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Technological Risk Methods

Technological Risk Methods. Fault Trees and Event Trees. The Mundane. “The mundane will kill you before the exotic” (Source unknown). Purpose of Lecture. Develop some technological risk methods Fault tree analysis Event tree analysis Explore statistics Probability theory

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Technological Risk Methods

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  1. Technological Risk Methods Fault Trees and Event Trees © 2003, David M. Hassenzahl

  2. The Mundane “The mundane will kill you before the exotic” (Source unknown) © 2003, David M. Hassenzahl

  3. Purpose of Lecture • Develop some technological risk methods • Fault tree analysis • Event tree analysis • Explore statistics • Probability theory • Boolean algebra ( “and/or”) © 2003, David M. Hassenzahl

  4. Fault Trees • Long history in engineering • Look at possible FAILURE • Trace back possible CAUSES • Applicable to many other risks • Carcinogenesis • Species loss © 2003, David M. Hassenzahl

  5. Event Trees • Looks at system, beginning with an event • Identifies (all) possible outcomes • Useful for decision analysis (more later) • Again, historically engineering, but broadly applicable © 2003, David M. Hassenzahl

  6. Remember Uncertainty! • Think through typology (see uncertainty lecture) • Common Mode Failures • Missing Components • The Human Element • Can’t leave this out • “Nuclear power is safe…operator error is to blame” is internally contradictory © 2003, David M. Hassenzahl

  7. Fault Trees • Potential adverse outcome • And/or gates • Excellent reading: Haimes, Yacov (1998) Risk Modeling, Assessment and Management Wiley Interscience, NY NY • Chapters 4, 9 and 14 © 2003, David M. Hassenzahl

  8. Car Accident Car Accident Fault Tree Non-deer accidents Car fails to Deer in stop Road Driver distracted Brakes Fail Brakes applied © 2003, David M. Hassenzahl

  9. Top Event • Primary undesired event of interest • Denoted by a rectangle Car Accident Haimes, Page 544 © 2003, David M. Hassenzahl

  10. Intermediate Event • Fault event that is further developed • Denoted by a rectangle Brakes Fail Haimes, Page 544 © 2003, David M. Hassenzahl

  11. Basic Event • Event requiring no further development • Denoted by a circle Deer in Roadway Haimes, Page 544 © 2003, David M. Hassenzahl

  12. Undeveloped Event • Low consequence event • Information not available • Denoted by a diamond All non-Deer Causes Haimes, Page 544 © 2003, David M. Hassenzahl

  13. “OR” Gate • Output event occurs only if one or more input event occurs • Systems in series • + ,  , union Haimes, Page 544 © 2003, David M. Hassenzahl

  14. “AND” Gate • Output event occurs only if all input events occur • Systems in parallel •  ,  , intersection Haimes, Page 544 © 2003, David M. Hassenzahl

  15. Reliability • Probability that the system operates correctly • Boolean algebra • Minimal set • Smallest combination of component failures leading to top event Haimes, Page 544 - 5 © 2003, David M. Hassenzahl

  16. Car Accident Car Accident Fault Tree Non-deer accidents Car fails to Deer in stop Road Driver distracted Brakes Fail Brakes applied © 2003, David M. Hassenzahl

  17. Boolean Algebra Haimes, Page 549 © 2003, David M. Hassenzahl

  18. Intersections and UnionsGraphical Representation A  B = Driver Distracted (A) A  B = 0 Deer in Road (C) (A  B)  C = Brakes applied, fail (B) © 2003, David M. Hassenzahl

  19. Probability Possibilities • If S = F + G P(S) = P(F) + P(G) – P(FG) = P(F) + P(G) – P(F)P(G|F) = P(F) + P(G) – P(F)P(G) if independent = P(F) +P(G) if rare events • If S = F  G P(S) = P(F)P(G) if independent Haimes, Page 546 - 8 © 2003, David M. Hassenzahl

  20. Deer Accident Equations • Car Accident (S) if • Deer in roadway (C) AND • Driver distracted (A) OR brakes fail (B) • S = (A  B) C • S = (A + B)  C • S = (A union B) intersect C • S = (A intersect C) union (B intersect C) © 2003, David M. Hassenzahl

