fuel cell systems engineering, f06 fuel cell systems engineering lecture 7 quantitative decision...

Fuel Cell Systems Engineering, F06

Fuel Cell Systems Engineering

Lecture 7

Quantitative Decision Methods


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.


Questions on OTC Solicitation

• Is methanol as a fuel a design constraint?

• Is 250 W or 300 W the specified output?


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”


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.


Utility of Alternative ai• The utility of an alternative equals the weighted

sum of the utilities of individual attributes.

U(ai)=w1U1(ai)+w2U2(ai)+…+ wnUn(ai)

OR

nU(ai)=ΣwjUj(ai)

j=1


Multi-Attribute Utility TheoryIdentify 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


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)


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)


Identify Hierarchy of Attributes

• Are there logical groupings of related attributes?

• Create a tree of attributes to facilitate easier identification of relative importance


Identify Hierarchy of Attributes(For Utility Vehicle)

Speed (mph on HLS)


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



0

1

Util

ity (

a j)

Performance

Typical shapes of utility curves relate to level of risk that the decision maker is willing to accept.



Ground Clearance (in)

10 12 14 16 18

1.0

0.5

0

Util

ity

Util

ity

1.0

0.5

0


8 9 10 11 12



• Methods– Survey of potential customers– Direction from “the boss”– Voting methods– Established in user requirements– Allocate 100 points



• 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)


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


Evaluate Multiple Attribute Value Scores

• U(a1) = W1U1(a1) +W2U2(a1) + ……

• U(a2) = W1U1(a2) +W2U2(a2) + ……

• U(a3) = W1U1(a3) +W2U2(a3) + ……


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.


Additional Sources

• Sage & Armstrong, Introduction to Systems Engineering, Wiley, 2000

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