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Risk Management.

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1 Risk Management

2 Road Ahead Risk Management Process Cost and Schedule Risk
Estimating Likelihood Mitigation Utility and Consequences Sensitivity Analysis

3 Reference Material Risk Management Guide for DOD Acquisition, 6th Ed, Ver 1.0, August INCOSE Systems Engineering Handbook, Ver 3, INCOSE-TP , June, 2006, Chapter 7.3

4 Why Do We Care? Every change from a current state to a future state occurs as a result of a process. The future behavior of any process is affected by uncertainties. Management of the process requires consideration of these uncertainties to minimize their influence on the desired final outcome of the process.

5 Elementary Process Output Input Transformation Unknowns Uncertainty

6 Risk vs. Issues Risk refers to a future uncertain event.
If an event has occurred it is no longer uncertain. It becomes an issue or a problem. Management of either requires expenditure of resources.

7 Risk Definitions Statistics: P[Undesirable Event]
Risk Management: P[Undesirable Event] Plus the Consequences of the Event INCOSE considers both Undesirable and Desirable events

8 Consequences Can Impact:
Technical Performance Key Performance Parameters Operational capability Supportability Schedule Cost The above are not mutually independent

9 Risk Categories Technical Risk – A technical requirement may not be satisfied during the life cycle Cost Risk – Available budget may be exceeded Schedule Risk – May fail to reach Scheduled Milestones Programmatic Risk – Events beyond the control of the Program Manager

10 A Risk Reporting Matrix
5 4 High Risk Moderate Risk Likelihood Level 3 2 Low Risk 1 1 2 3 4 5 Consequence Level

11 Possible Risk Likelihood Criteria
Level Likelihood P[Occur] 1 Not Likely p< 0.10 2 Low Likelihood 0.10<=p<0.30 3 Likely 0.30<=p<0.70 4 Highly Likely 0.70<=p<0.90 5 Near Certainty 0.90<=p

12 Possible Consequence Level Criteria
Technical Performance Schedule Cost 1 None to Minimal 2 Can be tolerated Little program impact Slip< ? mo C< 1% of Budget 3 Moderate, Limited program impact Slip<? mo Subsys slip>? Mo 1%<=C<5% of Budget 4 Significant degradation, May jeopardize program Critical path affected 5%<=C<10% of Budget 5 Severe degradation, Will jeopardize program success Cannot meet key program milestones 10% of Budget <= C

13 Risk Criteria Depend on Program
Risk Level Criteria 1 P<0.0001 2 P<0.02 3 P<0.05 4 P<0.25 5 P>0.25

14 Risk Reporting Illustration
Risk Title (Category) Cause Mitigation Approach 5 4 Likelihood Level 3 2 1 1 2 3 4 5 Consequence Level

15 Risk Management A process to minimize the adverse effects of uncertain future events on the achievement of end state objectives. Basic Tasks: Identify and characterize process properties. Decide on a course of action to minimize adverse affects of events on program objectives. Implement and control the course of action.

16 Risk Management Functions
Planning Resourcing Staffing Controlling

17 Planning Define the strategy and process to be used
Establish a Risk Management Plan (RMP) Tasks Schedules Reviews Reporting Define the resources required People Funds Space and support resources

18 An Example RMP Format Summary
1. Introduction 2. Program Summary 3. Risk Management Strategy and Process 4. Responsible/Executing Organization 5. Risk Management Process and Procedures 6. Risk Identification 7. Risk Analysis 8. Risk Mitigation Planning 9. Risk Mitigation Implementation 10. Risk Tracking

19 Events May Cause RMP Update
A change in acquisition strategy, Preparation for a milestone decision, Results and findings from event–based technical reviews, An update of other program plans, Preparation for a Program Objective Memorandum submission, or A change in support strategy.

20 Risk Management Process
Planning Identify Uncertain Events Estimate P[Occur] Estimate Consequences Formulate Alternative Courses of Action No Evaluate Alternatives Choose Approach Execute and Track Working? OR Yes Continue or Stop

21 Risk (Uncertain Event) Identification
What can go wrong? If EVENT happens then CONSEQUENCE results Find everywhere Mr. Murphy can rear his ugly head!

