Transcript I.2 Examples To Illustrate DOE Concepts

I.2 Examples To Illustrate DOE Concepts
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1. Optimally Feeding Fish
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2. Targeting A Process/Reducing
Process Variation
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Response Surfaces
Sony USA versus Sony Japan
(Specs versus “Defects”)
3. Improving A Process
4. Weighing Two Objects
I.2 Examples To Illustrate DOE Concepts
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5. Baking Bread
6. Mitigating Noise Factors
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Using Interactions Between Noise Factors
and Control Factors To Robustify A
Process
7. Comparing Tires
Example 1
Fitted Response Surface - With Design Points
Example 2
Targeting a Process/Reducing Variation
Example 2
Accuracy versus Precision
Not Accurate
but
Precise
Accurate
and
Precise
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Not Accurate
and
Not Precise
Accurate
but
Not Precise
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Example 2
Sony USA vs Sony JAPAN
Distribution of The Color Density in T elevision Sets
T arget Value is
Sony USA
Sony Japan
LSL
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USL
Example 2
What is the enemy?
VARIATION (Nonuniformity of Product)
 Why isn't it just defects?
– Well, for example,
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1. What was tolerable this week may not be next
week if your competitor has reduced the variation
of their process.
2. Oftentimes the definition of a defect is that it
does not meet spec's. Since spec's are manmade,
they are subject to the frailties therein.
Example 2
Statistical Thinking
(Snee, 1990)
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Improvement Comes From Finding Out
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1.
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Where The Variation Is
What Kind Exists
How Much There Is
How It Can Be Reduced
Deming - Reduce Variation to Improve
Quality and the Process
 Taguchi - Design Product to Reduce
Functional Variation
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Example 3
Improving a Process
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Goal - Determine which factors affect the mean of the
process and which ones affect the variation.
LOOK FOR (UNUSUAL) PATTERNS IN THE DATA
Example 3
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Which Factors Affect
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Improving a Process
Accuracy?
Precision?
1
2
Example 4
Weighing Two Objects
(Hotelling via Daniel)
M=A+E
 M  Measured Weight
 E Error
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Example 4
Weighing Two Objects
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Description Of The Problem:
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You Have Two Objects To Weigh On A Counter
Balance Scale.
What Are Some Different Ways That You Weigh The
Objects And Still Be Able To Calculate The Weights?
What Is The Best Way To Do It If You Are Only
Allowed Two Weighings (Best So That The Error Of
The Measured Weight Is Made As Small As Possible)?
Example 4
Hidden Replication
o
With A Properly Designed Experiment You
Can Make The Data Work Twice For You.
Example 5
Baking Bread
o
Here We Use Design Principles To
Discover What Factors In A Bread Recipe
Affect Some Responses Of Interest. Two
Designs Are Considered. The First Is
When The Factors Are Changed One At A
Time (OAT). The Second Design Is A
Factorial Design.
Example 5
Factors and Responses
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Factors
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A. Cake (-) or Dry (+)
Yeast
B. Water Temp
(Hi = +, Lo = -)
C. Amount of Sugar
(Two Levels -,+)
Example 5
Factors and Responses
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Responses (Yes or No)
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1. How Well Did Yeast Proof
(Froth Doubles Volume)
2. Rises Adequately
(Doubles Volume Within An
Hour)
3. Second Rising Is Adequate
Example 5
OAT Design
Example 5
OAT Design Responses
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What Factors Affect
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Response 1?
Response 2?
Response 3?
Example 5
Factorial Design
Example 5
Factorial Design Responses
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What Factors Affect
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Response 1?
Response 2?
Response 3?
Example 5
Detecting Interactions
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From The First Design, We Discovered
That Factor B Affected Response 1 And
That Factor C Affected Response 2. But,
Because It Was A OAT Design, We Could
Not Pick Up On The Interaction Between
Factors A And C Which Affected Response
3. But It Was Detected By The Factorial
Design.
Example 6
Mitigating Noise Factors
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Factors
 Machines 10 (+) and 16 (-)
 Treatment
 Silicone
 Operators
 Estella (-)
 Donald (+)
Response
 Number of picks (snags)
Example 6
Cube Plot
What Can We Learn From This Plot?
27
10
6
4
2
Machine
11
1
Donald
16
1
1
No
Silicone Treatment
Operator
Estella
Yes
Example 7
Comparing Tires
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Which of the two designs on the
next slide is more appropriate for
comparing four brands of tires?
Why?
Example 7
Comparing Tires
DESIGN 1
Tire Position
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II
III
IV
Car
1
a
b
c
d
2
b
a
d
c
3
a
b
c
d
4
b
a
d
c
a
b
c
d
b
a
d
c
c
d
a
b
d
c
b
a
DESIGN 2
I
II
III
IV