Structural Reliability and Time-Dependent Reliability

Preface
Contents
1 Introduction
	1.1 Performance Requirement of Engineering Structures
	1.2 Measure of Uncertainty
	1.3 Structural Reliability Assessment
	1.4 Overview of This Book
	References
2 Probability Models
	2.1 Probability Theory and Random Variables
		2.1.1 Probability Space
		2.1.2 Conditional Probability
		2.1.3 Random Variable
		2.1.4 Mean and Variance of Random Variables
		2.1.5 Independent Random Variables
		2.1.6 Moment Generating Function and Characteristic Function
	2.2 Selected Probability Distribution Types
		2.2.1 Bernoulli, Binomial and Geometric Distributions
		2.2.2 Uniform Distribution
		2.2.3 Poisson and Exponential Distributions
		2.2.4 Normal Distribution
		2.2.5 Lognormal Distribution
		2.2.6 Rayleigh Distribution
		2.2.7 Gamma and Beta Distributions
		2.2.8 Extreme Value Distributions
	2.3 Joint Probabilistic Behaviour of Random Variables
		2.3.1 Joint Distribution of Dependent Variables
		2.3.2 Conditional Distribution
		2.3.3 Constructing Joint CDF with Copula Function
	References
3 Monte Carlo Simulation
	3.1 Introduction
	3.2 Simulation of a Single Random Variable
		3.2.1 Inverse Transformation Method
		3.2.2 Composition Method
		3.2.3 Acceptance-Rejection Method
	3.3 Simulation of Correlated Random Variables
	3.4 Simulation of Some Special Stochastic Processes
		3.4.1 Poisson Process
		3.4.2 Renewal Process
		3.4.3 Gamma Process
		3.4.4 Markov Process
	3.5 Simulation Techniques
		3.5.1 Naïve Monte Carlo Simulation
		3.5.2 Importance Sampling
		3.5.3 Latin Hypercube Sampling
		3.5.4 Subset Simulation
	References
4 Structural Reliability Assessment
	4.1 Reliability and Reliability Index
	4.2 Computation of Structural Reliability
		4.2.1 First-Order Second-Moment Reliability Method
		4.2.2 First-Order Reliability Method
		4.2.3 Simulation-Based Reliability Assessment
		4.2.4 Moment-Based Reliability Assessment
	4.3 System Reliability
		4.3.1 Series System
		4.3.2 Parallel System
		4.3.3 k-Out-of-n System
	4.4 Reliability-Based Design and Safety Check
		4.4.1 Modelling Structural Resistance
		4.4.2 Modelling Spatially Distributed Loads
		4.4.3 Load Combination
		4.4.4 Reliability Calibration of Existing Design Criteria
		4.4.5 Reliability-Based Limit State Design
		4.4.6 Cost Analysis-Based Design Optimization
	4.5 Reliability Assessment with Imprecise Information
		4.5.1 Probability-Box
		4.5.2 Interval Monte Carlo Simulation
		4.5.3 Linear Programming-Based Approach
	References
5 Time-Dependent Reliability Assessment
	5.1 Why Time-Dependent Reliability?
	5.2 Resistance Deterioration Process
	5.3 Stochastic Load Process
		5.3.1 Discrete Load Process
		5.3.2 Continuous Load Process
	5.4 Time-Dependent Reliability Considering a Discrete Load Process
		5.4.1 Formulation of Time-Dependent Reliability for Some Simple Cases
		5.4.2 Hazard Function and Time-Dependent Reliability
		5.4.3 Simplified Approach for Time-Dependent Reliability Assessment
		5.4.4 Updating Structural Reliability with Prior Information
		5.4.5 Synthetic Approach for Time-Dependent Reliability Assessment
	5.5 Time-Dependent Reliability Considering a Continuous Load Process
		5.5.1 Reliability Assessment with a Continuous Load Process
		5.5.2 PSDF of the Load Process
		5.5.3 Comparison Between Reliabilities with Discrete and Continuous Load Processes
	References
Index