1. Fuel Cell Systems Engineering, F06 Fuel Cell Systems Engineering Lecture 7 Quantitative Decision Methods

2. Fuel Cell Systems Engineering, F06 Topics Discussion of individual assignment Review questions on OTC solicitation. Review Paladin LOA Discuss quantitative decision making process, Multi-Attribute Utility Theory, (MAUT) Group activities.

3. Fuel Cell Systems Engineering, F06 Questions on OTC Solicitation Is methanol as a fuel a design constraint? Is 250 W or 300 W the specified output?

4. Fuel Cell Systems Engineering, F06 How Do You Decide on a Course of Action? Let the Boss make the decision Take a vote Roll the dice Consult the Ouija board OR Use a quantitative decision making method to determine the “Best Technical Approach”

5. Fuel Cell Systems Engineering, F06 The Challenge Because the decision variables are many and varied, we need a method to “normalize” the ratings to some common basis. Examples: power in watts, mission duration in hours, efficiency in %, weight in pounds, etc. The concept of evaluating the Utility of various alternatives allows us to do that.

6. Fuel Cell Systems Engineering, F06 Utility of Alternative a i The utility of an alternative equals the weighted sum of the utilities of individual attributes. U(a i )=w 1 U 1 (a i )+w 2 U 2 (a i )+…+ w n U n (a i ) OR n U(a i )=Σw j U j (a i ) j=1

7. Fuel Cell Systems Engineering, F06 Multi-Attribute Utility Theory Identify Performance Attributes Identify Hierarchy of Attributes Establish Utility vs. Performance Curves for Attributes Establish Relative Importance Among Attributes Identify Alternatives and Related Performance for Each Attribute Evaluate Multiple Attribute Value Scores Conduct Sensitivity Analysis

8. Fuel Cell Systems Engineering, F06 Identify Performance Attributes Select attributes with the highest degree of importance Include ALL attributes with high importance Insure attributes are independent (you can trade off one for the other) and mutually exclusive (one attribute does not include another)

9. Fuel Cell Systems Engineering, F06 Identify Performance Attributes (For Utility Vehicle) Speed (mph on HLS) Acceleration (sec, 0-30 mph) Fuel Economy (mpg) Ground Clearance (in) Entrance Angle (degrees)Exit Angle (degrees) Ground Pressure (psi)Weight (lb)Payload (lb) Max Gradeability (degrees) Side Slope (degrees)Range (miles)

10. Fuel Cell Systems Engineering, F06 Identify Hierarchy of Attributes Are there logical groupings of related attributes? Create a tree of attributes to facilitate easier identification of relative importance

11. Fuel Cell Systems Engineering, F06 Identify Hierarchy of Attributes (For Utility Vehicle) Speed (mph on HLS) Acceleration (sec, 0-30 mph) Fuel Economy (mpg)Ground Clearance (in) Off-road Mobility Entrance Angle (degrees) Exit Angle (degrees) Ground Pressure (psi) Weight (lb) Payload (lb) Max Gradeability (degrees)Side Slope (degrees) Range (miles) Performance

12. Fuel Cell Systems Engineering, F06 Establish Utility vs. Performance Curves for Attributes 0 1 Utility (a j ) Performance Typical shapes of utility curves relate to level of risk that the decision maker is willing to accept.

13. Fuel Cell Systems Engineering, F06 Establish Utility vs. Performance Curves for Attributes Ground Clearance (in) 10 12 14 16 18 1.0 0.5 0 Utility 1.0 0.5 0 Acceleration (sec, 0-30 mph) 8 9 10 11 12

14. Fuel Cell Systems Engineering, F06 Establish Relative Importance Among Attributes Methods –Survey of potential customers –Direction from “the boss” –Voting methods –Established in user requirements –Allocate 100 points

15. Fuel Cell Systems Engineering, F06 Establish Relative Importance Among Attributes Off-road mobility(40) –Entrance angle.15 –Exit angle.15 –Side slope.25 –Ground Clearance.30 –Ground Pressure.15 Performance(35) –Speed.10 –Acceleration.30 –Gradeability.20 –Fuel economy.15 –Range.25 Weight(10) Payload(15)

16. Fuel Cell Systems Engineering, F06 Identify Alternatives and Related Performance for Each Attribute Alternatives should be unique Performance levels may be established by analysis, testing, system specifications, or based on similar systems An iterative process

17. Fuel Cell Systems Engineering, F06 Evaluate Multiple Attribute Value Scores U(a 1 ) = W 1 U 1 (a 1 ) +W 2 U 2 (a 1 ) + …… U(a 2 ) = W 1 U 1 (a 2 ) +W 2 U 2 (a 2 ) + …… U(a 3 ) = W 1 U 1 (a 3 ) +W 2 U 2 (a 3 ) + ……

18. Fuel Cell Systems Engineering, F06 Conduct Sensitivity Analysis Are overall scores of two or more alternatives close? Will a slight change in the rating of one attribute result in a significant change in the relative rankings of alternatives? Re-assess ratings scheme and identify any additional discrimators.

19. Fuel Cell Systems Engineering, F06 Additional Sources Sage & Armstrong, Introduction to Systems Engineering, Wiley, 2000