Utility Model for Minimizing Risk Chandru Mirchandani Lockheed-Martin August 9, 2004 P115/MAPLD2004...

Utility Model for Minimizing Risk Utility Model for Minimizing Risk

Chandru MirchandaniChandru Mirchandani

Lockheed-MartinLockheed-Martin

August 9, 2004August 9, 2004

P115/MAPLD2004P115/MAPLD2004MIRCHANDANIMIRCHANDANI 11

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….

P115/MAPLD2004P115/MAPLD2004MIRCHANDANIMIRCHANDANIMIRCHANDANIMIRCHANDANI 22

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


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


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)


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)


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


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


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


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


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


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


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


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)


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


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


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)


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


Utility Model for Minimizing Risk Chandru Mirchandani Lockheed-Martin August 9, 2004 P115/MAPLD2004...

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