22 What to Look At Current and proposed staffing, process, design, suppliers, concept of operation, resources, interfaces, interactions, etc. Test results and failures (especially readiness results) Potential Shortfalls Trends External Influences (programmatic, political)

23 Potential Root Causes of Risk Events
Need (Threat) Requirements Technical Baseline Test & Evaluation Modeling & Simulation Technology Logistics Production/Facilities Concurrency Industrial Capability Cost Management Schedule External Factors Budget Earned Value Realism

24 Possible Risk Management Actions
Avoid Redesign Change requirements Accept Control Expand resources Reduce likelihood and/or consequences Transfer By mutual agreement to party more qualified to mitigate

25 Interactions and Consequences
Schedule affects cost C = A +BT Budget constrains cost Forces B vs T tradeoff Schedule constraint affects cost Causes B increase Technology maturity and workforce skills affect all terms

26 Example:Program to modify an existing guided submunition
Current Characteristics Weight 20 kg Length 50 cm Diameter 15 cm Required Characteristics Weight 15 kg Length 40 cm Diameter 10 cm

27 Example Schedule

28 Uncertain Events? If Then

29 Example Guided Antitank Submunition
Effectiveness: Dictates minimum number/carrier Carrier Vehicle Constrains length, diameter, and weight

30 Technical Performance Vector
Element Required Current Length (L) 40 cm 50 cm Diameter (D) 10 cm 15 cm Weight (W) 15 kg 20 kg

31 Actions to Meet Requirements
Element Discrepancy Cause Corrective Action Length Use of discrete components Special chips Diameter Seeker antenna New detector Weight Discrete components, battery Reduce power requirements, use integrated circuits

32 Activities Required to Reduce Length
ID Description Time (Mo) Preceded by Expected Length A1 Analysis & Design 1 --- 50 A2 Breadboard Fabrication 2 A3 Test A4 Modify Breadboard 0.5 A5 Retest 43 A6 Admin Lead Time 1.5 A7 Develop Chips 3 A5, A6, C5 A8 Test Chips 40

33 Length Reduction Program
1.5 2.5 A1 1 A2 3 A3 4 A4 4.5 A5 5 A7 8 A8 9 1 2 1 0.5 0.5 3 1 From C5


35 Activities to Reduce Diameter
ID Description Time (Mo Preceded By Expected Diameter B1 Trade Offs 2 --- 15 B2 Subcontractor Lead Time 2.5 B3 Prototype design & Fab 5 B1, B2 13 B4 Prototype Test 1 B5 Redesign 3 B4, C5 B6 Retest 0.5 10

36 Diameter Reduction Program
From C5 B1 2 2 B3 7.5 B4 8.5 B5 11.5 B6 12 5 1 3 0.5 2.5 B2 2.5


38 Activities Required to Reduce Weight
ID Description Time (Mo) Preceded By Expected Weight C1 Trade Offs 2.5 --- 20 C2 Administrative Lead Time 1 C1, A1, B1, B2 C3 Design C4 Refine & Deliver C3, A3, B4 C5 Integrate & Test 1.5 17 C6 C7 Delivery 2 C8 15

39 Weight Reduction Program
From A1 From A3 2.5 4.5 C2 3.5 C4 5.5 C5 7 C6 8 C7 10 C1 C3 C8 2.5 1 1 1 1.5 1 2 12 2 From B1 From B2 From B4


41 Development Program A6 1.5 2.5 A1 1 A2 3 A3 4 A4 4.5 A5 5 A7 14 A8 15
50 43 40 1 2 1 0.5 0.5 3 1 11 D3 D1 D6 1 4 2.5 4.5 C2 3.5 C4 9.5 C5 11 C6 12 C7 14 C1 C3 20 17 C8 2.5 1 1 1 1.5 1 2 2 8.5 16 2.5 15 D2 D4 D5 B1 11 2 2 B3 7.5 B4 8.5 B5 14 B6 14.5 13 10 15 5 1 3 0.5 B2 2.5 2.5




45 Effect of Variability on Schedule
For the length reduction program: Average time to achieve 43 cm = 5 months 95% confidence band: 4.49 –5.51 months Assumes Normal Distribution of activity time and 10% coefficient of variation Activity time distributions are usually triangular (a,a,c) Moves mean and right tail to the right

