
| FCASE start VarDef Section | p. 227 |
| FCASE start System Section | p. 229 |
| FCASE start Results Section | p. 231 |
| Comments on FCASE Numerical Precision | p. 232 |
| Index | p. 235 |
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