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Decision Analysis and Risk Analysis Applications

Decision Analysis and Risk Analysis Applications. D. Warner North MS&E 290 Tuesday, January 25, 2005. New York Times - Sunday, August 11, 2002.

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Decision Analysis and Risk Analysis Applications

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  1. Decision Analysis and Risk Analysis Applications D. Warner North MS&E 290 Tuesday, January 25, 2005

  2. New York Times - Sunday, August 11, 2002 • If the Big One Hits the Big Easy, the Good Times May Be Over Forever By ADAM COHEN (NYT) 1018 words Late Edition - Final , Section 4 , Page 12 , Column 1 • ABSTRACT - Adam Cohen Editorial Observer on grave threat that big hurricane could wipe out low-lying city of New Orleans; describes complacency of its people and inadequate preparations by government Dot Wilson knows how bad the Big One could be. When Hurricane Betsy hit New Orleans in 1965 with 125 m.p.h. winds, leaving 75 dead in Louisiana and South Florida, she walked more than a mile in chest-high water, holding her infant daughter overhead. But when Ms. Wilson held a hurricane-preparedness teach-in recently at the community center she heads, attendance was sparse. ''A lot of people don't see storms as serious,'' she said with a sigh. But people who have been around for a while know better, she said, adding, ''We saw the bodies.'' • New Orleans -- home to the French Quarter's iron-latticed buildings and the Garden District's stately Greek Revival mansions, to Preservation Hall jazz and Mardi Gras parades -- may be America's most architecturally distinctive and culturally rich city. But it is also a disaster waiting to happen. New Orleans is the only major American city below sea level, and it is wedged between Lake Pontchartrain and the Mississippi. If a bad hurricane hit, experts say, the city could fill up like a cereal bowl, killing tens of thousands and laying waste to the city's architectural heritage. If the Big One hit, New Orleans could disappear.

  3. New York Times, Thursday, October 3, 2002 • Thousands Seek Safety as Hurricane Nears Gulf CoastBy JEFFREY GETTLEMAN (NYT) 1308 words Late Edition - Final , Section A , Page 24 , Column 3 • ABSTRACT - About half million people flee southern Louisiana and Texas with approach of Hurricane Lili, which is heading toward Gulf Coast with winds of more than 140 miles per hour, making it daunting Category 4 storm; map; chart of five most intense hurricanes to hit US since 1928; photos (M) Highways across southern Louisiana and Texas were solid columns of steel today as more than half a million people grabbed their valuables and fled their homes, looking for higher, safer ground before Hurricane Lili hit. • The exodus of cars and trucks, some with furniture lashed down on their roofs, began in low-lying areas but quickly spread inland as the storm intensified and threatened to become the worst natural disaster here in decades.

  4. Hurricane Lili October 4, 2002 — Using state-of-the-art equipment, including a radar collaboratively built by the NOAA National Severe Storms Laboratory, research scientists captured Hurricane Lili Thursday morning as she came onshore along the southern Louisiana coast. Three mobile Doppler radars, as well several instrumented towers, were strategically placed near Lafayette, La., in order to study the structure of the rainfall and wind flow around the storm. The data collected may help scientists develop better estimates of rainfall amounts, which could lead to more accurate and timely forecasts of inland flooding in the future.

  5. New York Times, Friday, October 4, 2002 • Hurricane Hits Gulf Coast, Weakened but Still Punishing By JEFFREY GETTLEMAN (NYT) 1052 words Late Edition - Final , Section A , Page 18 , Column 1 • ABSTRACT - Hurricane Lili slams into Louisiana, but with winds sharply diminished as storm devolves from Category 4 to Category 2 by time it makes landfall; still, there is widespread damage, with community of Abbeville being hardest hit; map; chart of Lili's wind speeds; map; photo (M) Hurricane Lili slammed into Louisiana today with tornado-force winds that ripped trees from the ground, smashed mobile homes and caused widespread blackouts that may last for weeks. • But it could have been worse. The storm lost significant strength overnight, dwindling from a Category 4 hurricane to Category 2, and no deaths or serious injuries were reported.

