Chapter 1

Probability and Statistics Foundations

Random variables, probability density and distribution functions

medium • 1 min read

Common distributions (Normal, Lognormal, Gumbel, Weibull)

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Jointly distributed random variables and correlation

medium • 3 min read

Extreme value distributions

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Statistical inference and parameter estimation

medium • 5 min read

Chapter 2

Concepts of Structural Reliability

Deterministic versus probabilistic design approaches

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Limit state functions (safety margin)

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Basic reliability problem (interference theory)

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Reliability index (Cornell and Hasofer-Lind reliability indices)

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Evaluation of probability of failure

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Chapter 3

Reliability Methods

First-Order Second-Moment (FOSM) method

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First-Order Reliability Method (FORM)

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Second-Order Reliability Method (SORM)

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Monte Carlo Simulation techniques

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Variance reduction techniques (Importance sampling)

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Chapter 4

System Reliability

Series systems (weakest link) and parallel systems

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Redundancy and failure pathways

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Bounds on system reliability (Ditlevsen bounds)

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Fault tree and event tree analysis

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Reliability of structures with multiple failure modes

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Chapter 5

Reliability-Based Design Codes

Development of partial safety factors

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Target reliability index selection

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Calibration of design codes to target reliability

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Load and Resistance Factor Design (LRFD) format

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Life-cycle cost and reliability-based optimization

medium • 5 min read