ISBN: 3540414371
TITLE: Dependability of Engeneering Systems
AUTHOR: Nahman
TOC:

1 Nonrenewable Two-State Systems 1
1.1 Characteristic Functions and Indices 1
1.2 Analysis of Failure Data 5
1.3 Characteristic Probability Distributions 9
1.3.1 Exponential Distribution 10
1.3.2 Weibull Distribution 12
1.3.3 Uniform Distribution 14
1.3.4 Normal Distribution 16
1.3.5 Gamma Distribution 18
1.3.6 Lognormal Distribution 20
1.3.7 Combination of Distributions 21
References 22
2 Renewable Two-State Systems 24
2.1 State Transition Diagrams and Associated Indices 24
2.2 Exponential Distribution of Up and Renewal Times 26
2.3 Absorbing States and the Equivalent Steady-State Transition Diagram 31
2.4 General Cdf of Renewal Duration 34
2.4.1 Method of Supplementary Variables 34
2.4.2 Fictitious States 37
2.4.3 Series Connection of Fictitious States 40
2.4.4 Parallel Connection of Fictitious States 44
2.4.5 Open Loop Sequence of Consecutive States 46
References 50
3 Markov Systems 51
3.1 Equations Determining the Probability of System States 51
3.2 Composition of System Equations from Component Models 54
3.2.1 Independent Components 54
3.2.2 Dependent Components 57
3.3 Simplification of the System State Probability Equations 58
3.3.1 Systems with Independent Components 58
3.3.2 Merging of States 58
3.4 System Dependability Indices 63
3.4.1 System Availability 63
3.4.2 System Reliability and Mean Time to First Failure (MTFF) 64
3.5 Steady-state System Dependability Indices 66
3.5.1 System States Indices 67
3.5.2 System Indices 68
3.5.3 Truncation of States 69
3.5.4 Transition Rate Matrix Deviation Concept 71
3.5.5 Matrix Gauss-Seidel Approach 74
3.6 Characteristic Applications 78
3.6.1 Independent Components 78
3.6.2 Preventive Maintenance 80
3.6.3 Restricted Repair 82
3.6.4 Partially Redundant Systems 82
3.6.5 Induced Failures 83
3.6.6 System with a Cold Standby Unit 84
References 87
4 Networks 88
4.1 Elementary Network Structures 89
4.1.1 Series Connection 89
4.1.2 Parallel Connection 92
4.1.3 Series-Parallel Connections 94
4.2 Composite Structures 96
4.2.1 General Expressions for the Steady-State Failure Frequency 97
4.2.2 Application of the Total Probability Theorem 98
4.2.3 Minimal Paths 100
4.2.4 Unreliable Nodes 104
4.2.5 Multiple Sources and Sinks 105
4.2.6 Minimal Cuts 106
4.2.7 Network Partition and Equivalents 110
4.2.8 Networks with Dependent Branches 112
4.2.9 Limited Transfer Capacity Networks 116
References 119
5 Event Inspection Methods 121
5.1 FMECA and FTA Approaches 121
5.1.1 Failure Mode, Effects and Criticality Analysis (FMECA) 121
5.1.2 Fault Tree Analysis (FTA) 122
5.2 Failure Event Set Enumeration 127
5.2.1 Minimal Cuts 127
5.2.2 System State-Spate Enumeration 129
5.2.3 Kronecker Algebra Application 131
References 134
6 Finite-Term Dependability Prediction 135
References 142
7 Simulation 143
7.1 Fundamentals 143
7.1.1 General 143
7.1.2 Processing the Outcomes 144
7.2 Generation of Uniformly Distributed Random Numbers 147
7.3 Steady-State Dependability Indices 148
7.3.1 Generation of System States 148
7.4 Time-Specific Dependability Evaluation 151
7.4.1 Generation of Random State-Residente Times 151
7.4.2 System Reliability Evaluation 152
7.4.3 Stochastic Processes 154
References 156
8 Dependability Grading and Optimization 157
8.1 Optimization Concept 157
8.2 Fuzzy Logic Based Dependability Evaluation 160
8.2.1 Fuzzy Sets 160
8.2.2 Fuzzy Logic 163
8.3 Dependability Grading 164
8.3.1 Dependability Evaluation in General 164
8.3.2 Network Dependability Evaluation 165
References 171
9 Uncertainties in the Dependability Evaluation 172
9.1 Mathematical Operations with Fuzzy Numbers 172
9.1.1 Fuzzy Numbers Representation and Evaluation 172
9.1.2 Functions of Fuzzy Numbers 174
9.2 Element Dependability Indices 177
9.2.1 Reliability 177
9.2.2 Steady-State Unavailability 179
9.2.3 Time-Specific Unavailability 181
9.3 Network Dependability Indices 182
9.4 Concluding Remarks 185
References 186
Index 187
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