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Risk analysis

Block name: Risk analysis
Language of instruction: Polish/English
Teaching methods/load: Lecture (30h / semester), exercises (30h / semester)
Teacher responsible: Marcin M. Smolarkiewicz, PhD

Knowledge of ordinary, linear, linear first-order differential equation. Knowledge of elementary integrals, knowledge of exponential function, knowledge of simple statistical distributions. Knowledge of using computer spreadsheets

Description of learning outcomes
Obtaining knowledge and skills in the area of: understanding selected methods of identification, evaluation and prioritisation of risk based on probability equation and mathematical statistics, additionally acquiring skills in designing and solving simple models of hazard spread resulting from unfavourable events.


  • Unfavourable event. Event space. Events set. Boolean algebra. Set operations. Empty set. Opposite set. Common part of sets. Defining a probability function on sets. De Morgan's laws. Probability axioms. Probability properties. Empty set probability. Probability of independent events and opposite events.
  • Introduction into combinatorics: permutation, combinations, n-tuples and k-permutations.
  • Selected probability distributions. Properties of density probability function. Properties of two-point distribution, properties of Poisson distribution, gamma beta distribution and normal distribution. Expected value, standard bias, ordinary and central moment, median, and quintile. Properties of distribution function. Designing risk profiles. Entropy properties. Stochastic processes.
  • Combustion processes. Fire parameters. Hazards occurring during an internal fire. The principle of retaining mass and energy. Equations describing both principles. Equations of mass flow. Gas exchange in a fire. Mass balance in water flows. Differential equations of flood surface change. Atmospheric properties and phenomena creating hazards. Dispersal of toxic clouds in the atmosphere. Three ways of heat transport. Defining critical parameters. Models of PF, FF, BLEVE, FB creations.
  • Risk definition. Risk - blurred term. Individual risk. Group risk. Qualitative definition of risk. Half-quantitative definition of risk. Quantitative definition of risk. Links of uncertainty, probability and frequency in risk calculation. Methods of risk determination: risk matrix (probability - consequence). APELL method. Basics of ARAMIS method. Initiating event. Critical event. Triplet of Kaplan - Gavrick. Logical gates (and; or). Constructing event scenarios. Fault tree, event tree. The method of connected trees. Expert methods in defining risk. Risk zones and profiles. Risk transfers. Accidents at a workplace. Elements of reliability theory of technical safety.
  • Risk and social unrest. Structural risk. Susceptibility, sensitivity, resistance. Risk in human's life. Introduction to prospect theory. Elements of games theory (extensive form - sorrow matrix). The notion of psychic availability. Aversion to risk. Risk analysis in the process of decision-making.

Pliki do pobrania

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