  6. The Decision to Seed Hurricanes R.A. Howard, J.E. Matheson, D.W. North Science, 176, 1191-1202, 1972 (paper on class website, pdf file)

  7. Decision Analysis of Hurricane Modification Background: The Cost of HurricanesAverage Annual Cost of Hurricane Damage: $400 Million Hurricane Betsy, 1965: $1.4 Billion Hurricane Camille, 1969: $1.4 Billion The Hurricane Debbie Experiment, 1969Reductions of 31%, 15% in Maximum Wind Speed Were Observed in the Two Seeding Experiments

  8. Decision Analysis of Hurricane Modification Decisions: • Strategic Decision:Should Operational Seeding by the U.S. Government be Permitted? • Research Policy Decision:Should the Present Level of Research and Experimentation be Changed? • Tactical Operational Decision:Should a Particular Hurricane be Seeded? (not analyzed in SRI study)

  9. The Operational Seeding Decision: Conceptual Overview Property Damage Economical Model Meteorological Knowledge Hurricane Model Decision Criteria Storm Parameters: Critical Storm Characteristics: Maximum Sustained Wind Legal/Social Model Government Responsibility Cost Seeding Decision Strategic

  10. Maximum Sustained Winds Over Time Maximum Sustained Winds, w w(t) Without Seeding w(t1) w’(t1) w’(t) With Seeding w(t) w(t0) 12 Hours t0 t1 Seeding Initiated Landfall

  11. The Seeding Decision: Decision Tree Resolution of Uncertainty: Change in Maximum Sustained Surface Wind Decision Alternatives Consequences Property Damage Government Responsibility Seed Do Not Seed Property Damage Government Responsibility

  12. Probabilistic Model for 12-Hour Change in Maximum Sustained Wind, Natural Hurricane Prob. Density Function No Predictability from Meteorological Environment Assumed. Probability Distribution Based on: • Observations of 12-Hour Changes in Central Pressure • Empirical Formula Relating Central Pressure to Maximum Sustained Wind time t = 0 (seeding initiated) 40 70 100 130 160 Maximum Sustained Wind, mph (or %) Prob. Density Function time t = 12 hours (landfall)  = 15.6 40 70 100 130 160 Maximum Sustained Wind, mph (or %)

  13. Probabilistic Model for 12-Hour Change in Maximum Sustained Wind, Natural Hurricane Probabilities Assigned to Hypotheses: m = 85  = 18.6 Probability Distribution Based on: • Probability Distribution for 12-Hour Change in Natural Hurricane • Expert Judgment on Average Effect of Seeding • Expert Judgment on Fluctuations From Average Effect in Seeding a Particular Storm H1: Stormfury Hypothesis: “Seeding Causes an Average Reduction in maximum Sustained Wind” 0.49 m = 100  = 15.6 0.49 H2: Null Hypothesis: “Seeding Has No Effect on Maxium Sustained Winds” 0.02 m = 110  = 18.6 H3: Pessimistic Hypothesis: “Seeding Causes an Average Increase in Maximum Sustained wind” 40 70 100 130 160 Maximum Sustained Wind, mph (or %)

  14. Probabilities for the Three Models Judgments from Hurricane Experts: • Before Debbie, P(H1) > P(H3) • After Debbie, P(H1) = P(H2) Resulting Probabilities: Before the Hurricane Debbie Seeding: P(H1)= 0.15; P(H2)= 0.75; P(H3)= 0.10 After Hurricane Debbie Seeding: P(H1)= 0.49; P(H2)= 0.49; P(H3)= 0.02 Before and After Probabilities Related by Bayes’ Rule H1: Stormfury Hypothesis: “Seeding Causes an Average Reduction in maximum Sustained Wind” H2: Null Hypothesis: “Seeding Has No Effect on Maximum Sustained Winds” H3: Pessimistic Hypothesis: “Seeding Causes an Average Increase in Maximum Sustained wind”

  15. Summary of Current Meteorological Information 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Unseeded Hurricane Probability the Wind Speed is Greater Than Amount Shown Seeded Hurricane 60 70 80 90 100 110 120 130 Maximum Sustained Wind 12 Hours After Seeding Decision (%)

