What do Coin Tosses, Decision Making under Uncertainty, The Vessel Traffic Risk Assessment 2010 and Average Return Time Uncertainty have in common?

Transcription

1 AN INTRO TO DECISION ANALYSIS What do Coin Tosses, Decision Making under Uncertainty, The Vessel Traffic Risk Assessment 2010 and Average Return Time Uncertainty have in common? Jason R.W. Merrick (VCU) and J. Rene van Dorp (GW) SAMSI Workshop Presentation May 16 May 20, 2016 Presented by: J. Rene van Dorp 5/16/2016 1

2 AN INTRO TO DECISION ANALYSIS OUTLINE 1. Coin Tosses 2. Decision Making under Uncertainty 3. Decision Trees or Influence Diagrams? 4. Elements of Decision Analysis 5. VTRA 2010 Case Study Base Case Traffic Description What-If and Benchmark Cases 6. Return Time Uncertainty 5/16/2016 2

3 AN INTRO TO DECISION ANALYSIS 1. Imagine we have a coin and we flip it repeatedly 2. When heads turns up you win when tails turns up you lose Suppose we flip the coin four times, how many times do you expect to win? Suppose we flip the coin ten times, how many times do you expect to win? 2 times 5 times WHAT ASSUMPTION(S) DID YOU MAKE? 5/16/2016 3

4 AN INTRO TO DECISION ANALYSIS Conclusion: you made reasonable assumptions 1. The coin has two different sides 2. When flipping it, each side turns up 50% of the time on average. Would it have made sense to assume the coin had only one face i.e. both sides show heads (or tails)? No Assuming both sides show heads or tails is equivalent to making a worst case or best case assumption. 5/16/2016 4

5 AN INTRO TO DECISION ANALYSIS Suppose you actually flip the fair coin ten times How many times will heads turn up? Answer could vary from 0 to 10 times, for example, First ten times : 3 times heads turns up Second ten times : 7 times heads turns up Third ten times : 6 times heads turns up Fourth ten times : 4 times heads turns up etc. We say on average 5 out of ten times heads turns up 5/16/2016 5

6 AN INTRO TO DECISION ANALYSIS 30% 25% 25% 20% 21% 21% 15% 12% 12% 10% 5% 4% 4% 0% 0% 1% 1% 0% Approximately 90% of ten throw series will have 3, 4, 5, 6 or 7 times heads turn up Conclusion: While we expect 5 times heads to turn up, the actual number is uncertain! 5/16/2016 6

7 AN INTRO TO DECISION ANALYSIS Decision Analysis Software: Precision Tree Probability Node Risk Profile (RP) Probability Mass Function (PMF) 25% Probabilities for Decision Tree '10 Tosses Coint 1' Optimal Path of Entire Decision Tree 20% 15% 10% 5% 0% Probability Cumulative Risk Profile (CRP) Cumulative Distribution Function (CDF) 100% Cumulative Probabilities for Decision Tree '10 Tosses Coint 1' Optimal Path of Entire Decision Tree 80% 60% 40% 20% 0% Cumulative Probability 5/16/2016 7

8 AN INTRO TO DECISION ANALYSIS OUTLINE 1. Coin Tosses 2. Decision Making under Uncertainty 3. Decision Trees or Influence Diagrams? 4. Elements of Decision Analysis 5. VTRA 2010 Case Study Base Case Traffic Description What-If and Benchmark Cases 6. Return Time Uncertainty 5/16/2016 8

9 AN INTRO TO DECISION ANALYSIS 1. Imagine we have two coins: Coin 1 shows heads 50% of the time Coin 2 shows heads 75% of the time Coin 1 Coin 2 2. When heads turns up, you win a pot of money. When tails turns up, you do not get anything. You have to choose between Coin 1 and Coin 2 Which one would you choose? Coin 2 WHAT ASSUMPTION DID YOU MAKE? You assumed that the pot of money you win is the same regardless of the coin you chose! 5/16/2016 9

10 AN INTRO TO DECISION ANALYSIS 1. Imagine we have two coins: Coin 1 shows heads 50% of the time Coin 2 shows heads 75% of the time Coin 1 Coin 2 2. Each time heads turns up, you win the same pot of money. When tails turns up you do not get anything, regardless of the coin you throw. You have to choose between two alternatives Alternative 1: Throwing ten times with Coin 1 Alternative 2: Throwing five times with Coin 2 Which alternative would you choose? Alternative 1 you expect to win 5 times and Alternative 2 you expect to win 3.75 times CHOOSE ALTERNATIVE 1 5/16/

11 AN INTRO TO DECISION ANALYSIS A DECISION TREE: The Basic Risky Decision Reference Nodes Decision Node Probability Nodes Our objective is to maximize pay-off. So faced with uncertainty of pay-off outcomes we choose the alternative with largest average pay-off.. 5/16/

