I.2 Examples To Illustrate DOE Concepts

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I.2 Examples To Illustrate DOE Concepts

• 1. Optimally Feeding Fish
• Response Surfaces
• 2. Targeting A Process/Reducing Process
  Variation
• Sony USA versus Sony Japan(Specs versus
  Defects)
• 3. Improving A Process
• 4. Weighing Two Objects

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I.2 Examples To Illustrate DOE Concepts

• 5. Baking Bread
• 6. Mitigating Noise Factors
• Using Interactions Between Noise Factors and
  Control Factors To Robustify A Process
• 7. Comparing Tires

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Example 1Fitted Response Surface - With Design
Points
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Example 2Targeting a Process/Reducing Variation
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Example 2Accuracy versus Precision
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Example 2Sony USA vs Sony JAPAN
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Example 2What is the enemy?

• VARIATION (Nonuniformity of Product)
• Why isn't it just defects?
• Well, for example,
• 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.

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Example 2Statistical Thinking(Snee, 1990)

• Improvement Comes From Finding Out
• 1. Where The Variation Is
• 2. What Kind Exists
• 3. How Much There Is
• 4. 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 3Improving a Process

• Goal - Determine which factors affect the mean of
  the process and which ones affect the variation.
• LOOK FOR (UNUSUAL) PATTERNS IN THE DATA

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Example 3Improving a Process

• Which Factors Affect
• Accuracy?
• Precision?

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Example 4Weighing Two Objects(Hotelling via
Daniel)

• M A E
• M ? Measured Weight
• E ??Error

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Example 4Weighing Two Objects

• Description Of The Problem
• 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)?

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Example 4Hidden Replication

• With A Properly Designed Experiment You Can Make
  The Data Work Twice For You.

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Example 5Baking Bread

• 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.
  

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Example 5Factors and Responses

• Factors
• A. Cake (-) or Dry () Yeast
• B. Water Temp (Hi , Lo -)
• C. Amount of Sugar (Two Levels -,)

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Example 5Factors and Responses

• Responses (Yes or No)
• 1. How Well Did Yeast Proof (Froth Doubles
  Volume)
• 2. Rises Adequately(Doubles Volume Within An
  Hour)
• 3. Second Rising Is Adequate

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Example 5OAT Design
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Example 5OAT Design Responses

• What Factors Affect
• Response 1?
• Response 2?
• Response 3?

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Example 5Factorial Design
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Example 5Factorial Design Responses

• What Factors Affect
• Response 1?
• Response 2?
• Response 3?

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Example 5Detecting Interactions

• 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.

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Example 6Mitigating Noise Factors

• Factors
• Machines 10 () and 16 (-)
• Treatment
• Silicone
• Operators
• Estella (-)
• Donald ()
• Response
• Number of picks (snags)

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Example 6Cube PlotWhat Can We Learn From This
Plot?
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Example 7Comparing Tires

• Which of the two designs on the next slide is
  more appropriate for comparing four brands of
  tires?
• Why?

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Example 7Comparing Tires
DESIGN 1 Car
Tire
Position 1 2 3 4 I a b a b II b a b a III c d c
d IV d c d c DESIGN 2 I a b c d II b a d c I
II c d a b IV d c b a