| Foreword | p. vii |
| Markov reliability and availability analysis | p. vii |
| Introduction | p. 1 |
| Discrete-time, discrete-state Markov processes | p. 2 |
| The conceptual model | p. 2 |
| State probabilities | p. 5 |
| Multi-step transition probabilities | p. 7 |
| Solution of the fundamental equation | p. 9 |
| Steady state probabilities for ergodic systems | p. 19 |
| First passage probabilities | p. 20 |
| Continuous time, discrete-state Markov processes | p. 24 |
| The conceptual model | p. 24 |
| Solution of the fundamental equation | p. 30 |
| Failure intensity | p. 34 |
| Average time of occupancy of a given state | p. 36 |
| System availability | p. 37 |
| System reliability | p. 38 |
| Monte Carlo simulations for reliability and availability analysis | |
| Introduction | p. 59 |
| Monte Carlo simulation for system engineering | p. 60 |
| Monte Carlo simulation for system unreliability and unavailability estimation | |
| Indirect and direct Monte Carlo simulation | p. 66 |
| Markov Chain Monte Carlo for applications to reliability and availability analysis | |
| Introduction | p. 71 |
| The Metropolis-Hastings algorithm | p. 73 |
| Application to the estimation of the failure rate of a deteriorating component | p. 74 |
| The Gibbs sampler | p. 78 |
| Application to the estimation of a rare failures process | p. 80 |
| The reversible-jump MCMC algorithm | p. 83 |
| Application to the estimation of the failure rate of a component subject to degradation or improvement | p. 88 |
| Application to the estimation of the parameters of a deterioration process due to fatigue | p. 95 |
| Bayesian updating | p. 103 |
| Practical issues in implementing MCMC algorithms | p. 108 |
| Choice of the kinetics K(. .) | p. 108 |
| Burn-in period | p. 109 |
| Number of iterations | p. 109 |
| Initial conditions | p. 110 |
| Other algorithms | p. 110 |
| Basics of genetic algorithms with application to system reliability and availability optimization | |
| Introduction | p. 115 |
| Genetic Algorithms at a glance | p. 117 |
| The standard Genetic Algorithm | p. 121 |
| Affine transforming the chromosome fitness | p. 124 |
| More sophisticated breeding procedures | p. 131 |
| Efficiency of breeding procedures | p. 134 |
| The figures of merit | p. 134 |
| The test functions | p. 138 |
| Results | p. 144 |
| Inducement of species and niches | p. 151 |
| Isolation by distance | p. 151 |
| Spatial mating | p. 152 |
| Sharing | p. 153 |
| Multi-objective optimization | p. 155 |
| Application of genetic algorithms to RAMS | p. 158 |
| Examples | p. 163 |
| Multi-objective optimization of system design: a simple application | p. 163 |
| Multi-objective optimization of the inspection policy of a nuclear safety system | p. 169 |
| Discussion | p. 180 |
| Dependent failures | |
| Introduction | p. 187 |
| General classification | p. 188 |
| Identification of dependent failures and protection from their occurrence | p. 191 |
| Definition of dependent failures | p. 192 |
| Methods for dependent-failure analysis | p. 194 |
| Examples of explicit methods | p. 194 |
| An example of an implicit method for modeling dependent failures | p. 205 |
| A methodological framework for common cause failures analysis | p. 208 |
| System logic model development | p. 208 |
| Identification of common cause component groups | p. 208 |
| Common cause failure modeling and data analysis | p. 212 |
| Importance measures | |
| Introduction | p. 235 |
| Birnbaum's measure | p. 238 |
| Relation with the system structure function | p. 239 |
| Criticality importance | p. 243 |
| Fussell-Vesely importance measure | p. 245 |
| Risk Achievement Worth and Risk Reduction Worth | p. 249 |
| Risk Achievement Worth | p. 249 |
| Risk Reduction Worth | p. 249 |
| Observations and limitations of importance measures | p. 252 |
| Generalized risk importance measure | p. 257 |
| Importance measures for multiple basic events | p. 259 |
| Risk Achievement Worth | p. 259 |
| Birnbaum importance measure | p. 261 |
| Fussell-Vesely importance | p. 262 |
| Risk Reduction Worth | p. 263 |
| Relationship of importance measures to system risk changes | p. 264 |
| The Differential Importance Measure (DIM) | p. 265 |
| Importance measures for multi-state systems | p. 277 |
| Introduction | p. 277 |
| The model of a multi-state system | p. 278 |
| Importance measures for multi-state systems | p. 279 |
| Importance measures based on limitations on the performance of multi-state components | p. 281 |
| Comparison of importance measures for multi-state systems | p. 288 |
| Basic concepts of uncertainty and sensitivity analysis | |
| Introduction | p. 295 |
| Local and global uncertainty analysis | p. 297 |
| Approximated analytical methods: the method of moments | p. 300 |
| Discrete methods | p. 302 |
| Sensitivity on the nominal range | p. 302 |
| Event and probability tree | p. 303 |
| Discrete probability method | p. 305 |
| Monte Carlo method | p. 306 |
| Linear regression method | p. 307 |
| The variance decomposition method | p. 310 |
| Sobol indexes and Fourier Amplitude Sensitivity Test | p. 323 |
| Model structure uncertainty | p. 325 |
| The alternative models approach | p. 325 |
| Adjustment factor approach | p. 326 |
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