Monte Carlo Simulation in Dependability Analysis

Franck Bayle trained as an electronic engineer. He has practiced for almost 15 years, working at Crouzet and then at Thalès in Valence, France. He has also worked as Design Authority in reliability and maturity.Laurent Denis is the CEO of StatXpert, a consulting, training, and software company specializing in statistics and operational reliability based in Pessac, France.Adrien Gigliati is Dependability Engineer at Thalès in Valence, France.

• Foreword by Philippe Bogdanik xiForeword by Gilles Zwingelstein xiiiList of Notations xvList of Acronyms xviiDefinitions xixIntroduction xxiPart 1. Reliability 1Chapter 1. Predictive Reliability 31.1. Concept of predictive reliability 31.2. FIDES methodology 41.3. Application example 71.4. Maintaining a reliability specification 111.5. Summary 12Chapter 2. Statistical Characteristics of Exponential and Weibull Distributions 132.1. Refresher about exponential and Weibull distributions 132.2. Parameter estimation for a reliability model using the maximum likelihood method 142.3. Estimator properties 172.4. Simulation of failure times by inverting the probability of failure 192.5. Impact of temperature 212.6. Relative bias and coefficient of variation of the Weibull parameters 222.7. Simulation scenarios considered from the different parameters 262.8. Summary 31Chapter 3. System Reliability 333.1. Assumptions 343.2. Maintenance-free systems 343.3. Maintenance-free systems 453.4. Series/parallel system 733.5. Parallel/serial system 783.6. Use cases 86Chapter 4. Impact of Temperature on Reliability 974.1. Arrhenius law 974.2. Operational life profile 984.3. Sedyakin's principle 984.4. Consequences for reliability estimates 1004.5. Taking the effect of maintenance into consideration 1074.6. Summary 114Chapter 5. Aging Tests 1155.1. Accelerated aging test 1175.2. Aging test design 1185.3. Sequential test at two constant temperatures 1215.4. Constant-level parallel testing 1245.5. Constant-level mixed testing 1255.6. Summary 125Chapter 6. Application of the Noncentral Beta Distribution 1276.1. Context 1276.2. The "noncentral beta" probability distribution 1296.3. Measurement modeling 1306.4. Rejection method 1326.5. Confidence interval for noncentral beta distribution 1366.6. Rationale for the choice of the noncentral beta distribution 1376.7. Summary 139Chapter 7. Statistical Characteristics of HPP and PLP Processes 1417.1. Reminders about Poisson processes 1417.2. HPP homogeneous Poisson process 1417.3. PLP power process 1437.4. Summary 148Part 2. Maintainability 151Chapter 8. Maintainability 1538.1. Average number of failures 1538.2. Serial system 1548.3. Parallel system 1598.4. k/n system 1628.5. Avionics system 1648.6. Summary 165Part 3. Availability 167Chapter 9. System Availability 1699.1. Assumptions 1699.2. Uptime and repair time: exponential distributions 1719.3. Exponential distribution uptime and constant repair time 1749.4. Exponential distribution uptime and uniform distribution repair time 1769.5. Exponential distribution uptimes and normal distribution repair times 1789.6. Uptimes exponential distribution and repair times Weibull distribution 1829.7. Serial system 1839.8. Parallel system 1869.9. k-out-of-n redundancy 1899.10. Series/parallel system 1929.11. Parallel/serial system 1939.12. Energy conversion 1949.13. Summary 200Part 4. Safety 203Chapter 10. FMEA Concurrent Failure Mechanisms 20510.1. Maintenance-free industrial applications 20910.2. Industrial applications with maintenance 21110.3. Consideration of physical contributions 21510.4. Summary 219Chapter 11. Feared Events (FTA) 22111.1. Introduction 22111.2. Regulatory aspects 22211.3. Probability of the occurrence of a feared event 22811.4. Practical application 23511.5. Summary 239Appendices 241References 249Index 251