PORTALE DELLA DIDATTICA

Monte Carlo methods, safety and risk analysis

02OKEND, 02OKEMW

A.A. 2020/21

2020/21

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

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. 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). 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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

GENERAL INTRODUCTION – PARTS A AND B 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; also, some specific information and procedures for the evaluation and management of major hazards in energy (e.g., nuclear) and, in general, industrial plants are given. PART A - MONTE CARLO METHODS The Monte Carlo method is a statistical sampling approach to the solution of complex problems, allowing to avoind all the steps of discretization/approximation typically associated to the deterministic solution of a physico-mathematical model and relating directly to the underlying statistical processes. Classic applications of the Monte Carlo method pertain to the nuclear engineering field (e.g. neutron and radiation transport simulation), and the whole risk analysis field heavily relies on the statistical treatment of the processes involved. This course aims at providing the basic information of statitistical analysis useful to the understanding of how the Monte Carlo method works, allowing the students to become proficient in developing code for the statistical simulation of phenomena, as well as in correcly interpreting the results of Monte Carlo calculations. Lectures are complemented with exercise sessions where specific problems are analysed and worked out as applications of the theoretical presentations. The programming language MATLAB is used to develop codes for the solution of engineering-relevant problems with the Monte Carlo approach.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

GENERAL INTRODUCTION – PARTS A AND B 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; also, some specific information and procedures for the evaluation and management of major hazards in energy (e.g., nuclear) and, in general, industrial plants are given. PART B – SAFETY AND RISK ANALYSIS Energy (e.g., nuclear) and, in general, industrial systems and plants are potentially subject to accidents, due to malfunctioning and failures of components, but also to catastrophic external events related to the surrounding environment. The evaluation and management of the associated risk require a systematic and systemic approach to the identification of the hazards and to the assessment of the probabilities/frequencies and consequences of the accident scenarios that can have a severe impact on the systems, the plants, the workers, the environment and the population. The objective of this course is to provide the students with competences on: (i) techniques for hazard identification; (ii) methodologies for safety (resp., risk) evaluation and analysis; (iii) methods for the control and reduction of the risks associated to the operation of energy (e.g., nuclear) and, in general, industrial systems and plants (preventive and mitigative actions). These multidisciplinary and transversal competences, typical of safety and reliability analysts and managers, are necessary in every field of modern engineering for the design and operation of safe and reliable systems.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

At the end of the course (part B) the student should: - 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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

PART A – MONTE CARLO METHODS 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 and neutral particle transport

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

PART B - SAFETY AND RISK ANALYSIS At the end of the course the students should know: ELO 1 – the (qualitative and quantitative) concepts and definitions of hazard, safety, risk, prevention and mitigation. ELO 2 – the main contents of the legislation about safety and risk of energy and industrial plants. ELO 3 – the systemic and systematic formulation of the safety and risk analysis process. ELO 4 – basic notions on the (qualitative and semi-quantitative) methods for hazard and scenario identification. ELO 5 – the quantitative approach to safety and risk analysis, and the related (analytical and stochastic simulation-based) evaluation techniques. ELO 6 – basic notions on the methodological tools to treat the uncertainty in the reliability and risk assessments and to build confidence in the corresponding results. At the end of the course the students should be able to: ELO 7 – develop and apply the (qualitative and quantitative, analytical, and stochastic simulation-based) methods for the safety and risk analysis of energy and industrial systems and plants. ELO 8 – critically evaluate the results obtained by the application of the methods learned, also in relation to the uncertainty and confidence, with which they can be used to take robust decisions about preventive, protective, mitigative and reactive measures. ELO 9 – communicate the results of their own activity in a technically sound way.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

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

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

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

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

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

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

PART B – SAFETY AND RISK ANALYSIS Fundamentals of mathematics, applied thermodynamics and physics; concepts on process plants, thermal-hydraulics and fluid dynamics.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

