1. 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

2. 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

3. Example 1 Fitted Response Surface - With Design Points

4. Example 2 Targeting a Process/Reducing Variation

5. Example 2 Accuracy versus Precision

6. Example 2 Sony USA vs Sony JAPAN

7. 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.

8. 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

9. 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

10. Example 3 Improving a Process  Which Factors Affect – Accuracy? – Precision?

11. Example 4 Weighing Two Objects (Hotelling via Daniel)  M = A + E  M  Measured Weight  E  Error

12. 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)?

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

14. 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.

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

16. 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

17. Example 5 OAT Design

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

19. Example 5 Factorial Design

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

21. 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.

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

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

24. Example 7 Comparing Tires  Which of the two designs on the next slide is more appropriate for comparing four brands of tires?  Why?

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