# Fuel Cell Systems Engineering

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```					 Fuel Cell Systems Engineering

Lecture 7
Quantitative Decision Methods

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

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?

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”

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.
Fuel Cell Systems Engineering, F06
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

n

U(ai)=ΣwjUj(ai)
j=1

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

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)
Fuel Cell Systems Engineering, F06
Identify Performance Attributes
(For Utility Vehicle)

Speed (mph on HLS)                Max Gradeability (degrees)    Fuel Economy (mpg)

Side Slope (degrees)        Range (miles)

Acceleration (sec, 0-30 mph)                            Ground Clearance (in)

Entrance Angle (degrees)                              Exit Angle (degrees)

Ground Pressure (psi)               Weight (lb)              Payload (lb)

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

Fuel Cell Systems Engineering, F06
Identify Hierarchy of Attributes
(For Utility Vehicle)

Entrance Angle (degrees)              Speed (mph on HLS)                Payload (lb)

Exit Angle (degrees)                  Acceleration (sec, 0-30 mph)

Side Slope (degrees)                  Max Gradeability (degrees)

Ground Clearance (in)                 Fuel Economy (mpg)

Ground Pressure (psi)                 Range (miles)

Fuel Cell Systems Engineering, F06
Establish Utility vs. Performance
Curves for Attributes

1                       Typical shapes of
utility curves relate
to level of risk that
the decision maker
Utility (aj)

is willing to accept.

0

Performance

Fuel Cell Systems Engineering, F06
Establish Utility vs. Performance
Curves for Attributes

1.0                                             1.0

Utility
Utility

0.5                                             0.5

0                                                0

10    12     14     16     18                   8     9   10     11    12

Ground Clearance (in)                      Acceleration (sec, 0-30 mph)

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

Fuel Cell Systems Engineering, F06
Establish Relative Importance
Among Attributes
–   Entrance angle                      .15
–   Exit angle                          .15
–   Side slope                          .25
–   Ground Clearance                    .30
–   Ground Pressure                     .15
• Performance                        (35)
–   Speed                               .10
–   Acceleration                        .30
–   Fuel economy                        .15
–   Range                               .25
• Weight                             (10)

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

Fuel Cell Systems Engineering, F06
Evaluate Multiple Attribute Value
Scores
• U(a1) = W1U1(a1) +W2U2(a1) + ……
• U(a2) = W1U1(a2) +W2U2(a2) + ……
• U(a3) = W1U1(a3) +W2U2(a3) + ……

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

Fuel Cell Systems Engineering, F06
• Sage & Armstrong, Introduction to
Systems Engineering, Wiley, 2000

Fuel Cell Systems Engineering, F06

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