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: neutron propagation and criticality problems, radiative heat transfer, evaluation of energy plants performance, evaluation of integrals, ... d. Introduction to the Monte Carlo neutron transport code Serpent

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

PART B – SAFETY AND RISK ANALYSIS 1. Introduction and description of the contents of the course: general overview of the safety and risk analysis topics offered and importance of the related transversal and multidisciplinary competences within the Master Degree in Energy and Nuclear Engineering. 2. Concepts of hazard, safety, risk (and risk tolerability), prevention and mitigation: qualitative and quantitative definitions. 3. Introduction (basics) on the Italian and European legislation on safety and risk in the design and operation of energy plants [safety of workers, safety of components, machines and systems, safety of plants subject to major accidents (e.g., nuclear plants, refineries, chemical plants, oil&gas installations)]. 4. Quantitative Risk Assessment (QRA) framework: a) Comparison between deterministic and probabilistic approaches: respective strengths and weaknesses. b) Basic notions on the qualitative (and/or semi-quantitative) methods for the identification of hazards in the safety (resp., risk) analysis of energy (e.g., nuclear) and, in general, industrial systems and plants: (i) Failure Mode Effect and Criticality Analysis (FMECA) method (for the identification of system failure modes and the corresponding criticality and maintainability analyses); (ii) HAZard and OPerability analysis (HAZOP) method (for the identification of process anomalies). c) Details on the quantitative techniques adopted in the safety (resp., risk) analysis of energy (e.g., nuclear) and, in general, industrial systems and plants: (i) Event Trees, for the identification of the possible accidental sequences (scenarios); (ii) Fault Trees and Reliability Block Diagrams, for the quantification of the probabilities/frequencies of the accidental sequences (scenarios); (iii) Common Cause Failure analysis, for the treatment of dependent failures between components. d) Risk matrices and curves, for a qualitative and quantitative ranking of the criticality of the hazards and scenarios identified. e) Risk analysis as a tool in support of regulatory licensing and operating requirements. 5. Quantitative (both analytical and stochastic, simulation-based) methodologies for the (time-dependent) reliability and availability analysis of equipment and components employed in energy (e.g., nuclear) and, in general, industrial systems and plants: a) Definitions of (time-dependent) system reliability and availability. b) Statistical methods for the estimation of reliability and availability parameters from field data (and the related confidence). c) Analysis and mathematical modeling of realistic procedures like inspection, maintenance, repair, renewal. d) Monte Carlo Simulation strategies (see also Part A of the Course) applied to the estimation of (time-dependent) system reliability and availability indicators. 6. Importance measures for the assessment of the criticality of industrial (energy) equipment and components. 7. The problem of uncertainty and its analysis: basic notions on the methodological tools to treat uncertainty in the reliability and risk assessments of industrial (energy) systems and to build confidence in the corresponding results. 8. Case studies: lectures will be complemented by examples concerning the safety and risk analyses of energy components, systems and plants exposed to hazards, as well as by quantitative exercise sessions developed by the teachers and/or by the students themselves (on paper or using laptops).

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

PART B - SAFETY AND RISK ANALYSIS The course is structured in lectures and and practical sessions to make exercises. In order to complete their preparation, students can 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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

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. Exercise session at the computer are also envisaged, with the use of the programming language MATLAB.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

PART B – SAFETY AND RISK ANALYSIS Lectures by the teachers will be complemented by examples concerning the safety and risk analyses of energy and industrial components, systems and plants exposed to hazards, as well as by quantitative exercise sessions carried out by the teachers and/or by the students themselves (on paper or using laptops).

