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

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

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

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

5. © 2003, David M. Hassenzahl 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

6. © 2003, David M. Hassenzahl 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

7. © 2003, David M. Hassenzahl 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

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

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

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

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

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

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

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

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

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

17. © 2003, David M. Hassenzahl Boolean Algebra OperationProbabilityMathematicsEngineering Union of A and B A or B A  B A + B Intersection of A and B A and B A  BA  B Complement of A Not AA' Haimes, Page 549

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

19. © 2003, David M. Hassenzahl 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

20. © 2003, David M. Hassenzahl 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)

21. © 2003, David M. Hassenzahl Probabilities EventProbability, f(time) Deer in roadway0.0026 Distracted driver0.001 Brakes applied0.999 Brake failure0.0002

22. © 2003, David M. Hassenzahl 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

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

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

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

26. © 2003, David M. Hassenzahl Probabilities OutcomeSub- outcome CalculationProbability Safe Stop(none) 0.8  0.99  0.6 0.4752 CollisionGlancing 0.8  (0.99  0.15 + 0.01  0.6) 0.3216 At speed 0.2 + 0.8  0.1  0.4 0.2032

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

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

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

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

31. © 2003, David M. Hassenzahl 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

32. © 2003, David M. Hassenzahl 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?

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

34. © 2003, David M. Hassenzahl 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

35. © 2003, David M. Hassenzahl 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

36. © 2003, David M. Hassenzahl Options for YMP Stance ForStance Against No ProblemsOK-OK+ Problems---+++

37. © 2003, David M. Hassenzahl 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!

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

39. © 2003, David M. Hassenzahl 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!”

40. © 2003, David M. Hassenzahl 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”

41. © 2003, David M. Hassenzahl 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?

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