Utility Model for Minimizing Risk
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Utility Model for Minimizing Risk Utility Model for Minimizing Risk
Chandru MirchandaniChandru Mirchandani
Lockheed-MartinLockheed-Martin
August 9, 2004August 9, 2004
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IntroductionIntroduction
To meet…To meet…• System ObjectivesSystem Objectives
Develop a Model to accept…Develop a Model to accept…• Reduced CapabilityReduced Capability• Alternatives for ImplementationAlternatives for Implementation
By developing a Utility Model….By developing a Utility Model….
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Problem StatementProblem Statement
Requirement: Display sensor data in Requirement: Display sensor data in near-real timenear-real time
Constraints: Within Cost and Constraints: Within Cost and Schedule and acceptable QualitySchedule and acceptable Quality
Information: Uncertain…to make a Information: Uncertain…to make a selection with lowest risk of failureselection with lowest risk of failure
Solution………...Utility ModelSolution………...Utility Model
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Conceptual FrameworkConceptual Framework
Develop Criteria for System Develop Criteria for System AcceptanceAcceptance
Rank Attributes in order of Rank Attributes in order of preferencepreference
Evaluate Attributes with respect to Evaluate Attributes with respect to meeting objectives meeting objectives
Quantify evaluations based on Quantify evaluations based on measurable metricsmeasurable metrics
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Option 1Option 1
Software solution to extract and display Software solution to extract and display data……..data……..
S1
S5
S4
S3
S1 = Data SourceS1 = Data Source S2 = Ingest SystemS2 = Ingest System S3 = Storage SystemS3 = Storage System S4 = Data Processor S4 = Data Processor
(S4-A)(S4-A) S5 = Data Display S5 = Data Display
Processor (S5-A)Processor (S5-A)
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Option 2Option 2
Hardware solution to extract data and Hardware solution to extract data and Software solution to display data……..Software solution to display data……..
S1
S5
S4
S3
S1 = Data SourceS1 = Data Source S3 = Storage SystemS3 = Storage System S4 = Data Processor S4 = Data Processor
(S4-B)(S4-B) S5 = Data Display S5 = Data Display
Processor (S5-B)Processor (S5-B)
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Option 3Option 3
Hardware solution to extract data and Hardware solution to extract data and display data……..display data……..
S1 = Data SourceS1 = Data Source S3 = Storage SystemS3 = Storage System S4 = Data Processor S4 = Data Processor
(S4-B)(S4-B) S5 = Data Display S5 = Data Display
Processor (S5-B)Processor (S5-B)
S1
S5
S4
S3
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MethodologyMethodology
Select weighting for the success or failure Select weighting for the success or failure criteria based on criticalitycriteria based on criticality
Evaluate cost based on Re-Engineering, Evaluate cost based on Re-Engineering, Implementation and ScheduleImplementation and Schedule
Evaluate cost of failure based on Loss of Evaluate cost of failure based on Loss of Performance and RequirementsPerformance and Requirements
Evaluate the Probability of Success and Evaluate the Probability of Success and FailureFailure
Factor in the Uncertainty in EvaluationFactor in the Uncertainty in Evaluation
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MetricsMetrics
Expected Value of SuccessExpected Value of Success
Constraint Attributes Factors Option 1 (S)
Option 2 (Y)
Option 3 (H)
Application x1 6 6 7 Performance x2 4 6 9
Cost & Sched Constant
Technology Success
Cost x3 5 5 5 Implementation x4 5 5 5 Tech & Sched
constant Cost
Re-engineering x5 3 5 7 Implementation x6 5 5 6 Cost & Tech
constant Schedule
Re-engineering x7 4 6 8 Value of Success 33 40 50 Average Value of Success V(x) 0.471 0.571 0.714
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Decision TreeDecision Tree
SgYgHg
SgYgHb
SgYbHg
SgYbHb
SbYgHg
SbYgHb
SbYbHg
SbYbHb
Ss
Sf Ys
YfHs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
SgYgHg
SgYgHb
SgYbHg
SgYbHb
SbYgHg
SbYgHb
SbYbHg
SbYbHb
Ss
Sf Ys
YfHs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Ys
Yf
Ss
Sf
Hs
Hf
S
H
Y
Decision Point
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UncertaintyUncertainty