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

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

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

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

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

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 - L. Lux and L. Koblinger, Monte Carlo particle transport methods : neutron and photon calculations, CRC, Boca Raton, 1991. - J. Spanier and E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems, Dover, 2008 - Lecture notes provided by the professor

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

PART B – SAFETY AND RISK ANALYSIS MANDATORY MATERIAL - Booklets and slides provided by the teachers. OPTIONAL MATERIAL Safety and Risk analysis (general): - E. Zio, “Introduction to the basics of reliability and risk analysis”, Editore: World scientific, Anno edizione: 2007. - E. Zio, “Computational methods for reliability and risk analysis”, Editore: World scientific, Anno edizione: 2009. - P. Baraldi, F. Cadini, E. Zio, “Introduction to reliability and risk analysis: worked out problems”, Editore: World Scientific, Anno edizione: 2011. - W. Kroger, E. Zio, “Vulnerable Systems”, Editore: World Scientific, Anno edizione: 2011. - T. Aven, P. Baraldi, R. Flage and E. Zio, “Uncertainty in risk assessment”, Editore: Wiley, Anno edizione: 2014. - A.K. Jardine, H.C. Tsang, A. Tsang, “Maintenance, Replacement, and Reliability: Theory and Applications”, Editore: CRC Press, Anno edizione: 2005. - European Safety and Reliability Association, “Maintenance Modeling and Applications”, Editore: ESRA, Anno edizione: 2010. Safety and Risk analysis (“nuclear”-oriented): - M. Modarres, I. S. Kim, “Deterministic and Probabilistic Safety Analysis - Handbook of Nuclear Engineering”, Editore: Springer, Anno edizione: 2010. - IAEA-TECDOC-1200, “Applications of probabilistic safety assessment (PSA) for nuclear power plants”, Anno edizione: 2001. - ASME, “Operation and Maintenance of Nuclear Power Plants”, Editore: ASME book, Anno edizione: 2009.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

Modalità di esame: Prova scritta tramite PC con l'utilizzo della piattaforma di ateneo; Prova scritta tramite l'utilizzo di vLAIB e piattaforma di ateneo;

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

Modalità di esame: Prova orale obbligatoria; Prova scritta su carta con videosorveglianza dei docenti;

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

PART A – MONTE CARLO METHODS The exam aims at verifying the competence of the students on both basics statistics and on the application of the Monte Carlo Method. Therefore, the students are requested to solve some exercises, ranging from basic statistics to applications of the Monte Carlo method to simplified problems by developing small MATLAB programs. The grade obtained by the exercise part can be modified (max +3 points, min -2 points, not compulsory) by answering to a theoretical question provided in the online quiz together with the exercises. The total duration of the test is 2.5 hours. Students are not allowed to use any material (books, notes, ...) during 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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

The exam is carried out separately for the two parts of the course (A+B) and a grade >=18 is to be obtained on both parts. For Part B, the evaluation consists in a written and oral exam. The written test includes both numerical exercises and theoretical questions on all the macro-topics treated (items 2-8 of the Contents section). The exercises are mainly aimed at evaluating the student’s capability of applying the qualitative and quantitative methods for the safety and risk assessment of energy equipment and plants (ELO 7). The theoretical questions will allow verifying the student’s comprehension of the concepts of safety, risk, prevention and mitigation, his/her knowledge of the main legislation related to safety, of the qualitative methods of hazard and scenario identification and characterization, of the fundamentals of the systemic and quantitative approaches to the evaluation of safety and risk of energy plants (ELO 1-6). This part will allow verifying acquired (conceptual, theoretical, and possibly “foundational”) knowledge that cannot be evaluated by numerical exercises. The duration of the written exam is 2h (max). The use of any learning resource (books, handouts, etc.) is not allowed. This part of the exam will contribute 65% of the final score. The oral exam will mainly assess the student’s capability of autonomously and critically formulating, in a clear and convincing way, judgments about the confidence and uncertainty in the results of a safety and risk analysis (ELO 8, 9). This part of the exam will contribute 35% of the final score. The minimum score that allows passing the exam is 18/30. Maximum score is 30/30 cum laude. The final grade of the exam (A+B) is evaluated as the average of the grades 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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

Exam: Computer-based written test using the PoliTo platform; Written test via vLAIB using the PoliTo platform;

