The course is divided in two parts. In the first part (A), 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 (B), 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). For both parts, lectures are complemented with exercise sessions where specific problems are analysed and worked out as applications of the theoretical presentations. For part (B), 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, by correctly identifying the statistical phenomena involved, carry our the random sampling and perform the corresponding statistical analysis to evaluate averages and uncertainties - apply the Monte Carlo approach to problems involving statistical phenomena 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.

PART A - 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. Tchebycheff 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. sampling methodologies c. simulation of discrete and continuous random walks c. Applications of the Monte Carlo method to engineering problems: radiative heat transfer, evaluation of energy plants performance, evaluation of integrals, ... PART B - 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.

PART A – 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.

PART A – 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

Modalità di esame: Test informatizzato in laboratorio; Prova scritta (in aula);

Exam: Computer lab-based test; Written test;

... PART A – 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 (duration: 2 hours). 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 (duration: 30 minutes). Students are not allowed to bring any material (books, notes, ...) to the final exam. 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 (part A) and Safety and Risk Analysis (part B), rounded to the upper integer.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.