46 Parameter – Time Relationship
95 % Confidence Regions Tech Parameter Time

47 Cost C = A + B*T C = Activity cost A = Fixed Cost B = Expenditure Rate
T = Elapsed Time


49 Schedule and Cost Risk

50 Summary All activities affecting the desired end result and their interactions must be considered. Network representation takes care of this Activities must be considered at a low enough level to permit reasonable accurate time estimates

51 Summary (cont’d) Cost for development programs is a function of time
There is variability in everything Variability can cause the critical path to change Plan for the occurrence of bad outcomes

52 Decision Environments
Certainty Uncertainty Risk

53 Probability Refresher

54 Classical Interpretation
N possibilities Equally likely One must occur S of N possibilities = event “success” P[success] =S/N

55 Frequency Interpretation
P[event] = proportion of the time event occurs over the long run Not very practical for situations that result in only one trial

56 Probability Axioms Consider sample space S for events A, B, C … in S.
0 ≤ P[A] ≤ 1 for all A in S P[S] = 1 If A and B are mutually exclusive, P[A B] = P[A or B or both] = P[A] + P[B]

57 Theorem If A is an event in finite S, and Ei, i = 1, 2, …n are events comprising A, then

58 Theorem If A and B are two events in S then
where is the common part of A and B

59 Total Probability If Bi , i = 1, 2, …n, are mutually exclusive events, then

60 Conditional Probability

61 Bayes’ Theorem If Bi , i = 1, 2, …n, are mutually exclusive events, then P[Bi] are prior, or “a priori” probabilities and must be determined prior to some experiment that results in event A based on the nature of the problem, data, experience, or subjectively based on experience.

62 Expected Value Discrete Distribution Continuous Distribution

63 Subjective Probability
Consider the following Events Flip a coin and let it hit the floor. Before looking at the coin, what is the probability it is “heads”? What is the probability that the coin flip before the 2009 Auburn/Alabama football game resulted in “tails”? Both events have occurred.The outcome is certain. The only uncertainty is in your mind; i.e., in your “degree of belief”

64 Subjective Probability Problems
Same phrase has different connotations with different people Interpretation is context dependent People are uncomfortable doing it There is no “correct” value

65 Example You and a friend disagree on P[Your team will win its next game]. Discussion of factors, home advantage, injuries, weather, etc., does not result in agreement. How do you resolve the disagreement?

66 Assessing Subjective Probabilities
Direct Inquiry Just make an estimate based on knowledge and perception May not be able to come up with a value May not have much confidence in the result Analysis of bets Comparison of Lotteries

67 Analysis of Bets Compare two bets Look for indifference point Example
LA Lakers vs Boston Celtics What do you think is P[Lakers Win] Bets Win X$ if LA wins, lose Y$ if LA loses Lose X$ if LA wins, win Y$ if LA loses

68 Analysis of Bets (Cont’d)
LA wins Procedure: Change X and Y until willing to take either bet. X Bet for LA LA loses -Y LA wins -X Bet Against LA Y LA loses

69 Analysis of Bets (Cont’d)
Expected Value At indifference EV should be the same

70 Example For LA Round 1 Against LA For LA Against LA Round 2 . Round n

71 Reference Lottery Lottery 1 Lottery 2 (Reference) Win A if LA wins
Win B if LA loses Lottery 2 (Reference) Win A with probability p Win B with probability 1-p

72 Reference Lottery (Cont’d)
LA wins Procedure: Change p until willing to take either bet. Outcome of lottery 2 is determined by a random process. Choose p, generate a random variate, x, from U(0,1) distribution. If x p then win A; otherwize, win B A Lottery 1 LA loses B p A Lottery 2 Reference B 1-p

73 } } } Example Prefer lottery 2 Round 1 Prefer lottery 1
Home in slowly. Check for consistency with probability axioms and theorems.