  21. Probabilities © 2003, David M. Hassenzahl

  22. Deer Accident Probability S = (A + B)  C P(S) = [P(A) + P(B) – P(A)P(B|A)]  P(C) Note: A and B are dependent (why?) P(S) = [P(A) +P(B)]  P(C) P(S) = (0.001 + 0.0002  0.999)  0.0026 P(S) = 3  10-6 © 2003, David M. Hassenzahl

  23. Event Tree: Car Accident • Given potential initiating event, what possible outcomes? • Deer runs into road • Brakes applied? • Brakes function? • Braking effectiveness? © 2003, David M. Hassenzahl

  24. Glancing blow abrupt Brakes Function effective Safe stop Brakes Applied late Glancing blow partial Brakes Fail Glancing blow complete Collision at speed Brakes not Applied Collision at speed Deer in Road Event Tree Deer runs into road © 2003, David M. Hassenzahl

  25. (P = 0.99) (P = 0.01) Deer in Road Event Tree Probabilities Glancing (P = 0.25) abrupt Safe effective Brakes Function (P = 0.60) (P = 0.8) Glancing late (P = 0.15) Brakes Applied partial Glancing (P = 0.60) Brakes Fail Deer runs into road Collision complete (P = 0.40) (P = 1) (P = 0.2) Brakes not Applied Collision © 2003, David M. Hassenzahl

  26. Probabilities © 2003, David M. Hassenzahl

  27. Complexity • Inputs can be distributional • More than simple probabilities • Monte Carlo analysis • Can take entire engineering courses on this • Theoretical and empirical inputs © 2003, David M. Hassenzahl

  28. The Exotic Low Probability, High Consequence © 2003, David M. Hassenzahl

  29. The Mundane “The mundane will kill you before the exotic” (Source unknown) But the exotic fascinates us! © 2003, David M. Hassenzahl

  30. Purpose of Lecture • Methods • A bit more probability (digging out of a hole) • Poisson method • Extreme events • “Normal Accidents” © 2003, David M. Hassenzahl

  31. Poisson method • Has nothing to do with fish • Has nothing to do with gambling! • Method for calculating the probability of rare events! • Late 1800’s, a number of Prussian cavalry officers were kicked to death by their horses • New Problem? • Statistical anomaly? • M. Poisson came up with a method © 2003, David M. Hassenzahl

  32. Military Flight Risk • 90,000 flight hours per week • About 1 accident per 80,000 flight hours • 6 accidents in one week • Is this a problem? © 2003, David M. Hassenzahl

  33. Poisson Calculation •  = expected frequency • x = frequency of concern • P(6|  = 1) = 0.0005, or 1:2000 • Is this a problem? © 2003, David M. Hassenzahl

  34. Exercise • You are the Chairman of the Joint Chiefs of Staff • You’re before Congress • I’m sitting next to you with my Poisson calculation • What do you tell Congress? • Think for 5, then discuss © 2003, David M. Hassenzahl

  35. Extreme Events and Expected Values • We seldom make extreme event decisions based on expected values • Decision makers rewarded for avoiding failure • They choose rationally • Expected value choice is not rational for extreme events • Minimax: minimize the worst case • Common decision rule After Haimes, Chapter 8 © 2003, David M. Hassenzahl

  36. Options for YMP © 2003, David M. Hassenzahl

  37. Cost and Extreme Events • Unfortunately we may not be fulfilling our preferences when we make decisions • NOT simply a case of “irrationality” or “ignorance” • Can’t be solved by giving decisions to risk analysts! © 2003, David M. Hassenzahl

  38. “Average” Decisions? • Average load on a bridge? • Average electricity supply? • Average drivers? • Sometimes there’s an enormous cost! © 2003, David M. Hassenzahl

  39. Individual Decisions: Alar • Alar: growth inhibitor on apples • You know the story • Data from a few animal studies • Low probability of causing cancer • High consequence (cancer!) • Focal argument “children are at risk!” © 2003, David M. Hassenzahl

  40. Individual Decisions: Saccharine • Saccharine: sugar substitute, no-cal, no risk for diabetics • Data from a few animal studies • Low probability of causing cancer • High consequence (cancer!) • Focal argument “100 sodas a day” © 2003, David M. Hassenzahl

  41. What’s the difference? • Can children and diabetes account for it all? • In which case did people focus on consequence? • In which case did people focus on probability? • Is there a general lesson? • Can we make predictions? © 2003, David M. Hassenzahl

  42. Normal Accidents (Discussion) © 2003, David M. Hassenzahl

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