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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