Monte Carlo Simulation in Dependability Analysis

Foreword by Philippe Bogdanik xi
Foreword by Gilles Zwingelstein xiii
List of Notations xv
List of Acronyms xvii
Definitions xix
Introduction xxi

Part 1. Reliability 1

Chapter 1. Predictive Reliability 3
1.1. Concept of predictive reliability 3
1.2. FIDES methodology 4
1.3. Application example 7
1.4. Maintaining a reliability specification 11
1.5. Summary 12

Chapter 2. Statistical Characteristics of Exponential and Weibull Distributions 13
2.1. Refresher about exponential and Weibull distributions 13
2.2. Parameter estimation for a reliability model using the maximum likelihood method 14
2.3. Estimator properties 17
2.4. Simulation of failure times by inverting the probability of failure 19
2.5. Impact of temperature 21
2.6. Relative bias and coefficient of variation of the Weibull parameters 22
2.7. Simulation scenarios considered from the different parameters 26
2.8. Summary 31

Chapter 3. System Reliability 33
3.1. Assumptions 34
3.2. Maintenance-free systems 34
3.3. Maintenance-free systems 45
3.4. Series/parallel system 73
3.5. Parallel/serial system 78
3.6. Use cases 86

Chapter 4. Impact of Temperature on Reliability 97
4.1. Arrhenius law 97
4.2. Operational life profile 98
4.3. Sedyakin's principle 98
4.4. Consequences for reliability estimates 100
4.5. Taking the effect of maintenance into consideration 107
4.6. Summary 114

Chapter 5. Aging Tests 115
5.1. Accelerated aging test 117
5.2. Aging test design 118
5.3. Sequential test at two constant temperatures 121
5.4. Constant-level parallel testing 124
5.5. Constant-level mixed testing 125
5.6. Summary 125

Chapter 6. Application of the Noncentral Beta Distribution 127
6.1. Context 127
6.2. The "noncentral beta" probability distribution 129
6.3. Measurement modeling 130
6.4. Rejection method 132
6.5. Confidence interval for noncentral beta distribution 136
6.6. Rationale for the choice of the noncentral beta distribution 137
6.7. Summary 139

Chapter 7. Statistical Characteristics of HPP and PLP Processes 141
7.1. Reminders about Poisson processes 141
7.2. HPP homogeneous Poisson process 141
7.3. PLP power process 143
7.4. Summary 148

Part 2. Maintainability 151

Chapter 8. Maintainability 153
8.1. Average number of failures 153
8.2. Serial system 154
8.3. Parallel system 159
8.4. k/n system 162
8.5. Avionics system 164
8.6. Summary 165

Part 3. Availability 167

Chapter 9. System Availability 169
9.1. Assumptions 169
9.2. Uptime and repair time: exponential distributions 171
9.3. Exponential distribution uptime and constant repair time 174
9.4. Exponential distribution uptime and uniform distribution repair time 176
9.5. Exponential distribution uptimes and normal distribution repair times 178
9.6. Uptimes exponential distribution and repair times Weibull distribution 182
9.7. Serial system 183
9.8. Parallel system 186
9.9. k-out-of-n redundancy 189
9.10. Series/parallel system 192
9.11. Parallel/serial system 193
9.12. Energy conversion 194
9.13. Summary 200

Part 4. Safety 203

Chapter 10. FMEA Concurrent Failure Mechanisms 205
10.1. Maintenance-free industrial applications 209
10.2. Industrial applications with maintenance 211
10.3. Consideration of physical contributions 215
10.4. Summary 219

Chapter 11. Feared Events (FTA) 221
11.1. Introduction 221
11.2. Regulatory aspects 222
11.3. Probability of the occurrence of a feared event 228
11.4. Practical application 235
11.5. Summary 239

Appendices 241
References 249
Index 251