12 AN INTRO TO DECISION ANALYSIS Cumulative Risk Profiles of both Alternatives Observe from CRP s on the Right Pr X x CCCC 1 Pr X x CCCC 2 Pr X > x CCCC 1 Pr X > x CCCC 2 1. Deterministic Dominance 2. Stochastic Dominance 3. Make Decision Based on Averages Chances of an Unlucky Outcome Increase going from 1, 2 to 3 Cumulative Probability 100% 80% 60% 40% 20% 0% -2 Cumulative Probabilities for Decision Tree 'Coin Choice' Choice Comparison for Node 'Decision' 5/16/ Flip Coin 1 10 Times Flip Coin 2 5 Times

13 AN INTRO TO DECISION ANALYSIS 1. Imagine we have two coins: Coin 1 shows heads 50% of the time Coin 2 shows heads 75% of the time Coin 1 Coin 2 2. Each time heads turns up with Coin 1 you win $2. Each time heads turns up with Coin 2 you win $4. When tails turns up you do not get anything. You have to choose between two ALTERNATIVES Alternative 1: Throwing ten times with Coin 1 Alternative 2: Throwing five times with Coin 2 Which alternative would you choose? Alternative 1 you average 5 * $2 = $10 Alternative 2 you average 3.75 * $4 = $15 CHOOSE ALTERNATIVE 2 5/16/

14 AN INTRO TO DECISION ANALYSIS Alternative 1 Alternative 2 Average Pay-Off Alt. 1: $10 Average Pay-Off Alt. 2: $15 40% Probability 0% 0% 1% 4% 1% 12% 21% 9% 25% 21% 26% 12% 4% 1% 0% 24% Pay - Off Outcome Our objective is to maximize pay-off. So faced with uncertainty of pay-off outcomes we choose the alternative with largest average pay-off. 5/16/

15 AN INTRO TO DECISION ANALYSIS Please Note Optimal Choice And Stochastic Dominance Schwitched CRP S of both Alternatives Observe from CRP s on the Right Pr X x CCCC 2 Pr X x CCCC 1 Pr X > x CCCC 2 Pr X > x CCCC 1 1. Deterministic Dominance 2. Stochastic Dominance 3. Make Decision Based on Averages Chances of an Unlucky Outcome Increase going from 1, 2 to 3 Cumulative Probability 100% 80% 60% 40% 20% 0% -5 Cumulative Probabilities for Decision Tree 'Coin Choice' Choice Comparison for Node 'Decision' 5/16/ Flip Coin 1 10 Times Flip Coin 2 5 Times

16 AN INTRO TO DECISION ANALYSIS Conclusion? When choosing between two alternatives entailing a series of coin toss trials, the following comes into play: 1. The number of trials N in each alternative 2. The probability of success P per trial 3. The pay-off amount W per trial AVERAGE PAY-OFF = N P W Is it required to know the absolute value of N, P and W to choose between these two alternatives? 5/16/

17 AN INTRO TO DECISION ANALYSIS 1. Imagine we have two coins: Coin 2 shows heads 1.5 times more than Coin 1 2. When heads turns up with Coin 2 you win 2 times the amount when heads turns up with Coin 1. You have to choose between Two Alternatives Alternative 1: Throwing 2*N times with Coin 1 Alternative 2: Throwing N times with Coin 2 P = % Heads turns up with Coin 1, W = $ amount you win with Coin 1. Average Pay Off Alternative 2 : N 1.5 P 2 W Average Pay Off Alternative 1 : 2 N P W Average Pay-Off Alt. 2/Average Pay-Off Alt. 1 = 1.5 5/16/

18 AN INTRO TO DECISION ANALYSIS Conclusion? When choosing between two alternatives entailing a series of trials, we can make a choice if we know the multiplier between the average pay-offs, even when the absolute pay-off values over the two alternatives are unknown/uncertain 5/16/

19 AN INTRO TO DECISION ANALYSIS 2D Strategy Region Diagram 2D Strategy Region Diagram Difference in Pay-Off Coin 2 Alternative Pay-Off Factor -20 Coin 1 Alternative Probability Factor 5/16/

20 AN INTRO TO DECISION ANALYSIS Conclusion? When choosing between two alternatives entailing a series of trials, we can make a choice if we know the sign of the difference between the average pay-offs, even when only ranges are available for the pay-off probability factors using a strategy region diagram. 5/16/

21 AN INTRO TO DECISION ANALYSIS What if your Value for Money depends on the amount you win per Coin Toss? 1 at Max 0 at Min Utility Linear: Risk Neutral Utility Concave: Risk Averse 1 at Max 0 at Min Pay-Off Pay-Off Scenario 1: Winning $2 with Heads Coin 1 Scenario 2: Winning $20,000 with Heads Coin 1 5/16/

