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 Matrix5 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 LengthID
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 DiameterID
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 WeightID
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 1550 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
Indifferent

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
0.249=

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 0.52V1
(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