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

Exam: Compulsory oral exam; Paper-based written test with video surveillance of the teaching staff;

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

The exam is carried out separately for the two parts of the course and a grade >=18 is to be obtained on both parts. PART A – MONTE CARLO METHODS The exam aims at verifying the competence of the students on both basics statistics and on the application of the Monte Carlo Method. Therefore, the students are requested to solve some exercises, ranging from basic statistics to applications of the Monte Carlo method to simplified problems by developing small MATLAB programs. The grade obtained by the exercise part can be modified (max +3 points, min -2 points, not compulsory) by answering to a theoretical question provided in the online quiz together with the exercises. The total duration of the test is 2.5 hours. Students are not allowed to use any material (books, notes, ...) during the final exam. FINAL GRADE The final grade of the exam is evaluated as the average of the grades 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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

For Part A + B: The exam is carried out separately for the two parts of the course (A+B) and a grade >=18 is to be obtained on both parts. For Part B, the evaluation consists in a written and oral exam. The written test includes both numerical exercises and theoretical questions on all the macro-topics treated (items 2-8 of the Contents section). The exercises are mainly aimed at evaluating the student’s capability of applying the qualitative and quantitative methods for the safety and risk assessment of energy equipment and plants (ELO 7) (in particular, Event Trees, Fault Trees, Common Cause Failures, Reliability Block Diagrams, time-dependent reliability and availability analyses, importance measures). The theoretical questions will allow verifying the student’s comprehension of the concepts of safety, risk, prevention and mitigation, his/her knowledge of the main legislation related to safety, of the qualitative methods of hazard and scenario identification and characterization, of the fundamentals of the systemic and quantitative approaches to the evaluation of safety and risk of energy plants (ELO 1-6). This part will allow verifying acquired (conceptual, theoretical, and possibly “foundational”) knowledge that cannot be evaluated by numerical exercises. The theoretical questions can be of different nature: (brief) open questions (e.g., definitions of relevant concepts), or true/false or multiple-choice. The duration of the written exam is 2h (max). The use of any learning resource (books, handouts, etc.) is not allowed. This part of the exam will contribute 65% of the final score. The oral exam will mainly assess the student’s capability of autonomously and critically formulating, in a clear and convincing way, judgments about the confidence and uncertainty in the results of a safety and risk analysis (ELO 8, 9). This part of the exam will contribute 35% of the final score. The minimum score that allows passing the exam is 18/30. Maximum score is 30/30 cum laude. The final grade of the exam (A+B) is evaluated as the average of the grades 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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

Modalità di esame: Prova scritta (in aula); Prova scritta tramite PC con l'utilizzo della piattaforma di ateneo; Prova scritta tramite l'utilizzo di vLAIB e piattaforma di ateneo;

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

Modalità di esame: Prova scritta (in aula); Prova orale obbligatoria; Prova scritta su carta con videosorveglianza dei docenti;

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

PART A – MONTE CARLO METHODS The exam aims at verifying the competence of the students on both basics statistics and on the application of the Monte Carlo Method. Therefore, the students are requested to solve some exercises, ranging from basic statistics to applications of the Monte Carlo method to simplified problems by developing small MATLAB programs (the exam is carried out in the PoliTO LAIB when in person, using the vLAIB when in remote). The grade obtained by the exercise part can be modified (max +3 points, min -2 points, not compulsory) by answering to a theoretical question provided in the online quiz together with the exercises. The total duration of the test is 2.5 hours. Students are not allowed to use any material (books, notes, ...) during the final exam.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