22 AN INTRO TO DECISION ANALYSIS What if your Value for Money Changes depends on your wealth? Linear Utility Function implies the Decision Maker (DM) is Risk Neutral. A DM is Risk Neutral if he/she is indifferent between a bet with an expected pay-off and a sure amount equal to the expected pay-off. Concave Utility Function implies a Decision Maker (DM) is Risk Averse. A DM is Risk Averse if he/she is willing to accept less money for a bet with a certain expected pay-off than the expected pay-off. Convex Utility Function implies a Decision Maker (DM) is Risk Seeking. A DM is Risk Seeking if he/she is willing to pay more money for a bet with a certain expected pay-off than the expected pay-off. 5/16/

23 AN INTRO TO DECISION ANALYSIS 2D Strategy Region Diagram 2D Strategy Region Diagram Now Max. Exp. Utility Difference in Utility Coin 1 Alternative Coin 2 Alternative Pay-Off Factor Probability Factor 5/16/

24 AN INTRO TO DECISION ANALYSIS Now Max. Exp. Utility For how much money are you willing to sell this decision? $142,018 Called Certainty Equivalent (CE) Provides for an Operational Interpretation of the Utility Concept. Utility $142,018 < $150,000 Pay-Off 5/16/

25 AN INTRO TO DECISION ANALYSIS Now Max. Exp. Utility How much money are you willing to give up to not play? $150,000 - $142,018 = $7,982 Called Risk Premium Utility $142,018 < $150,000 Pay-Off 5/16/

26 AN INTRO TO DECISION ANALYSIS OUTLINE 1. Coin Tosses 2. Decision Making under Uncertainty 3. Decision Trees or Influence Diagrams? 4. Elements of Decision Analysis 5. VTRA 2010 Case Study Base Case Traffic Description What-If and Benchmark Cases 6. Return Time Uncertainty 5/16/

27 AN INTRO TO DECISION ANALYSIS Decision Trees or Influence Diagrams? Coin 1 Coin 2 Pay Throw Coin 1 2*N Times Pay Throw Coin 2 N times Coin Series Choice Max Pay- Off Lot of Detail, but become Unwieldy Lack of Detail, Higher level View And Makes Dependence Explicit 5/16/

28 AN INTRO TO DECISION ANALYSIS Some Basic Influence Diagram Examples Basic Risky Decision Business Result Arc? Yes or No? Investment Choice Return on Investment Source: Clemen and Reilly (2014), Making Hard Decisions, Cengage Learning 5/16/

29 AN INTRO TO DECISION ANALYSIS Some Basic Influence Diagram Examples Imperfect Information Time Sequence Arc Weather Forecast Reverse Influence Arc? Hurricane Path Evacuate? Consequence Source: Clemen and Reilly (2014), Making Hard Decisions, Cengage Learning 5/16/

30 AN INTRO TO DECISION ANALYSIS Influence Diagram Example EPA Decision Usage Survey Two Imperfect Information Diagrams in one Influence Diagram Lab Tests Allow Chemical? Max. Economic Value Min. Cancer Cost Max. Net Value Exposure to Usage Carcinogenic Potential Multiple Conflicting Objectives Source: Clemen and Reilly (2014), Making Hard Decisions, Cengage Learning 5/16/

31 AN INTRO TO DECISION ANALYSIS Current Reliability Outcome Test 1 Reliability after Test 1 Outcome Test 2 Reliability after Test 2 Release 1? Release 2? Final Release? Profit if released after 1 Cost of Test 1 & Redesign Profit if released after 2 Cost of Test 2 & Redisgn Profit if released after final Influence Diagram Example Reliability Growth Decision FINAL PROFITS Multiple Sequential Decisions 5/16/

32 AN INTRO TO DECISION ANALYSIS OUTLINE 1. Coin Tosses 2. Decision Making under Uncertainty 3. Decision Trees or Influence Diagrams? 4. Elements of Decision Analysis 5. VTRA 2010 Case Study Base Case Traffic Description What-If and Benchmark Cases 6. Return Time Uncertainty 5/16/

33 AN INTRO TO DECISION ANALYSIS Elements of Decision Analysis (DA) Multiple Decisions: The immediate one and possibly more. Decisions are sequential in time. The DP is called dynamic. Multiple Uncertainties: Each uncertainty node requires a probability model. Multiple uncertainty nodes may be statistically dependent. Multiple or Single Objectives: In case of multiple conflicting objective the trade-off between objectives needs to be modelled. Multiple values: Evaluation of achievements of each individual objective requires description of a utility function for each one (linear, concave, convex?) DA s are Complex! 5/16/

