Utility Model for Minimizing Risk Chandru Mirchandani Lockheed-Martin August 9, 2004 P115/MAPLD2004 MIRCHANDANI 1

Introduction  To meet… System ObjectivesSystem Objectives  Develop a Model to accept… Reduced CapabilityReduced Capability Alternatives for ImplementationAlternatives for Implementation  By developing a Utility Model…. P115/MAPLD2004 MIRCHANDANIMIRCHANDANI 2

Problem Statement  Requirement: Display sensor data in near-real time  Constraints: Within Cost and Schedule and acceptable Quality  Information: Uncertain…to make a selection with lowest risk of failure Solution………...Utility Model P115/MAPLD2004 MIRCHANDANI 3

Conceptual Framework  Develop Criteria for System Acceptance  Rank Attributes in order of preference  Evaluate Attributes with respect to meeting objectives  Quantify evaluations based on measurable metrics P115/MAPLD2004 MIRCHANDANI 4

Option 1  Software solution to extract and display data……..  S1 = Data Source  S2 = Ingest System  S3 = Storage System  S4 = Data Processor (S4-A)  S5 = Data Display Processor (S5-A) P115/MAPLD2004 MIRCHANDANI 5

Option 2  Hardware solution to extract data and Software solution to display data……..  S1 = Data Source  S3 = Storage System  S4 = Data Processor (S4-B)  S5 = Data Display Processor (S5-B) P115/MAPLD2004 MIRCHANDANI 6

Option 3  Hardware solution to extract data and display data……..  S1 = Data Source  S3 = Storage System  S4 = Data Processor (S4-B)  S5 = Data Display Processor (S5-B) P115/MAPLD2004 MIRCHANDANI 7

Methodology  Select weighting for the success or failure criteria based on criticality  Evaluate cost based on Re-Engineering, Implementation and Schedule  Evaluate cost of failure based on Loss of Performance and Requirements  Evaluate the Probability of Success and Failure  Factor in the Uncertainty in Evaluation P115/MAPLD2004 MIRCHANDANI 8

Metrics  Expected Value of Success P115/MAPLD2004 MIRCHANDANI 9

Decision Tree Decision Point P115/MAPLD2004 MIRCHANDANI 10

Uncertainty  Uncertainty in how ‘good’ or ‘bad’ is the evaluation  Probability of Success or Failure based on the Uncertainty P115/MAPLD2004 MIRCHANDANI 11

Value Function  Based on Success of the Option If Option S is successful…… Value (S) = w(x1 + x2+ x3+ x4+ x5+ x6+ x7)/7 = Ss If Option S Fails……….. Value (F) = 1 - w(x1 + x2+ x3+ x4+ x5+ x6+ x7)/7 = Sf ………….together with metrics P115/MAPLD2004 MIRCHANDANI 12

Measures  Cost of Success= C ss = 8T + 30(C+T)  Cost of Failure= RE sf (p,r,c,t) = X sf (C+T) = 0.529(C+T) P115/MAPLD2004 MIRCHANDANI 13

Utility Function For Option A: S S =U(x 1, x 2, x 3, x 4, x 5, x 6, x 7 ) = C ss =8T + 30(C+T) and, S F =U(x 1, x 2, x 3, x 4, x 5, x 6, x 7 ) + RE sf (p,r,c,t) = C ss + RE sf (p,r,c,t) =8T + 30(C+T) + X sf (C+T) =8T + 30(C+T) (C+T) P115/MAPLD2004 MIRCHANDANI 14

Decision Process SgYgHg = Probability of Options 1, 2 and 3 all being correctly evaluated P(success with S|Sg) = = 0.62 P115/MAPLD2004 MIRCHANDANI 15

Decision Table P115/MAPLD2004 MIRCHANDANI 16

Utility Function  At each node in the tree, the Decision Maker selects the minima  Finally at the Decision Point the optimal choice is quantitatively provided P115/MAPLD2004 MIRCHANDANI 17

Summary  Tree can be expanded to accommodate more options  Framework can be expanded to include intermediate decision points  Decision points can be analyzed in a dependent manner  Re-evaluation at a node can be enhanced using additional attributes P115/MAPLD2004 MIRCHANDANI 18