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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 1 Fitted Response Surface - With Design Points

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Example 2 Targeting a Process/Reducing Variation

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Example 2 Accuracy versus Precision

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Example 2 Sony USA vs Sony JAPAN

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Example 2 What 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 2 Statistical 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 3 Improving 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 3 Improving a Process Which Factors Affect – Accuracy? – Precision?

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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 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 4 Hidden Replication o With A Properly Designed Experiment You Can Make The Data Work Twice For You.

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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.

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Example 5 Factors and Responses Factors – A. Cake (-) or Dry (+) Yeast – B. Water Temp (Hi = +, Lo = -) – C. Amount of Sugar (Two Levels -,+)

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Example 5 Factors 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 5 OAT Design

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Example 5 OAT Design Responses What Factors Affect – Response 1? – Response 2? – Response 3?

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Example 5 Factorial Design

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Example 5 Factorial Design Responses What Factors Affect – Response 1? – Response 2? – Response 3?

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Example 5 Detecting 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 6 Mitigating Noise Factors Factors Machines 10 (+) and 16 (-) Treatment Silicone Operators Estella (-) Donald (+) Response Number of picks (snags)

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Example 6 Cube Plot What Can We Learn From This Plot?

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Example 7 Comparing 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 7 Comparing Tires DESIGN 1 Car Tire Position1234 Iabab IIbaba IIIcdcd IVdcdc DESIGN 2 Iabcd IIbadc IIIcdab IVdcba

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1.Basic Principles & Definitions 2.The Advantage 3.Two-Factorial Design 4.Number of Replicates 5.General Factorial Design 6.Response Surfaces & Contour.

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