34 AN INTRO TO DECISION ANALYSIS Skill Set/Techniques for Decision Analysis (DA) Decision Tree/Influence Diagrams: To structure and visualize DP s, identify its elements and prescribe the method towards evaluation. Expert Judgement (EJ) Elicitation: To describe/specify probability models of on-off uncertainty nodes and to combine expert judgements. Statistical Inference: In DA the inference is typically Bayesian in nature. Is used when uncertainties reveal themselves over time to refine/update probability models or combine available data with Expert Judgement. Utility Theory: To describe The Decision Maker s risk attitude/ appetite for the evaluation of a single objective and to formalize trade-off between multiple objectives. Thus, a DA s is Normative in Nature! 5/16/

35 AN INTRO TO DECISION ANALYSIS OUTLINE 1. Coin Tosses 2. Decision Making under Uncertainty 3. Decision Trees or Influence Diagrams? 4. Elements of Decision Analysis 5. VTRA 2010 Case Study Base Case Traffic Description What-If and Benchmark Cases 6. Return Time Uncertainty 5/16/

36 IMAGES FROM THE SALISH SEA 5/16/

37 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 Kinder Morgan: Tankers Delta Port: Cont. & 67 Bulkers Gateway: Bulkers VTRA 2010 Study Area 5/16/

38 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 BP Cherry Point Refinery Ferndale Refinery March Point Refinery VTRA 2010 Study Area 5/16/

39 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 What was The Objective in Coin Toss Example? Maximize Average Pay-Off What is the Objective in a Maritime Risk Assesment? Minimize Average Potential Oil Loss Truth be told, for some the objective is to Maximize Average Pay-Off, for some it is to Minimize Average Potential Oil Loss and for others it is to Achieve Both. For sake of argument, lets take in Maritime Risk Assessment a focus towards Minimizing Average Potential Oil Loss, while recognizing the Maximize Average Pay-Off Objective is also at play. 5/16/

40 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 An Oil Spill is a series of cascading events referred to as a Causal Chain Situations Incidents Accidents Oil Spill Maritime Simulation Incident Data Expert Judgment + Data Oil Outflow Model R = { < s, l, x > } i Traffic Situations i i Likelihoods c Consequences Risk Analysis Objective: Evaluate Oil Spill System Risk described by a complete set of traffic situations Coin Toss Analogy: Trials % of Heads (P) Winnings ($) Pay-off Risk was defined by N identical Trials 5/16/

41 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 VTRA 2010 Analysis Approach In light of uncertainties inherent to any risk analysis, we choose not to focus on; absolute evaluations of risk levels, but to focus on relative risk changes from a base case scenario by adding or removing traffic to or from that base case. 5/16/

42 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 VTRA 2010 Analysis Approach A Base Case (BC) Analysis Framework is constructed while; making reasonable assumptions (not worst or best case), and What-if (WI), Bench-Mark (BM) and Risk Mitigation Measure (RMM) cases are analyzed within that framework. 5/16/

43 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 VTRA 2010 Analysis Approach Base Case (BC) system wide risk levels are set at 100%, and System wide % changes up or down are evaluated for What-if (WI), Bench-Mark (BM) and Risk Mitigation Measure (RMM), moreover Location-Specific Multipliers are evaluated for 15 Waterway Zones. 5/16/

44 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 DEFINITION OF 15 WATERWAY ZONES VTRA 2010 Waterway Zones 5/16/ Buoy J ATBA WSJF ESJF Rosario Guemes Saddlebag Georgia Str. 9. Haro/Boun. 10. PS North 11. PS South 12. Tacoma 13. Sar/Skagit 14. SJ Islands 15. Islands Trt

45 Generating Traffic Situations: A Counting Collision Accident Scenario s B C Counting Drift Grounding Accident Scenario s D Counting Powered Grounding Accident Scenario s E 5/16/2016 F 45 GW-VCU : DRAFT 45

46 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 VTRA 2010 Analysis Approach Map is divided in squares of grid cells with dimension half nautical mile by half nautical mile and The VTRA 2010 Evaluates per Grid Cell! # of traffic situations per year potential accident frequency per year potential oil loss per year 5/16/

47 A 5/16/ B

48 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 Recall Coin Toss Analogy: Trials (N) % of Heads (P) Winnings (W) EVALUATE AVERAGE PAY-OFF = N P W Risk Assessment: Traffic Situations Likelihoods Consequences R = { < s, l, x > } Per Grid Cell!! Display results visually in 2D and 3D geographic profiles i i i c Oil Spill System Risk is described by complete set of traffic situations EVALUATE AVERAGE VESSEL TIME EXPOSURE EVALUATE AVERAGE OIL TIME EXPOSURE Driver for Driver for EVALUATE AVERAGE ANNUAL POTENTIAL ACC. FREQ. EVALUATE AVERAGE ANNUAL POTENTIAL OIL LOSS 5/16/

