Utility Model for Minimizing Risk

1
Utility Model for Minimizing Risk

• Chandru Mirchandani
• Lockheed-Martin
• August 9, 2004

MIRCHANDANI
P115/MAPLD2004
1
2
Introduction

• To meet
• System Objectives
• Develop a Model to accept
• Reduced Capability
• Alternatives for Implementation
• By developing a Utility Model.

MIRCHANDANIMIRCHANDANI
P115/MAPLD2004
2
3
Problem Statement

• Requirement Display sensor data in near-real
  time
• Constraints Within Cost and Schedule and
  acceptable Quality
• Information Uncertainto make a selection with
  lowest risk of failure
• Solution...Utility Model

MIRCHANDANI
P115/MAPLD2004
3
4
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

MIRCHANDANI
P115/MAPLD2004
4
5
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)

MIRCHANDANI
P115/MAPLD2004
5
6
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)

MIRCHANDANI
P115/MAPLD2004
6
7
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)

MIRCHANDANI
P115/MAPLD2004
7
8
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

MIRCHANDANI
P115/MAPLD2004
8
9
Metrics

• Expected Value of Success

MIRCHANDANI
P115/MAPLD2004
9
10
Decision Tree
Decision Point
MIRCHANDANI
P115/MAPLD2004
10
11
Uncertainty

• Uncertainty in how good or bad is the
  evaluation
• Probability of Success or Failure based on the
  Uncertainty

MIRCHANDANI
P115/MAPLD2004
11
12
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

MIRCHANDANI
P115/MAPLD2004
12
13
Measures

• Cost of Success Css
• 8T 30(CT)
• Cost of Failure REsf(p,r,c,t) Xsf(CT)
• 0.529(CT)

MIRCHANDANI
P115/MAPLD2004
13
14
Utility Function

• For Option A
• SS U(x1, x2, x3, x4, x5, x6, x7) Css
• 8T 30(CT)
• and,
• SF U(x1, x2, x3, x4, x5, x6, x7)
  REsf(p,r,c,t)
• Css REsf(p,r,c,t)
• 8T 30(CT) Xsf(CT)
• 8T 30(CT) 0.529(CT)

MIRCHANDANI
P115/MAPLD2004
14
15
Decision Process

• SgYgHg Probability of Options 1, 2 and 3 all
  being correctly evaluated
• P(success with SSg)
• 0.62

MIRCHANDANI
P115/MAPLD2004
15
16
Decision Table
MIRCHANDANI
P115/MAPLD2004
16
17
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

MIRCHANDANI
P115/MAPLD2004
17
18
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

MIRCHANDANI
P115/MAPLD2004
18