The exam is carried out separately for the two parts of the course (A+B) and a grade >=18 is to be obtained on both parts. For Part B, the evaluation consists in a written and oral exam. The written test includes both numerical exercises and theoretical questions on all the macro-topics treated (items 2-8 of the Contents section). The exercises are mainly aimed at evaluating the student’s capability of applying the qualitative and quantitative methods for the safety and risk assessment of energy equipment and plants (ELO 7). The theoretical questions will allow verifying the student’s comprehension of the concepts of safety, risk, prevention and mitigation, his/her knowledge of the main legislation related to safety, of the qualitative methods of hazard and scenario identification and characterization, of the fundamentals of the systemic and quantitative approaches to the evaluation of safety and risk of energy plants (ELO 1-6). This part will allow verifying acquired (conceptual, theoretical, and possibly “foundational”) knowledge that cannot be evaluated by numerical exercises. The duration of the written exam is 2h (max). The use of any learning resource (books, handouts, etc.) is not allowed. This part of the exam will contribute 65% of the final score. The oral exam will mainly assess the student’s capability of autonomously and critically formulating, in a clear and convincing way, judgments about the confidence and uncertainty in the results of a safety and risk analysis (ELO 8, 9). This part of the exam will contribute 35% of the final score. The minimum score that allows passing the exam is 18/30. Maximum score is 30/30 cum laude. The final grade of the exam (A+B) is evaluated as the average of the grades 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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

Exam: Written test; Computer-based written test using the PoliTo platform; Written test via vLAIB using the PoliTo platform;

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

Exam: Written test; Compulsory oral exam; Paper-based written test with video surveillance of the teaching staff;

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis A)

The exam is carried out separately for the two parts of the course and a grade >=18 is to be obtained on both parts. PART A – MONTE CARLO METHODS The exam aims at verifying the competence of the students on both basics statistics and on the application of the Monte Carlo Method. Therefore, the students are requested to solve some exercises, ranging from basic statistics to applications of the Monte Carlo method to simplified problems by developing small MATLAB programs (the exam is carried out in the PoliTO LAIB when in person, using the vLAIB when in remote). The grade obtained by the exercise part can be modified (max +3 points, min -2 points, not compulsory) by answering to a theoretical question provided in the online quiz together with the exercises. The total duration of the test is 2.5 hours. Students are not allowed to use any material (books, notes, ...) during the final exam. FINAL GRADE The final grade of the exam is evaluated as the average of the grades 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.

Monte Carlo methods, safety and risk analysis (Monte Carlo methods, safety and risk analysis B)

For Part A + B: The exam is carried out separately for the two parts of the course (A+B) and a grade >=18 is to be obtained on both parts. For Part B, the evaluation consists in a written and oral exam. The written test includes both numerical exercises and theoretical questions on all the macro-topics treated (items 2-8 of the Contents section). The exercises are mainly aimed at evaluating the student’s capability of applying the qualitative and quantitative methods for the safety and risk assessment of energy equipment and plants (ELO 7) (in particular, Event Trees, Fault Trees, Common Cause Failures, Reliability Block Diagrams, time-dependent reliability and availability analyses, importance measures). The theoretical questions will allow verifying the student’s comprehension of the concepts of safety, risk, prevention and mitigation, his/her knowledge of the main legislation related to safety, of the qualitative methods of hazard and scenario identification and characterization, of the fundamentals of the systemic and quantitative approaches to the evaluation of safety and risk of energy plants (ELO 1-6). This part will allow verifying acquired (conceptual, theoretical, and possibly “foundational”) knowledge that cannot be evaluated by numerical exercises. The theoretical questions can be of different nature: (brief) open questions (e.g., definitions of relevant concepts), or true/false or multiple-choice. The duration of the written exam is 2h (max). The use of any learning resource (books, handouts, etc.) is not allowed. This part of the exam will contribute 65% of the final score. The oral exam will mainly assess the student’s capability of autonomously and critically formulating, in a clear and convincing way, judgments about the confidence and uncertainty in the results of a safety and risk analysis (ELO 8, 9). This part of the exam will contribute 35% of the final score. The minimum score that allows passing the exam is 18/30. Maximum score is 30/30 cum laude. The final grade of the exam (A+B) is evaluated as the average of the grades 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.