49 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 VTRA 2010 Analysis Approach Collision System Exposure in Base Case: Approximately 10,000 grid cells of 0.5 x 0.5 mile in VTRA study area with Vessel to Vessel traffic situations. Approximately 1.8 Million Vessel to Vessel Traffic Situations per year generated by VTRA 2010 Model. Vessel to Vessel Traffic Situations per cell per year range from 1 7,000 (or on average about 0 20 per day per cell). Recall Coin Toss Traffic Situation Analogy: 1.8 Million Coin Tosses with very small probability of Tails 5/16/

50 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 VTRA 2010 Analysis Approach Grounding System Risk in Base Case: Approximately 4,000 grid cells of 0.5 x 0.5 mile in VTRA study area with Vessel to Shore traffic situations. Approximately 10 Million Vessel to Shore Traffic Situations per year generated by VTRA 2010 Model. Vessel to Shore Traffic Situations per cell per year range from 1 55,000 (or on average about per day). Recall Coin Toss Traffic Situation Analogy: 10 Million Coin Tosses with very small probability of Tails 5/16/

51 AN INTRO TO DECISION ANALYSIS OUTLINE 1. Coin Tosses 2. Decision Making under Uncertainty 3. Decision Trees or Influence Diagrams 4. Elements of Decision Analysis 5. VTRA 2010 Case Study Base Case Traffic Description What-If and Benchmark Cases 6. Return Time Uncertainty 5/16/

52 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 P: Base Case 3D Risk Profile MAP TO DISPLAY - Vessel Time Exposure VESSEL TIME EXPOSURE (VTE) = Annual amount of time a location is exposed to a vessel moving through it Bellingham Victoria Neah Bay Seattle Tacoma /16/

53 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 P: Base Case 3D Risk Profile ALL TRAFFIC - Vessel Time Exposure: 100%Total VTE VESSEL TIME EXPOSURE (VTE) = Annual amount of time a location is exposed to a vessel moving through it Bellingham Victoria Neah Bay Seattle ALL VTRA TRAFFIC VTOSS 2010 TRAFFIC + SMALL VESSEL EVENTS Tacoma /16/

54 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 NON FV TRAFFIC P: Base Case 3D Risk Profile NON FV - Vessel Time Exposure: 75%Total VTE 2010 NON FV 75% of 2010 Total 41.3% - FISHINGVESSEL 18.1% - FERRY 06.8% - BULKCARGOBARGE 06.0% - UNLADENBARGE 04.0% - YACHT 03.9% - NAVYVESSEL 03.3% - TUGNOTOW 02.8% - FERRYNONLOCAL 02.7% - PASSENGERSHIP 02.2% - WOODCHIPBARGE % - LOG_BARGE 01.7% - TUGTOWBARGE 01.5% - USCOASTGUARD 01.1% - FISHINGFACTORY 00.8% - RESEARCHSHIP 00.7% - OTHERSPECIFICSERV 00.6% - CONTAINERBARGE 00.2% - SUPPLYOFFSHORE 00.2% - CHEMICALBARGE 00.0% - DERRICKBARGE Bellingham Victoria Seattle Neah Bay Tacoma /16/

55 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 P: Base Case 3D Risk Profile Cargo FV - Vessel Time Exposure: 17% of Base Case VTE 2010 CARGO FV 17.0% of 2010 Total % - BULKCARRIER 27.8% - CONTAINERSHIP 08.1% - OTHERSPECIALCARGO 04.9% - VEHICLECARRIER 02.3% - ROROCARGOCONTSHIP 01.1% - ROROCARGOSHIP 00.8% - DECKSHIPCARGO 00.4% - REFRIGERATEDCARGO % of Base Victoria Bellingham Seattle Neah Bay Tacoma /16/

56 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 P: Base Case 3D Risk Profile Tank FV - Vessel Time Exposure: 8% of Base Case VTE 2010 TANK FV 8% of 2010 Total 54.5% - OILBARGE 24.4% - OILTANKER 11.3% - CHEMICALCARRIER 09.8% - ATB % of Base Bellingham Victoria Neah Bay Seattle Tacoma /16/

57 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 FV = Focus Vessel P: Base Case 3D Risk Profile All FV - Vessel Time Exposure: 100% of Base Case VTE ALL FV (100%) Bulk Carriers ( 33%) Container Ships ( 20%) Other Cargo ( 13%) Oil Tankers ( 9%) Chemical Carriers ( 4%) Oil Barges ( 19%) ATB s ( 3%) Where do Focus Vessels Travel? Victoria Bellingham Seattle Neah Bay FV TRAFFIC ACCOUNTS FOR ( 25%) OF TOTAL TRAFFIC Tacoma /16/ GW-VCU : DRAFT 57

