Computational Methods for Reliability and Risk Analysis

by Zio, Enrico

• ISBN13: 9789812839015
• ISBN10: 9812839011
• Format: Hardcover
• Copyright: 2009-01-22
• Publisher: World Scientific Pub Co Inc

Summary

This book illustrates a number of modelling and computational techniques for addressing relevant issues in reliability and risk analysis. In particular it provides: i) a basic illustration of some methods used in reliability and risk analysis for modelling the stochastic failure and repair behaviour of systems, e.g. the Markov and Monte Carlo simulation methods: ii) an introduction to Genetic Algorithms, tailored to their application for RAMS (Reliability Availability, Maintainability and Safety) optimization; iii) an introduction to key issues of system reliability and risk analysis, like dependent failures and importance measures; and iv) a presentation of the issue of uncertainty and of the techniques of sensitivity and uncertainty analysis used in support of reliability and risk analysis.

Table of Contents

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
Table of Contents provided by Ingram. All Rights Reserved.