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Risk Management

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**Road Ahead Risk Management Process Cost and Schedule Risk**

Estimating Likelihood Mitigation Utility and Consequences Sensitivity Analysis

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

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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.

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Elementary Process Output Input Transformation Unknowns Uncertainty

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**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.

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**Risk Definitions Statistics: P[Undesirable Event]**

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

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**Consequences Can Impact:**

Technical Performance Key Performance Parameters Operational capability Supportability Schedule Cost The above are not mutually independent

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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

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**A Risk Reporting Matrix**

5 4 High Risk Moderate Risk Likelihood Level 3 2 Low Risk 1 1 2 3 4 5 Consequence Level

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**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

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**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

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**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

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**Risk Reporting Illustration**

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

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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.

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**Risk Management Functions**

Planning Resourcing Staffing Controlling

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**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

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**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

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**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.

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**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

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**Risk (Uncertain Event) Identification**

What can go wrong? If EVENT happens then CONSEQUENCE results Find everywhere Mr. Murphy can rear his ugly head!

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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)

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**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

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**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

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**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

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**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

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Example Schedule

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Uncertain Events? If Then

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**Example Guided Antitank Submunition**

Effectiveness: Dictates minimum number/carrier Carrier Vehicle Constrains length, diameter, and weight

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**Technical Performance Vector**

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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**Parameter – Time Relationship**

95 % Confidence Regions Tech Parameter Time

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

T = Elapsed Time

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Schedule and Cost Risk

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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

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**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

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**Decision Environments**

Certainty Uncertainty Risk

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**Probability Refresher**

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**Classical Interpretation**

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

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**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

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**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]

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

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**Theorem If A and B are two events in S then**

where is the common part of A and B

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

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**Conditional Probability**

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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.

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Expected Value Discrete Distribution Continuous Distribution

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**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”

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**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

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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?

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**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

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**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

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**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

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**Analysis of Bets (Cont’d)**

Expected Value At indifference EV should be the same

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

Indifferent

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**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

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**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

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**} } } Example Prefer lottery 2 Round 1 Prefer lottery 1**

Home in slowly. Check for consistency with probability axioms and theorems.

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**Continuous Probability Distributions**

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

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**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

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

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**Example Estimate time to get home from work Min 20 min F(t)=0.00**

Max 40 F(t)=0.95

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**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

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

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**Heuristics and Biases Representativeness Availability**

Anchoring and adjusting Motivational bias

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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

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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

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**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

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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

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**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

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Coherence All assessed probabilities MUST obey the laws of probability

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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

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**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

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**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

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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

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**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

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**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

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**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?

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**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?

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**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

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**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

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**Problem Need to find conditional probabilities for chance events**

Solution Total probability law Bayes’ theorem

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**Solution Total Probability Where: R=Relief S=Same I=Increase**

“R” denotes predict Relief, etc.

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Bayes’ Theorem

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**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

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**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

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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

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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

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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

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Utility Functions Tabular Math functions Graph

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Risk Attitudes

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**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

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**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

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Mixed Risk Attitude

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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

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**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:

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**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

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**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

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**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

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**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

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**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

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**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

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**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.

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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

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**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

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

0.249=

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**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)

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**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

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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)

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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

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**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

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Change Utility for $1.0M

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**Change in Probabilities**

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**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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