The course is divided in two parts. In the first part, concerning statistical methods and Monte Carlo techniques, the fundamentals of probability and statistics are given, the Monte Carlo method is introduced and its possible applications to various technical fields are illustrated. The objective of this part of the course is to give the students the required knowledge to solve a technical problem with a statistical approach.
In the second part of the course, focused on risk analysis, the methodologies adopted for the improvement workers' safety and prevent/mitigate the risks associated to major accidents are presented in relations to different technological applications. Deterministic and statistical techniques adopted for risk analysis are presented and some specific information and procedures for the evaluation and management of major hazards in process plants are given (Seveso Directive).
Lectures are complemented with exercise sessions where specific problems are analysed and worked out as applications of the theoretical presentations. The students are required to carry out independent activities on the subjects of the course and to present a written report on the work done.

At the end of the course the student should:
- know the fundaments of probability and statistiscs and of the Monte Carlo method;
- be able to apply the Monte Carlo method for the solution of problems in different fields of application, including risk analysis
- be able to provide the structure of the risk analysis in the industrial field, identifiying relevant hazards, defining the expected accidental sequences, estimating their probability, and assessing, by simplified tools, the related consequences.
- be able to suggest prevention and mitigation measures to reach an acceptable risk level.

Basic concepts of mathematics, chemistry and physics as obtained in the bachelor's degree program, concepts on process plants, thermal-hydraulics and fluid dynamics.

FIRST PART - MONTE CARLO METHODS
-1- Probability and statistics
a. Concept of probability and its properties
b. Probability density functions, expected value and variance
c. Simulation of random event - sample average
d. Techebycheff inequality and Central Limit Theorem
e. Statistical laws of interest for applications in the energy engineering field
f. Properties of correlated statistical quantities
-2- The Monte Carlo method
a. Origin ad motivations
b. discrete and continuous random walk
c. Applications of the Monte Carlo method to engineering problems (e.g. radiative heat transfer, evaluation of performance of energy plants)

SECOND PART - SAFETY AND RISK ANALYSIS
-1- The Risk concept: definition, assessment and tolerability
-2- Methodologies for the safety assessment:
a. Hazard identification
b. Methodologies for the reliability assessment of complex systems,
c. Methodologies for the study of accidental sequences,
d. Risk Assessment,
-3- Major hazards:
a. EU and Italian legislation,
b. Description of accidental phenomena by simple methods (loss of containment, fires, explosions, gas dispersion),
c. Vulnerability analysis,
d. Emergency planning.

FIRST PART – MONTE CARLO METHODS
All the concepts explained during lectures are applied directly by the professor during the exercise session in class. The students are given suggestions for further individual exercises to be carried out at home.

SECOND PART - SAFETY AND RISK ANALYSIS
Students have to apply the content of the lectures to perform a safety assessment of a part of a real industrial plant. They have to prepare a report describing the analysis performed, that will be discussed during the final examination.

FIRST PART – MONTE CARLO METHODS
- G. Vicario and R. Levi, Statistica e probabilità per ingegneri, Progetto Leonardo, Bologna, 2001
- S. M. Ross, Introduction to probability and statistics for engineers and scientists, Wiley, New York, 1987
- Lux and L. Koblinger, Monte Carlo particle transport methods : neutron and photon calculations, CRC, Boca Raton, 1991.
- Lecture notes provided by the professor

SECOND PART - SAFETY AND RISK ANALYSIS
The professor provides a booklet and the set of slides used in class during lectures

FIRST PART – MONTE CARLO METHODS
The exam is at the computer (in PoliTO LAIB). The students are requested to solve some exercises, ranging from basic statistics to applications of the Monte Carlo method to simplified problems. The grade obtained by the exercise part can be modified (max +4 points, min -2 points, not compulsory) by answering to two theoretical questions provided at the end of the exercise part.

SECOND PART - SAFETY AND RISK ANALYSIS
The final exam is organised as a written text that is mandatory. In the written text students have to develop some exercises in order to demonstrate their ability in applying theory and solve practical problems related to safety and risk assessment. The maximum grade that can be obtained in the written test is 27/30.
Student can ask, at the beginning of the course, to enroll for the Project Work, a practical application of Risk Analysis to a portion of a real plant. The Project Work must be made in team working with other 2 or 3 students. Project work will be discussed by an oral exam, planned when the written test has been already passed. The oral discussion of the Project Work can add maximum 3/30 marks.

FINAL MARK
The final mark of the exam is evaluated as the average of the marks obtained in the two parts of the exam, i.e. Monte Carlo Methods and Safety and Risk Analysis, rounded to the upper integer.