58 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 FV = Focus Vessel ALL FV Bulk Carriers Container Ships Other Cargo Oil Tankers ( 9%) Chemical Carriers Oil Barges ATB s P: Base Case 3D Risk Profile Tanker - Vessel Time Exp.: 9% of Base Case VTE Where do Tankers Travel? Cherry Point Ferndale March Point Port Angeles /16/

59 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 P: Base Case 3D Risk Profile MAP MAP TO TO DISPLAY - -Vessel Oil Time Exposure Oil OIL TIME EXPOSURE (OTE) = Annual amount of time a location is exposed to a cubic meter of oil moving through it Bellingham Victoria Neah Bay Seattle Tacoma /16/

60 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 FV = Focus Vessel ALL FV (100%) Bulk Carriers ( 8%) Container Ships ( 9%) Other Cargo ( 3%) Oil Tankers ( 48%) Chemical Carriers ( 9%) Oil Barges ( 21%) ATB s ( 3%) P: Base Case 3D Risk Profile All FV - Oil Time Exposure: 100% of Base Case OTE Where does Oil on Focus Vessels Travel? Cherry Point Ferndale March Point Port Angeles /16/

61 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 FV = Focus Vessel ALL FV (100%) Bulk Carriers Container Ships Other Cargo Oil Tankers ( 48%) Chemical Carriers Oil Barges ATB s P: Base Case 3D Risk Profile Tanker - Oil Time Exposure: 48% of Base Case OTE Where does Oil on board Tankers Travel? Cherry Point Ferndale March Point Port Angeles /16/

62 AN INTRO TO DECISION ANALYSIS OUTLINE 1. Coin Tosses 2. Decision Making under Uncertainty 3. Decision Trees or Influence Diagrams 4. Elements of Decision Analysis 5. VTRA 2010 Case Study Base Case Traffic Description What-If and Benchmark Cases 6. Return Time Uncertainty 5/16/

63 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 WHAT IF SCENARIO ROUTES GW487: BULK CARRIERS + Bunkering Support KM348: TANKERS + Bunkering Support BUNKERING SUPPORT ROUTES DP415: 348 BULK CARRIERS + 67 CONTAINER SHIPS + Bunkering Support 5/16/

64 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 BENCH-MARK TANKER ROUTES P: BC & HIGH TAN 3D Risk Profile What-If FV - Vessel Time Exp.: 2% of Base Case VTE Tankers added to Base Case (2007 Historical High Year) /16/

65 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 BENCH-MARK TANKER + CARGO ROUTES P: BC & HIGH TAN + CFV 3D Risk Profile What-If FV - Vessel Time Exp.: 6% of Base Case VTE Tankers added to Base Case 2010 (2007 Historical High Year) Cargo Vessels added to Base Case 2010 (2011 Historical High Year) /16/

66 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 WHAT IF SCENARIO ANALYSES Vessel Time Exposure (VTE) Oil Time Exposure (OTE) Pot. Accident Frequency (PAF) Pot. Oil Loss (POL) P - Base Case 100% 100% 100% 100% P - Base Case Q - GW R - KM S - DP T - GW - KM - DP Vessel Time Exposure (VTE) WHAT IF SCENARIO ANALYSIS WHAT IF SCENARIO ANALYSIS Modeled Base Case 2010 year informed by VTOSS 2010 data amongst other sources. Gateway expansion scenario with 487 additional bulk carriers and bunkering support Transmountain pipeline expansion with additional 348 tankers and bunkering support Delta Port Expansion with additional 348 bulk carriers and 67 container vessels Combined expansion scenario of above three expansion scenarios WHAT IF SCENARIO ANALYSIS Oil Time Exposure (OTE) Pot. Accident Frequency (PAF) Pot. Oil Loss (POL) P - Base Case 100% 100% 100% 100% Q - GW % 113% +5% 105% +12% 112% +12% 112% R - KM % 107% +51% 151% +5% 105% +36% 136% S - DP % 105% +3% 103% +6% 106% +4% 104% T - GW - KM - DP +25% 125% +59% 159% +18% 118% +68% 168% 5/16/

