(1) Review of Probability
Probability density functions, expectations, moment correlation and rank correlation, dependency, Law of Large Number, Central Limit Theorem, quantiles, Q-Q plot and quantile function, information entropy
(2) Characterization of geotechnical uncertainties
Inherent and spatial variability, measurement and transformation errors
Estimating PDF from data
Estimating random properties from spatial data
Simulation of geotechnical variabilities
(3) Reliability analysis
First-Order Second-Moment (FOSM)
First-Order Reliability Methods (FORM)
Moment and quantile function methods
Monte Carlo simulation and importance sampling
Subset simulation
Response surface methods
(4) Reliability-based design
First-Order Second-Moment (FOSM)
Partial factors and Load and Resistance Factor Design (LRFD)
Limit-state factor design
Calibration of factors
(5) System reliability
Systems with multiple failure modes
Slope reliability