Risk modelling and quantification
The probabilistic approach to safety

Overview

Rather than using point values to represent random quantities, as in deterministic approaches, probabilistic approaches to risk assessment represent each random quantity by a probability distribution. Analysis results are presented as probability distributions, or as selected quantiles of a probability distribution.

The probabilistic approach to risk analysis estimates risk as a function of:

• the severity — or magnitude — of each consequence
• the likelihood (probability) of the occurrence of each consequence

In the safety domain, the consequences and types of events assessed are generally adverse (they represent losses, that we try to avoid). In other areas such as finance, events and their consequences may be either positive (profits) or negative (losses).

Consequences are expressed quantatively (for instance, the number of people potentially injured) and their likelihoods of occurrence are expressed as probabilities.

Course material

• Modelling correlations with Python and NumPy

• Linear regression analysis with Python

• Statistical modelling with Python

• Reliability engineering

• Reliability analysis, including reliability data

• Monte Carlo methods for risk analysis

• Copula methods for multivariate modelling

• Value at Risk: measuring financial risk

• Case study: height of a dike

Other resources

We recommend the following sources of further information on this topic:

• MIT OpenCourseWare materials on probability and its applications to reliability, quality control and risk assessment

• Slides which supplement the book Risk Assessment — Theory, Methods and Applications

• The ReliaWiki, a wiki on reliability engineering

• Briefing notes on control of risk in health and safety, by the Institution of Engineering and Technology (IET)