67 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 BENCH MARK ANALYSES ON BASE CASE Vessel Time Exposure (VTE) Oil Time Exposure (OTE) Pot. Accident Frequency (PAF) Pot. Oil Loss (POL) P - Base Case 100% 100% 100% 100% P - Base Case P - BC & LOW TAN + CFV P - BC & LOW TAN P - BC & HIGH TAN P - BC & HIGH TAN + CFV P - RMM SCENARIO REFERENCE POINT CASE P BENCHMARK (BM) & SENSITIVITY ANALYSIS Modeled Base Case 2010 year informed by VTOSS 2010 data amongst other sources. Base Case with Tankers and Cargo Focus Vessels set at a low historical year Base Case with Tankers set at a low historical year Base Case with Tankers set at a high historical year Base Case with Tankers and Cargo Focus Vessels set at a high historical year CASE P BENCHMARK (BM) & SENSITIVITY ANALYSIS Vessel Time Exposure (VTE) Oil Time Exposure (OTE) Pot. Accident Frequency (PAF) Pot. Oil Loss (POL) P - Base Case 100% 100% 100% 100% P - BC & LOW TAN + CFV -3% 97% -14% 86% -5% 95% -20% 80% P - BC & LOW TAN -2% 98% -13% 87% -4% 96% -22% 78% P - BC & HIGH TAN +2% 102% +14% 114% +3% 103% +9% 109% P - BC & HIGH TAN + CFV +7% 107% +15% 115% +4% 104% +8% 108% 5/16/

68 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 DEFINITION OF 15 WATERWAY ZONES VTRA 2010 Waterway Zones 5/16/ Buoy J ATBA WSJF ESJF Rosario Guemes Saddlebag Georgia Str. 9. Haro/Boun. 10. PS North 11. PS South 12. Tacoma 13. Sar/Skagit 14. SJ Islands 15. Islands Trt

69 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 Zone: Diff. Factor Guemes : +5.3% x 1.31 Rosario : +0.5% x 1.03 Saddlebag : -0.8% x 0.94 PS South : 0.0% x 1.00 PS North : +0.3% x 1.03 ESJF : +13.9% x 2.42 Haro/Boun. : +36.9% x 4.75 WSJF : +5.0% x 2.04 Islands Trt : +1.8% x 1.38 Georgia Str. : +3.2% x 1.81 Buoy J : +1.9% x 4.44 Tac. South : +0.0% x 1.00 ATBA : 0.0% x 0.93 Sar/Skagit : 0.0% x SJ Islands : +0.2% x 2.89 CASE-T +68% Comparison of Potential Oil Loss by Waterway Zone 22.3% 17.0% 15.5% 14.9% 12.6% 13.4% 10.0% 10.0% 10.3% 10.0% 23.8% 9.8% 46.7% 9.8% 9.8% 4.8% 6.5% 4.8% 7.1% 3.9% 2.5% 0.6% 0.4% 0.4% 0.2% 0.2% 0.2% 0.2% 0.3% 0.1% 0.0% 10.0% 20.0% 30.0% 40.0% 50.0% % Base Case Pot. Oil Loss (POL) - ALL_FV T: GW - KM - DP : 168% ( +68.2% x 1.68) P: Base Case : 100% 5/16/

70 VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 RISK MITIGATION ANALYSES ON CASE T Vessel Time Exposure (VTE) Oil Time Exposure (OTE) Pot. Accident Frequency (PAF) Pot. Oil Loss (POL) T - GW - KM - DP +25% 125% +59% 159% +18% 118% +68% 168% T - GW - KM - DP & OW ATB T - GW - KM - DP & EC T - GW - KM - DP & EH T - GW - KM - DP & ER T - GW - KM - DP & 6RMM T - RMM SCENARIO REFERENCE POINT CASE T - RISK MITIGATION MEASURE (RMM) ANALYSIS Case T with ATB's adhering to one way Rosario traffic regime Case T with Cape Class bulk carrier given benefit of+ 1 escort on Haro and Rosario routes Case T with all Focus Vessels given benefit of +1 escort vessel on Haro routes Case T with Cape bulkers, laden Tankers, ATB's given benefit of +1 esc. on Rosario routes Case T with benefit OW ATB, EH, ER, P-HE50, Q-NB and P-CONT17 KNTS CASE T - RISK MITIGATION MEASURE (RMM) ANALYSIS Vessel Time Exposure Pot. Accident Frequency Oil Time Exposure (OTE) Pot. Oil Loss (POL) (VTE) (PAF) T - GW - KM - DP +25% 125% +59% 159% +18% 118% +68% 168% T - GW - KM - DP & 6RMM +4% 128% +4% 163% -29% 89% -44% 123% T - GW - KM - DP & OW ATB +1% 126% +2% 161% 0% 118% 0% 168% T - GW - KM - DP & EC 0% 125% +0% 159% -2% 116% -4% 164% T - GW - KM - DP & EH 0% 125% +0% 159% -7% 111% -24% 143% T - GW - KM - DP & ER 0% 125% +0% 159% -8% 111% -12% 156% 5/16/