  16. Maximum Sustained Wind Versus Property Damage 100 x 106 Total Equivalent Residential Property Damage (1969 $) 10 x 106 d = c1wc2 c2 = 4.363 1 x 106 50 60 70 80 90 100 110 120 130 140 150 160 180 200 w, Maximum Sustained Surface wind Speed (mph)

  17. Probability Distributions on Property Damage for the Seeded and Unseeded Hurricane 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Unseeded Probability That Property Damage is Greater than Amount Shown Seeded 0 50 100 150 200 250 300 350 400 Property Damage (M$)

  18. The Seeding Decision for the Nominal Hurricane Resolution of Uncertainty: Change in Maximum Sustained Wind Property Damage Loss (M$) Probabilities Assigned to Outcomes +32 % +16 0 -16 -34 $335.8 191.1 100.0 46.7 16.3 0.038 0.143 Seed: Expected Loss 0.392 = $94.08 + $0.25 = $94.33 0.255 0.172 Cost of Seeding = $0.25 +32 % +16 0 -16 -34 $335.8 191.1 100.0 46.7 16.3 0.054 Do Not Seed: Expected Loss 0.206 = $116.00 0.480 0.206 0.054 Expected Value (M$) Economic Value of Seeding = $21.67 million (18.7% reduction in loss) Decision not sensitive to specific assumptions.

  19. Public Outrage? Lawsuits? If a Seeded Hurricane Intensifies Government Responsibility Costs When a Hurricane Labeled “U.S. Government Seeded” it is No longer a “Natural Disaster” Concept: What Increment of Property Damage Reduction Justifies the Assumption of Responsibility Entailed by Seeding a Hurricane?

  20. Government Responsibility Cost Assumed for Strategic Analysis($100 Million Storm)

  21. The Seeding Decision for the Nominal Hurricane (Government Responsibility Cost Included) Government Responsibility Cost (% of property damage) Change in Maximum Sustained Wind Property Damage Loss (M$) Probabilities Assigned to Outcomes Total Cost (M$) +32 % +16 0 -16 -34 $335.8 191.1 100.0 46.7 16.3 +50 % +30 +5 0 0 $503.7 248.4 105.0 46.7 16.3 0.038 0.142 Seed: Expected Loss 0.392 = $110.67 + $0.25 = $110.92 0.255 0.172 Cost of Seeding = $0.25 +32 % +16 0 -16 -34 $335.8 191.1 100.0 46.7 16.3 - - - - - $335.8 191.1 100.0 46.7 16.3 0.054 Do Not Seed: Expected Loss 0.206 = $116.00 0.480 0.206 0.054 Expected Value (M$) Value of Seeding = $5.08 million (4.4% reduction)

  22. Legal findings: No firm Legal Basis for Operational Seeding Currently Appears to Exist Sovereign Immunity:In conclusion, existing immunity law provides only partial and unpredictable protection at best. There are also grounds for recognizing that immunity defenses may be avoided in most cases if the plaintiff carefully chooses his remedy, his legal theory, and his forum. Only specific Congressional action offers a prospect of substantial, predictable immunity protection. - Appendix D, p. 9 Basis for Lawsuits:The common law and inverse condemnation theories appear to offer plaintiff's attorneys substantial grounds for recovering damages where they can prove that modification activities caused injury, death, or property damage. This is particularly significant in the light of recent procedural developments (especially the decline of immunity defenses as discussed in an earlier memorandum). These tentative results suggest that the project agency may wish specific Congressional authorization for its project. - Appendix E, p. 15

  23. The Value of an Expanded Research and Experimentation Program Limiting Case: What is the Value of Perfect Information Concept: How Much Should the Government be Willing to Pay a Clairvoyant to Learn Which of the Three Hypotheses, H1’ H2’ or H3’ Is Actually True Before making the Operational Seeding Decision For a Single Hurricane?