74 Continuous Probability Distributions
Strategies Direct assessment of p Fractile assessment of X Probability Distribution Function (Cumulative probability)

75 Direct Assessment Estimate range of values for x, xmin, xmax
Pick value xi : xmin < xi < xmax Estimate Repeat for a number of points (for 3 points pick mid range, then mid range of the two segments unless distribution is strongly skewed) Use Reference lottery approach to find indifference

76 Reference Lottery x<xi $1000 Lottery 1 x>xi $0 F(x) $1000

77 Example Estimate time to get home from work Min 20 min F(t)=0.00
Max 40 F(t)=0.95

78 Fractile Method Pick range values for x: xmin, xmax
Pick a number of fractiles F(x)=0.05 Min F(x)=0.95 Max F(x)=0.50 F(x)=0.25 F(x) =0.75 Note order Use Reference lottery to find indifference

79 Reference Lottery x<xi $1000 Lottery 1 x>xi $0 p $1000 Lottery 2

80 Heuristics and Biases Representativeness Availability
Anchoring and adjusting Motivational bias

81 Representativeness Judge that something or someone belongs to a particular category Stereotyping Insensitive to base rates and prior probabilities Unreliable information Failure to account for inherent uncertainty Misunderstanding random processes Regression to the mean Extreme outcomes likely to be followed by one closer to the mean

82 Availability Judge P[event] according to ease of recalling similar events Influenced by unbalanced reporting Illusory correlation – pair of events perceived as happening together frequently

83 Anchoring and Adjusting
Choose initial point then adjust about it Affects continuous distributions more that discrete probabilities If initially estimate median will tend to underestimate extremes so distribution is too narrow Estimate extremes first- the “worst” extreme before the other

84 Motivational Bias Incentives often exist that motivate person to report forecasts or probabilities that do not reflect their true beliefs Salesman forecasting sales Weather forecasters forecasting rain Program managers predicting lower cost, shorter schedule, and low risk

85 Decomposition Break problem down to make probability assessment easier
Permits using people with subject matter knowledge More likely to get a realistic estimate Look at fault tree analysis and hazard analysis Use laws of probability to reconstruct the problem Very important concept for planning and constructing mitigation efforts

86 Coherence All assessed probabilities MUST obey the laws of probability

87 Using Test Results Requirements are often placed on characteristics that are stochastic Reliability Accuracy Can use probability to estimate probability of not satisfying the requirement if test data exist Example: Impact accuracy of a projectile specified by the standard deviation of miss distance

88 Example Requirement: Data yield sample estimate S, sample size n where
Recall Then Look up alpha in a table or use the chidist(chi,dof) function in Excel to find Alpha=0.067 Alpha is the risk probability


90 Value of Information Information reduces uncertainty
Toss a pair of dice and do not look at result Estimate the probability that it is 7 If told it is not 5, does this change your estimate? Information has a cost and a worth Should never pay more than it is worth

91 Example* A new manufacturing process has been developed. It will cost $0.5M to implement. It will save $0.5M over investment if implemented by your current vender. There are two other vendors willing to implement the process, but both require some relief from EPA regulations in order to provide savings, which could be least double those offered by the current vendor. No relief offers savings, but not as great as keeping the current vendor. It is known the EPA is re-examining these regulations and could either provide relief, make no change, or increase the requirements. The current vendor is not impacted regardless of any changes. An increase will cause a loss by both of the other vendors which you must reimburse. * Based on an example in Making Hard Decisions, An introduction to Decision Analysis; PWS Kent, 1991; Robert T. Clemen

92 Payoffs EPA Action Vendor Relief P= 0.5 Same P= 0.3 Increase P=0.2 V1
$0.5 V2 $1.0 $0.2 -$0.1 V3 $1.5 $0.1 -$1.0

93 Decision Tree Structure
$0.5M V1 (0.5M) Relief 0.5 $1.0M V2 Same 0.3 $0.2M ($0.54M) Increase 0.2 -$0.1M Relief 0.5 V3 $1.5M ($0.58M) Same 0.3 $0.1M Increase 0.2 -$1.0M (xxx)=EMV

94 Dilema Highest expected saving is obtained by choosing Vendor 3
This choice also involves the highest potential loss Risk probability is 0.2 Risk consequence is -$1.0 M High Yellow How to mitigate?


96 Possible Actions Obtain Information Questions:
Re-estimate probabilities Hire knowledgeable consultant Knows for sure Probably knows Questions: What is information worth? How reliable is the consultant’s result?