71 AN INTRO TO DECISION ANALYSIS OUTLINE 1. Coin Tosses 2. Decision Making under Uncertainty 3. Decision Trees or Influence Diagrams 4. Elements of Decision Analysis 5. VTRA 2010 Case Study Base Case Traffic Description What-If and Benchmark Cases 6. Return Time Uncertainty 5/16/

72 SUPPLEMENT ANALYSIS - VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 VTRA 2010 Analysis Approach The ORIGINAL VTRA 2010 Study did not evaluate average accident return times as its risk metric of choice. Other Maritime Risk Studies, however, do evaluate average accident return times as its risk metric of choice. I am presenting this type of analysis here to allow for a comparison between these studies. 5/16/

73 SUPPLEMENT ANALYSIS - VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 Why did we not use average return times as risk metric of choice? Imagine we have had two accidents in a calendar year and we would like to evaluate the average return time over that year > 4 months Accident Accident 3 months > 5 months Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec What is the value of the average return time? > ( )/3 = 4 Months!!! 5/16/

74 SUPPLEMENT ANALYSIS - VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 Why did we not use average return times as risk metric of choice? The prevailing wisdom, however, converts 2 accidents/year to an average return time of ½ year = 6 months Accident Accident 6 months 6 months Accident Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec 5/16/

75 SUPPLEMENT ANALYSIS - VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 Why did we not use average return times as risk metric of choice? Conclusion? The definition: Average Return Time = 1 / # Accidents per Year Assumes that accidents are equally spaced, which they are not!!! Some would argue: It s an average and thus this evens out in the long run This would only be true if # Accidents per year is large, which does not apply to low probability high consequence events!!! 5/16/

76 SUPPLEMENT ANALYSIS - VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 Why did we not use average return times as risk metric of choice? Suppose you have multiple years of data Average Return Time = 1 / # Accidents per Year # Accidents per year Average Return Time Year months Year months Year months Average 3 6 months But: 1/3 year = 4 months Conclusion? 1/ Average (# Accidents per Year) < Average (Average Return Time) Both methods are used to evaluate average return times which only adds to confusion! 5/16/

77 SUPPLEMENT ANALYSIS - VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 Evaluating average return uncertainty Recall VTRA 2010 Maritime Simulation Model generated 1.8 Million Vessel to Vessel Traffic Situations per Year 10 Million Vessel to Shore Traffic Situations per Year Used VTRA 2010 Model to create table of following format Accident Probability per Traffic Situation POTENTIAL OIL LOSS VOLUME (m 3 ) CATEGORY ( ] ( ] (15000 or More) 1 e -10 N 1 N 2 N 3 1 e -9 N 4 N 5 N 6 1 e -8 N 7 N 8 N 9 5/16/

78 SUPPLEMENT ANALYSIS - VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 Evaluating average return uncertainty Accident Probability per Traffic Situation POTENTIAL OIL LOSS VOLUME (m 3 ) CATEGORY ( ] ( ] (15000 or More) 1 e -10 N 1 N 2 N 3 1 e -9 N 4 N 5 N 6 1 e -8 N 7 N 8 N 9 Recall coin Toss Analogy Probability of Tails Trials Sample # Accidents per year using Coin Toss Analogies Step 1 Set Average Return Time = 1/ # Accidents per year Step 2 Repeat Step 1 and Step 2 (2500 Samples) 5/16/

79 SUPPLEMENT ANALYSIS - VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 Explanation Average Return Time Statistics 1 Average Return Time Uncertainty Distribution [ ) Oil Spill Volume (in m 3 ) Category P: BASE CASE - ALL FOCUS VESSELS Cumulative Perecentage Median Mean 50% Credibility Range 25% Percentile % Percentile Average Return Time (in years) 5/16/

80 SUPPLEMENT ANALYSIS - VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 Average Return Time (Yrs) WI - SCEN VTRA 2010: ALL FOCUS VESSELS - Collision & Grounding ( ] P - BC R - KM348 P - BC R - KM348 ( ] P - BC R - KM348 ( ] P - BC R - KM348 ( ] P - BC R - KM348 ( ] P - BC R - KM348 ( ] P - BC R - KM348 ( More] UNCERTAINTY ANALYSIS AVERAGE RETURN TIMES BY SPILL SIZE CATEGORY ALL FOCUS VESSELS 5/16/ Comments for interpretation: 1. Spill Sizes are evaluated in cubic meters. 2. Average Return Time are evaluated in years. 3. Labels are median values of average return times. 4. Boxes provide 50% credibility range of average return times. 5. Average Return Time Uncertainty tends to increases with spill size. 6. Observe significant difference in average return times in the following spill size categories: ( ], ( ], ( ], (15000 More).

81 SUPPLEMENT ANALYSIS - VESSEL TRAFFIC RISK ASSESSMENT (VTRA) 2010 QUESTIONS? 5/16/