  24. Expected Value of the Clairvoyant’s Information: Which Hypothesis Describes the Effect of Seeding? Choice of Whether to Gather Information Seeding Decision Property Damage Loss (M$) Results of Information Outcomes +32 % +16 0 -16 -34 +32 +16 0 -16 -34 +32 +16 0 -16 -34 +32 +16 0 -16 -34 +32 +16 0 -16 -34 +32 +16 0 -16 -34 +32 +16 0 -16 -34 +32 +16 0 -16 -34 $335.8 191.1 100.0 46.7 16.3 335.8 191.1 100.0 46.7 16.3 335.8 191.1 100.0 46.7 16.3 335.8 191.1 100.0 46.7 16.3 335.8 191.1 100.0 46.7 16.3 335.8 191.1 100.0 46.7 16.3 335.8 191.1 100.0 46.7 16.3 335.8 191.1 100.0 46.7 16.3 $69.42 H1 True Seed Do Not Seed $69.42 $116.00 0.49 $116.25 H2 True Seed 0.49 $93.17 Do Not Seed 0.02 $116.00 Obtain Information $116.00 $167.61 $93.17 H3 True Seed Do Not Seed $116.00 $94.33 $116.00 Do not Obtain Information $94.33 Seed Expected Value (M$) Do Not Seed Value = $1.16 property damage only Value = 13.63 property damage plus government responsibility cost. Value is Higher if Seeding is not Permitted with Present Information. $94.33 $116.00

  25. Value of A Seeding Experiment(Government Responsibility Cost Included) Total Cost (millions of dollars) Choice of Whether to Perform Experiment Results of Experiment Operational Seeding Decision Outcomes $116.00 0.038 0.143 +32 % +16 0 -16 -34 +32% +16 0 -16 -34 +32% +16 0 -16 -34 +32% +16 0 -16 -34 $503.7 248.4 105.0 46.7 16.3 503.7 248.4 105.0 46.7 16.3 503.7 248.4 105.0 46.7 16.3 503.7 248.4 105.0 46.7 16.3 $116.00 0.392 $103.44 Perform Experiment 0.255 $116.00 Seed $107.96 Do Not Seed $103.44 0.172 $116.00 $87.83 $110.92 $110.92 Do not Perform Experiment Seed Do Not Seed $110.92 Expected Value (M$) $116.00 Value = $2.96 million Actual cost = $0.25 million

  26. Summary of the Value of Additional Information on the Effect of Seeding (Values in Millions of Dollars) Considering only the 50% of hurricanes that are assumed to be possible candidates for seeding because of tactical consideration. If all hurricanes are assumed to be candidates for operational seeding, the figures of the last two columns should be doubled.

  27. Findings 1. Current meteorological and economic information indicates that the seeding alternative stochastically dominated the non-seeding alternative 2. No firm legal basis for operational seeding appears to exist 3. The decision to seed a particular hurricane should take into account its specific characteristics 4. Resolving meteorological uncertainty on the effect of hurricane modification is worth over $20 millions/year Recommendations 1. The present policy prohibiting seeding any hurricane threatening the U.S. should be rescinded 2. A hurricane modification agency with authority to seed operationally should be established 3. Decision procedures supported by further analysis should be developed 4. Modification experiments should be conducted on an expanded scale to provide a more refined basis for making each operational seeding decision Findings and Recommendations

  28. http://www.csmonitor.com/2003/0102/p10s02-sten.html Tinkering with clouds Researchers say evolving technologies could allow manipulation of major weather patterns. But should humans tamper? By Peter N. Spotts | Staff writer of The Christian Science Monitor, Jan 2, 2003 On Sept. 11, 1992, hurricane Iniki slammed into the Hawaiian island of Kauai, packing winds gusting up to 175 m.p.h. The storm inflicted an estimated $2 billion in damage and 105 casualties, damaged or destroyed 10,000 homes and businesses, and left once-lush tropical mountainsides looking as though they'd been mowed by a giant weed-whacker

  29. http://www.csmonitor.com/2003/0102/p10s02-sten.html Tinkering with clouds (2) • Over the past two decades, the idea of modifying large-scale storms such as hurricanes has lain dormant, following 20 years of inconclusive research. Now, however, a small group of atmospheric scientists is giving the concept a fresh look. • Researchers seeded hurricanes in a 20-year federal research project dubbed Project Storm Fury. Scientists were testing the idea that seeding could be used to take some of the punch out of hurricanes before they made landfall. But the program foundered on inconclusive results.

