1. RISK ANALYSIS & MANAGEMENT Budapest University of Technology and Economics Prof. Janos LEVENDOVSZKY, Attila CEFFER levendov@hit.bme.hu

2. Outline Administrative course information The basic concept of risk analysis and management Fundamental challenges Course objectives

3. Course Information I – classes & readings Lectures – Monday 12-14 (IB 110) Lab practices – Monday 14-16 (IL 108, Attila Ceffer, ceffer@hit.bme.hu) Suggested literarture: Wose: Risk Analysis: A Quantitative Guide, 2nd edition. Wiley, 2000., Lecture notes and materials on the website

4. Course Information II – requirements Completing the lab assignments (each is assignment is evaluated) 1 mid term test (1 recap) Exam (similar to mid term test) Grading: Grading policy:

5. What is risk and risk analysis ? System (project, process, financial operation, complex machinery …etc.) Input Output (system performance according to a given performance index) RISK= a set of events which may jeopardize the succesful outcome of a planned process (e.g. in the case of a project, the delays in cash flow, delivery/production failures …etc.) System components How the output performance is affected ? SYSTEM RISK CHALLENGE OF RISK ANALYSIS: How to determine the possible performance degradation based on the component uncertainties ?

6. An “input-output” interpretation of Risk Analysis SYSTEM (interdependence of components) Component performance uncertainty (input risk) System performance uncertainty (global risk) Fast and real time calculations Component statistics Risk measures on global performance Computational challenge

7. Statistical model of risk It may or may not occur or uncertainty in the degree Risk is a random variable with a p.d.f. Complex system Elementary risk factors with known statistics Evaluation of global risk factors defined over system performance COMPUTATIONAL RISK ANALYSIS Failure of a component: Uncertainty in delay :

8. Risk analysis – the mathematical framework Average performance Tail p.d.f CALCULATE: SYSTEM

9. Basic steps of Risk Analysis 1.Identify the risks 2.Identify the corresponding p.d.f.-s 3.Define the performance index 4.Define the statitical measure on the performance index to be evaluated for risk analysis 5.Calculate the defined statistical measures Identification of risks Prob. of failure

10. Risk management (mitigation) 1.Evaluate the risk of the process under investigation 2.Check if system risk complies with a pre-defined criterion 3.Re-design if necessary 4.Re-calculate the performance index 5.Demonstrate the improvement and do it iteratively until you reach the pre-defined risk objective The risk is mitigated

11. Course objectives Knowledge and skills of basic risk measures; mathematical tools for their evaluation; real-time calculation of system risk measures. Expertise in COMPUTATIONAL RISK ANALYSIS and ability to perform the steps of ISO 31000 !

12. Risk Analysis standard – ISO 31000 http://www.iso.org/iso/iso_31000_for_smes.pdf

13. What is risk and risk analysis ? System (project, process, financial operation, complex machinery …etc.) Input Output (system performance according to a given performance index) “Components” (SW, HW…etc.) RISK= a set of events which may jeopardize the succesful outcome of a planned process (e.g. in the case of a project, the delays in cash flow, delivery/production failures …etc.) What is the probability of a given performance degradation ? RISK ANALYSIS

14. Risk analysis – the mathematical framework Given some statistical measures on the performance index ! Average performance Tailp.d.f Average performance Tail p.d.f