Uncertainty in how ‘good’ or ‘bad’ is the Uncertainty in how ‘good’ or ‘bad’ is the evaluationevaluation
Probability of Success or Failure based on Probability of Success or Failure based on the Uncertaintythe Uncertainty
Success based on Probability of
Good Evaluation
Failure based on Probability of
Good Evaluation
Success based on Probability of Bad Evaluation
Failure based on Probability of
Bad Evaluation
Option S Sgs = 0.9 Sgf = 0.1 Sbs= 0.1 Sbf= 0.9 Option Y Ygs= 0.7 Ygf= 0.3 Ybs= 0.3 Ybf= 0.7 Option H Hgs= 0.5 Hgf= 0.5 Hbs= 0.5 Hbf= 0.5
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Value FunctionValue Function
Based on Success of the OptionBased on Success of the OptionIf Option S is successful……If Option S is successful……
Value (S) = w(x1 + x2+ x3+ x4+ x5+ x6+ x7)/7 = SsValue (S) = w(x1 + x2+ x3+ x4+ x5+ x6+ x7)/7 = Ss
If Option S Fails………..If Option S Fails………..Value (F) = 1 - w(x1 + x2+ x3+ x4+ x5+ x6+ x7)/7 = SfValue (F) = 1 - w(x1 + x2+ x3+ x4+ x5+ x6+ x7)/7 = Sf
…………………….together with metrics.together with metrics
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MeasuresMeasures Cost of SuccessCost of Success = = CCssss
= = 8T + 30(C+T)8T + 30(C+T) Cost of FailureCost of Failure = = REREsfsf(p,r,c,t) = X(p,r,c,t) = Xsfsf(C+T)(C+T)
= 0.529(C+T)= 0.529(C+T)
Tasks Option 1 (S) Option 2 (Y) Option 3 (H) Requirements(t) R T R T R T Allocations(t) As T Ay T Ah T Analysis(t) ANs 2T ANy 2T ANh 2T Design(c,t) Ds 10(C+T) Dy 7(C+T) Dh 5(C+T) Development(c,t) Dvs 10(C+T) Dvy 7(C+T) Dvh 5(C+T) Implementation(c,t) Is 10(C+T) Iy 7(C+T) Ih 5(C+T) Verification(t) Vs 2T Vy 2T Vh 2T Re-Engineering(p,r,c,t) REs REy REh Validation(t) Vds 2T Vdy 2T Vdh 2T
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Utility FunctionUtility Function
For Option A:For Option A:SS = U(x1, x2, x3, x4, x5, x6, x7) = Css
= 8T + 30(C+T)
and,
SF = U(x1, x2, x3, x4, x5, x6, x7) + REsf(p,r,c,t)
= Css + REsf(p,r,c,t)
= 8T + 30(C+T) + Xsf(C+T)
= 8T + 30(C+T) + 0.529(C+T)
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Decision ProcessDecision Process
SgYgHg SgYgHg = Probability of Options 1, 2 and 3 all = Probability of Options 1, 2 and 3 all being correctly evaluated being correctly evaluated
P(success with S|Sg)P(success with S|Sg)
==
= 0.62 = 0.62
)().|()().|(
)().|(
failureSPfailureSSPsuccessSPsuccessSSP
successSPsuccessSSP
gg
g
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Decision TableDecision TableDecision Point 3
Minimum of Probability x Decision
Point 2 Probability 2
Decision Point 2 Minimum of Minimums
Decision Point 1 Minimum of
Probability x Utility Probability 1 Utility
0.62 Ss0.38 Sf0.70 Ys
SgYgHg 0.15 0.40 Yf0.93 Hs0.07 Hf
0.62 Ss0.38 Sf0.70 Ys
SgYgHb 0.24 0.40 Yf0.58 Hs0.42 Hf
0.62 Ss0.38 Sf0.30 Ys
SgYbHg 0.11 0.60 Yf0.93 Hs0.07 Hf
Decision
0.62 Ss0.38 Sf0.30 Ys
SgYbHb 0.18 0.60 Yf0.58 Hs0.42 Hf
0.15 Ss0.85 Sf0.70 Ys
SbYgHg 0.07 0.40 Yf0.93 Hs0.07 Hf
0.15 Ss0.85 Sf0.70 Ys
SbYgHb 0.11 0.40 Yf0.58 Hs0.42 Hf
0.15 Ss0.85 Sf0.30 Ys
SbYbHg 0.05 0.60 Yf0.93 Hs0.07 Hf
0.15 A0.85 Af0.30 B
SbYbHb 0.08 0.60 Bf0.58 C0.42 Cf
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Utility FunctionUtility Function
At each node in the tree, the Decision At each node in the tree, the Decision Maker selects the minimaMaker selects the minima
Finally at the Decision Point the optimal Finally at the Decision Point the optimal choice is quantitatively providedchoice is quantitatively provided
Options Utility Function S Success | Good/Bad Evaluation 8T + 30(CT) S Failure | Good/Bad Evaluation 8T + 30(CT) + 0.529(C+T) Y Success | Good/Bad Evaluation 8T + 21(CT) Y Failure | Good/Bad Evaluation 8T + 21(CT) + 0.429(C+T) H Success | Good/Bad Evaluation 8T + 15(CT) H Failure | Good/Bad Evaluation 8T + 15(CT) + 0.286(C+T)
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SummarySummary
Tree can be expanded to Tree can be expanded to accommodate more optionsaccommodate more options
Framework can be expanded to Framework can be expanded to include intermediate decision pointsinclude intermediate decision points
Decision points can be analyzed in a Decision points can be analyzed in a dependent mannerdependent manner
Re-evaluation at a node can be Re-evaluation at a node can be enhanced using additional attributesenhanced using additional attributes
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