97 Perfect Information EMVPI = $1.0M - $0.58M = $0.42M No Information
From previous analysis) V1 $0.5 Relief 0.5 ($ V2 $1.0 V3 $1.5 Perfect Information V1 $0.5 Same 0.3 ($1.0M) V2 $0.2 V3 $0.1 V1 $0.5 Increase 0.2 V2 -$0.1 V3 -$1.0 EMVPI = $1.0M - $0.58M = $0.42M (xxx)=EMV

98 Imperfect Information
? ($0.58M) Relief $1.5M V3 Same $0.1M Increase No Consultant -$1.0M Relief $1.0M “Relief” V2 Same $0.2M Increase -$0.1M V1 $0.5M Relief $1.5M V3 Same $0.1M Increase -$1.0M Relief $1.0M V2 Same “Same” $0.2M Increase Hire Consultant -$0.1M V1 $0.5M Relief $1.5M V3 Same $0.1M Increase -$1.0M Relief $1.0M V2 Same $0.2M “Increase” Increase -$0.1M V1 $0.5M (xxx)=EMV

99 Problem Need to find conditional probabilities for chance events
Solution Total probability law Bayes’ theorem

100 Solution Total Probability Where: R=Relief S=Same I=Increase
“R” denotes predict Relief, etc.

101 Bayes’ Theorem


103 Imperfect Information
Relief 0.8247 $1.5M V3 Same 0.0928 $0.1M Increase 0.0825 No Consultant -$1.0M Relief 0.8247 ($0.835M) $1.0M 0.0928 “Relief” V2 Same $0.2M 0.485 Increase 0.0825 -$0.1M V1 $0.5M Relief 0.1667 $1.5M ($0.187M) V3 Same 0.700 $0.1M Increase 0.1333 -$1.0M Relief 0.1667 ($0.293M) $1.0M V2 Same “Same” 0.700 $0.2M Hire Consultant 0.300 Increase 0.1333 -$0.1M V1 $0.5M ($0.822M) -($0.188) Relief 0.2326 $1.5M V3 Same 0.2093 $0.1M Increase 0.5581 -$1.0M EMVI=$0.822M-$0.580M=$0.242M ($0.219M) Relief 0.2326 $1.0M V2 Same 0.2093 $0.2M “Increase” Increase 0.5581 -$0.1M 0.215 V1 $0.5M (xxx)=EMV

104 Impact on Risk Probability of $1M loss reduced from 0.2 to 0.0825
Risk changed from high yellow to low level Can pay consultant up to $0.242M

105 Problem Using EMV may lead to solutions that may not be intuitively appealing Example: A1 Win $30, p=0.5 EMV = $14.50 Lose $1, p=0.5 A2 Win $2000, p=0.5 EMV = $500 Lose $1000, p=0.5 Choose A2 based on EMV What about Risk and Consequence? Would probably rather have A1

106 Reason EMV is valid for the long run; i.e., multiple occurrences of the chance event This is a one time event Ignores the range of possible outcomes Play 10 times Max loss A1 = $10 Max loss A2 = $20000

107 Solution Find a transformation of consequence into a utility measure, U Must accommodate attitude toward the risk/consequence combination Risk averse Risk taking Risk neutral

108 Utility Functions Tabular Math functions Graph

109 Risk Attitudes

110 Scenario Forced gamble Would you pay $x to get out of this gamble?
Win $500, p=0.5 Lose $500, p=0.5 Would you pay $x to get out of this gamble? If so, you are risk averse Examples Insurance Ransom

111 Comment Not everyone is risk averse
Many people are risk seeking over some range and risk averse over others Depends on wealth level (range of consequences) Risk attitudes are important in analyzing mitigation alternatives

112 Mixed Risk Attitude

113 Transformation Utility function transforms wealth (consequence) into a measure that accounts for risk attitude Certainty equivalent (CE) Gamble: Win $2000, p=0.5 EMV=$990 Lose $20, p=0.5 Offered $300 for the gamble. Ask $301, won’t accept $299 Then CE=$300 for this gamble If CE ~ EMV then U(CE)=EMV($) Can substitute U(x) for $x EMV – CE = Risk Premium

114 Utility Function Assessment CE Method
Fix min and max values of wealth Set U(min)=0, U(max)=1 Structure a lottery 0.5 min 0.5 max CE1 4. Find CE1. Then Example:

115 CE Method (Cont’d) 5. Pick another range, say CE1 – max
6. Structure a new lottery 0.5 CE1 0.5 max CE2 7. Set range 0 –CE1 8. Repeat 6. To obtain U(CE3) = 0.25 9. Stop or further subdivide the intervals 10. Either draw the curve or fit a function