  30. http://www.csmonitor.com/2003/0102/p10s02-sten.html Tinkering with clouds (3) … during the Vietnam War, the US military seeded monsoon clouds in Operation Popeye in an attempt to use weather to hamper troop and supply movements along the Ho Chi Minh Trail. When information about the program was declassified in the mid-1970s, the international community established the UN Convention on the Prohibition of Military or Any Other Hostile Use of Environmental Modification Techniques. • Federal funds for weather-modification research have dried up as well. According to Colorado State University atmospheric scientist William Cotton, federal dollars for weather modification research peaked at roughly $19 million a year in the 1970s. They dropped to less than $5 million a year during the '90s, and now hover at about $500,000. • The field has entered what Dr. Cotton calls the "dark ages," where weather-modification programs are forging ahead with little or no scientific research programs to back them.

  31. New Methodology for Assessing the Probability of Contaminating Mars D. W. North, B.R. Judd, and J.P. Pezier, Life Sciences and Space Research XIII, P. A. Sneath, ed., Akademie-Verlag, Berlin, pp. 103-109, 1975. “Limitations, Definitions, Principles, and Methods of Risk Analysis,” Risk Assessment for Veterinary Biologicals, special issue, Office International des Epizooties, Scientific and Technical Review, Vol. 14, pp. 913-923, 1995. (on class website)

  32. Assessment of the Probability of Contaminating Mars • Carried out during 1972-3 for NASA Headquarters, Office of Planetary Programs, NASA Contracts 2451, 2535 • Background: Committee on Space Research (COSPAR) Resolution: Total probability of contaminating Mars during the quarantine period shall be less than 10-3. • Mariner 9 photos – evidence of past liquid water • Difficulties of dry-heat sterilization for 1975 Viking Lander

  33. Mission Contamination Model

  34. Bio-burden Submodel • Input Elements: • Pre-sterilization burden by location • Sensitivity to sterilization • Sterilization regime • Recontamination • Inflight mortality or proliferation • Contamination and subsequent amplification in biology experiment: • (probability = 10-6) • Outputs: • Bio-burden estimates by Viking Project • Expected number of Viable Terrestrial • Organisms (VTOs), by location on • spacecraft

  35. Release Submodel • Input Elements: • Bioburden by location • (from bio-burden submodel) • Probability of hard landing • Fracture ratio for hard landing • Lethality for release, given location and landing • (hard versus nominal) • Outputs: • Implantation: microbes (VTOs) directly • deposited in Martian soil, without UV exposure • Erosion: VTOs relaeased through aeolian • erosion of spacecraft into Martian atmosphere • Vibration: VTOs fall from spacecraft onto • surface of Mars due to mechanical vibration, • thermal effects, etc. VTOs require shielding to • survive UV exposure.

  36. Transport Submodel Input Elements: • Expected number of VTOs released, by mechanism • Lethality of UV radiation, in normal atmosphere and dust storm (probability that a VTO survives transit) • Extent of usable water • Probability it exists anywhere • Portion of surface covered Output • Expected number of VTOs that will reach usable water

  37. Reproduction Submodel Input Elements: • Fraction of VTOs that are facultatively anaerobic and psychrophilic: (0.05) • Probability that nutrients needed for reproduction will be present in the water microenvironment (0.10) Output: • Expected number of VTOs that reproduce at least once, defined as “contamination”

  38. Mission Contamination Model Results

  39. Mission Contamination Model Marginal Sensitivity Analysis

  40. Mission Contamination Model Marginal Sensitivity Analysis -2

  41. National Academy of Sciences, Viewpoint -1992 “… it is the unanimous opinion of the task group that terrestrial organisms have almost no chance of multiplying on he surface of Mars and in fact have little chance of surviving for long periods of time, especially if they are exposed to wind and to UV radiation.” ---- Space Studies Board, National Research Council, Biological Contamination of Mars, 1992, page 49.

  42. Retrospective • Impact of our analysis: • Acceptance of mission risk by scientific leaders • NASA’s decision to eliminate the mid-course correction on the Mars Orbiter • Planetary Quarantine since Viking: • Not a major concern, perhaps excepting Mars sample return • Example of Quantitative Risk Analysis built on highly judgmental information

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