Computational methods for reliability and risk analysis

Foreword	p. vii
1 Markov reliability and availability analysis	p. vii
1.1 Introduction	p. 1
1.2 Discrete-time, discrete-state Markov processes	p. 2
1.2.1 The conceptual model	p. 2
1.2.2 State probabilities	p. 5
1.2.3 Multi-step transition probabilities	p. 7
1.2.4 Solution of the fundamental equation	p. 9
1.2.5 Steady state probabilities for ergodic systems	p. 19
1.2.6 First passage probabilities	p. 20
1.3 Continuous time, discrete-state Markov processes	p. 24
1.3.1 The conceptual model	p. 24
1.3.2 Solution of the fundamental equation	p. 30
1.3.3 Failure intensity	p. 34
1.3.4 Average time of occupancy of a given state	p. 36
1.3.5 System availability	p. 37
1.3.6 System reliability	p. 38
2 Monte Carlo simulations for reliability and availability analysis
2.1 Introduction	p. 59
2.2 Monte Carlo simulation for system engineering	p. 60
2.3 Monte Carlo simulation for system unreliability and unavailability estimation
2.3.1 Indirect and direct Monte Carlo simulation	p. 66
3 Markov Chain Monte Carlo for applications to reliability and availability analysis
3.1 Introduction	p. 71
3.2 The Metropolis-Hastings algorithm	p. 73
3.2.1 Application to the estimation of the failure rate of a deteriorating component	p. 74
3.3 The Gibbs sampler	p. 78
3.3.1 Application to the estimation of a rare failures process	p. 80
3.4 The reversible-jump MCMC algorithm	p. 83
3.4.1 Application to the estimation of the failure rate of a component subject to degradation or improvement	p. 88
3.4.2 Application to the estimation of the parameters of a deterioration process due to fatigue	p. 95
3.5 Bayesian updating	p. 103
3.6 Practical issues in implementing MCMC algorithms	p. 108
3.6.1 Choice of the kinetics K(.\|.)	p. 108
3.6.2 Burn-in period	p. 109
3.6.3 Number of iterations	p. 109
3.6.4 Initial conditions	p. 110
3.6.5 Other algorithms	p. 110
4 Basics of genetic algorithms with application to system reliability and availability optimization
4.1 Introduction	p. 115
4.2 Genetic Algorithms at a glance	p. 117
4.3 The standard Genetic Algorithm	p. 121
4.4 Affine transforming the chromosome fitness	p. 124
4.5 More sophisticated breeding procedures	p. 131
4.6 Efficiency of breeding procedures	p. 134
4.6.1 The figures of merit	p. 134
4.6.2 The test functions	p. 138
4.6.3 Results	p. 144
4.7 Inducement of species and niches	p. 151
4.7.1 Isolation by distance	p. 151
4.7.2 Spatial mating	p. 152
4.7.3 Sharing	p. 153
4.8 Multi-objective optimization	p. 155
4.9 Application of genetic algorithms to RAMS	p. 158
4.10 Examples	p. 163
4.10.1 Multi-objective optimization of system design: a simple application	p. 163
4.10.2 Multi-objective optimization of the inspection policy of a nuclear safety system	p. 169
4.11 Discussion	p. 180
5 Dependent failures
5.1 Introduction	p. 187
5.2 General classification	p. 188
5.3 Identification of dependent failures and protection from their occurrence	p. 191
5.4 Definition of dependent failures	p. 192
5.5 Methods for dependent-failure analysis	p. 194
5.5.1 Examples of explicit methods	p. 194
5.5.2 An example of an implicit method for modeling dependent failures	p. 205
5.6 A methodological framework for common cause failures analysis	p. 208
5.6.1 System logic model development	p. 208
5.6.2 Identification of common cause component groups	p. 208
5.6.3 Common cause failure modeling and data analysis	p. 212
6 Importance measures
6.1 Introduction	p. 235
6.2 Birnbaum's measure	p. 238
6.2.1 Relation with the system structure function	p. 239
6.3 Criticality importance	p. 243
6.4 Fussell-Vesely importance measure	p. 245
6.5 Risk Achievement Worth and Risk Reduction Worth	p. 249
6.5.1 Risk Achievement Worth	p. 249
6.5.2 Risk Reduction Worth	p. 249
6.6 Observations and limitations of importance measures	p. 252
6.7 Generalized risk importance measure	p. 257
6.8 Importance measures for multiple basic events	p. 259
6.8.1 Risk Achievement Worth	p. 259
6.8.2 Birnbaum importance measure	p. 261
6.8.3 Fussell-Vesely importance	p. 262
6.8.4 Risk Reduction Worth	p. 263
6.9 Relationship of importance measures to system risk changes	p. 264
6.10 The Differential Importance Measure (DIM)	p. 265
6.11 Importance measures for multi-state systems	p. 277
6.11.1 Introduction	p. 277
6.11.2 The model of a multi-state system	p. 278
6.11.3 Importance measures for multi-state systems	p. 279
6.11.4 Importance measures based on limitations on the performance of multi-state components	p. 281
6.11.5 Comparison of importance measures for multi-state systems	p. 288
7 Basic concepts of uncertainty and sensitivity analysis
7.1 Introduction	p. 295
7.2 Local and global uncertainty analysis	p. 297
7.3 Approximated analytical methods: the method of moments	p. 300
7.4 Discrete methods	p. 302
7.4.1 Sensitivity on the nominal range	p. 302
7.4.2 Event and probability tree	p. 303
7.4.3 Discrete probability method	p. 305
7.5 Monte Carlo method	p. 306
7.6 Linear regression method	p. 307
7.7 The variance decomposition method	p. 310
7.8 Sobol indexes and Fourier Amplitude Sensitivity Test	p. 323
7.9 Model structure uncertainty	p. 325
7.9.1 The alternative models approach	p. 325
7.9.2 Adjustment factor approach	p. 326

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