116 Probability Equivalent (PE) Method
Fix max and min of wealth Set U(min) = 0, U(max) = 1 Pick CE: min < CE < max Structure lottery p min 1-p max CE 5. Find p: CE ~ p(min) + (1-p)(max) Then: 6. Repeat steps 3. – 5. For other values of CE

117 Risk Tolerance Consider the utility function R determines shape
Larger R -> Flatter function Smaller R -> more concave (risk averse) Hence, R depends on risk attitude

118 Determination of R Consider a lottery 0.5 Y A1 0.5 Y/2 A2
Find largest value of Y for which A1 > A2 R = Y To find CE, Find E(U) for the decision. Solve For x = CE

119 Caveats Utilities do not add U(A+B) = U(A)+U(B)
Utilities do not express strength of preference. They only provide a numerical scale for ordering preferences Utility functions are not the same person to person They are subjective and express personal preferences

120 Example Revisited $ U 1.5M 1.00 1.0M 0.86 0.5M 0.65 0.2M 0.52
Relief 0.5 $1.0M V2 Same 0.3 $0.2M ($0.54M) Increase 0.2 -$0.1M Relief 0.5 V3 $1.5M ($0.58M) Same 0.3 $0.1M Increase 0.2 -$1.0M

121 Utility Axioms Ordering and transitivity
Consider events A1, A2, A3. Then A1> A2, A2> A1, or A1~ A2 If A1> A2 and A2> A3, then A1> A3 Reduction of compound uncertain events A DM is indifferent between compound uncertain events (a complicated mix of gambles and lotteries) and a simple uncertain event as determined using standard probability manipulations.

122 Example 2 E1 0.17 5 A1 0.2 E4 10.3 0.5 E5 0.5 5 A2 E2 0.3 E6 E7 0.2 10.3 E3 E8 0.5 5 0.33 0.3 E9

123 Example Continued 2 E1 0.17 5 A1 E4 0.1=0.5*0.2 10.3 E5 0.25=0.5*0.5 5
0.15=0.5*0.3 A2 E7 0.066=0.33*0.2 10.3 E8 0.165=0.33*0.5 5 E9 0.099=0.33*0.3

124 Example Concluded 2 A1 0.166=0.10+0.066 10.3 A2 0.585=0.17+0.25+0.165

125 Axioms Continued Continuity Substitutability
A DM is indifferent between outcome A and an uncertain event with outcomes A1 and A2 where A1>A>A2. Hence we can construct a reference gamble with p(A1) and (1-p)(A2) such that the DM is indifferent between A and the gamble Substitutability A DM is indifferent between an uncertain event A and one found by substituting for A an equivalent uncertain event (gamble can be substituted for CE)

126 Axioms Continued Monotonicity Invariance Boundedness
Given two reference gambles having the same possible outcomes, a DM will prefer the one with higher probability of winning the preferred outcome. Invariance Only outcome payoffs and probabilities are needed to determine DM’s preferences Boundedness No outcomes are infinitely bad or infinitely bad

127 Comments There are some controversies and paradoxes regarding some of the axioms If you accept them then There exist U1, U2, … , Un (utilities) with associated payoffs such that the overall preference for uncertain events A and B can be determined by E(U) You should be using E(U) to make decisions (rational behavior)

128 Sensitivity Analysis To manage risk we need both probabilities and consequences Probabilities, utilities, and maybe consequences are likely subjective estimates Need to find out how much change will impact the decision

129 Example Problem Again $ U 1.5M 1.00 1.0M 0.86 0.5M 0.65 0.2M 0.52
V1 (0.5M) Relief 0.5 0.652 $1.0M 0.86 V2 Same 0.3 $0.2M 0.52 ($0.54M) Increase 0.2 -$0.1M 0.33 0.638 Relief 0.5 V3 $1.5M 1.00 ($0.58M) Same 0.3 $0.1M 0.46 Increase 0.2 -$1.0M 0.00

130 Change Utility for $1.0M

131 Change in Probabilities

132 Summary Risk management process Cost and schedule risk
Models Monte carlo simulation Estimation of likelihoods Analysis of mitigation alternatives Value of information Estimation of utility metrics EMV vs Expected utility Sensitivity analysis

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