- Review of basic principles in probability theory and statistics: Quantification of uncertainty and risk in Civil Engineering (descriptive statistics).
- Events and their properties, independence, total probability theorem, conditional probability theorem, Bayes’ theorem.
- Random variables and their probability distribution functions. Mean value, variance, higher order moments. Important distribution models (Bernoulli, Poisson, uniform, exponential, gamma, normal, lognormal). Censored and truncated observations, hazard and reliability functions, mean residual lifetime. Functions of random variables.
- Random vectors and their probability distribution functions. Propagation of uncertainty. Functions of random vectors: min/max functions, sums of variables.
- Second moment (SM) characterization of random variables and vectors, covariance and autocorrelation functions, first order second moment (FOSM) propagation of uncertainty for random variables and vectors, conditional second moment (CSM) analysis for random variables and vectors. Multivariate normal distribution.
- Introduction to system reliability: Reliability index and its calculation based on second moment properties of random vectors.
- Estimation of distribution parameters: General principles, method of least squares, method of moments, maximum likelihood estimation.
- Simple and multiple linear regression.
- Application of the developed concepts and methods in Civil Engineering.
Risk and Reliability Analysis
The postgraduate student familiarizes with the use tools from probability theory, to model risk and analyze the reliability of natural and engineered systems, for the design of Civil Engineering projects under conditions of uncertainty.