2. &SixAdvanced Statistics_DOE11 實驗目的 : &13 DOE 簡介 對 y 影響最大的變數為 何？ 如何設定 x 1, x 2, …, x p 使 y 值趨近最佳值？ 如何設定 x 1, x 2, …, x p 使 y 值得變異最小？ 如何設定 x 1, x 2, …, x p 使不可控制因素 z 1, z 2, …, z p 之影響最小？

3. &SixAdvanced Statistics_DOE12 An Example ： Play Golf Objective: Lower score without much practicing. Response Variable: Score (per round) Possible Factors: The type of driver used (oversized or regular-sized) The type of ball used (balata or three-piece) Walking or riding in a golf cart Beverage Type (water or beer) Time (in the morning or afternoon) Weather (cool or hot, windy or calm) The type of golf shoe spike (metal or soft)

4. &SixAdvanced Statistics_DOE13 一般實驗進行方式 Best-guess approach No Good, Guess Again Switching the levels of one (perhaps two) factors for the next test based on the outcome of the current test Good Enough, Stop! On-factor-at-a-time Selecting a baseline starting point Varying each factor over its range with the other factors held constant at the baseline level Interactions ruin everything

5. &SixAdvanced Statistics_DOE14 最佳因子水準組合為？ Driver: Regular Mode of travel: Ride Beverage: Water But what if………………… Results of the one-factor-a-time strategy for the golf experiment

6. &SixAdvanced Statistics_DOE15 The two-factor factorial design for the golf experiment (I)

7. &SixAdvanced Statistics_DOE16 The two-factor factorial design for the golf experiment (II) Ball Effect = ？ Ball-Driver Interaction Effect = ？

8. &SixAdvanced Statistics_DOE17 Other Designs for the Golf Experiment Four-factor factorial design Three-factor factorial design

9. &SixAdvanced Statistics_DOE18 Other Designs for the Golf Experiment Four-factor fractional factorial design

10. &SixAdvanced Statistics_DOE19 實驗計劃法 (DOE) 在一個或連串的試驗中刻意地改變製程輸入參數值, 以 便觀察並找出影響製程輸出變數之因素. 應用 : 改進製程產出率 降低製程變異, 改善產品品質 降低研發時間 降低總體成本 評估各種可行之設定值 評估各替代原料 確定影響產品特性之因素

11. &SixAdvanced Statistics_DOE110 Example: Optimizing a Process

12. &SixAdvanced Statistics_DOE111 基本原則 複製 (Replication) 隨機化 (Randomization) 區隔化 (Blocking) 增進實驗之精確度 估計自然誤差 中央極限定理 “Averaging out” the effects from uncontrollable variables

13. &SixAdvanced Statistics_DOE112 DOE 之程序 問題之認知與陳述 選擇因子與其水準 選擇反應變數 選擇適當之實驗設計 執行實驗 資料分析 結論與建議 Follow-up run and confirmation test Iterative No more than 25% of available resources should be invested in the first experiment

14. &SixAdvanced Statistics_DOE113 Notes 使用統計以外之專業知識 實驗之設計與分析應愈簡單愈好 實驗之統計分析結果與現實上之差異 成本 技術 時間 實驗通常是遞迴式的 前幾次實驗通常只是學習經驗而已

15. &SixAdvanced Statistics_DOE114 二因子實驗設計 二因子無交互作用

16. &SixAdvanced Statistics_DOE115 二因子有交互作用

17. &SixAdvanced Statistics_DOE116 One-factor at a time 之方法

18. &SixAdvanced Statistics_DOE117

19. &SixAdvanced Statistics_DOE118 二因子實驗設計之模式

20. &SixAdvanced Statistics_DOE119 Data Sheet

21. &SixAdvanced Statistics_DOE120 ANOVA 表 – Two-Factor Factorial

22. &SixAdvanced Statistics_DOE121

23. &SixAdvanced Statistics_DOE122 Example

24. &SixAdvanced Statistics_DOE123

25. &SixAdvanced Statistics_DOE124 決策模式： 因為 F 0 (Primer Types) = 28.63 > F 0.05,2,12 = 3.89 F 0 (Application Methods) = 61.38 > F 0.05,1,12 = 4.75 所以此二因子對黏著力皆有顯著影響。 但 F 0 (Interaction) = 1.5 < F 0.05,2,12 = 3.89 ，所以此二因子的交互作 用對黏著力無明顯之影響。

26. &SixAdvanced Statistics_DOE125 Another Example

27. &SixAdvanced Statistics_DOE126 ANOVA Results Computer Output (Model Adequacy Checking)

28. &SixAdvanced Statistics_DOE127 Multiple Comparisons

29. &SixAdvanced Statistics_DOE128 &6 2 k 因子階層設計 k 個因子，每個因子 2 個水準 (+,-) ，共 2 k 次實驗（當 n = 1 時）。 在因子數不多的狀況下，常用於實驗初期，來了解因 子對反應變數之可能影響。 只能看出因子對反應變數之線性作用 (linear effect) ， 無法預估高階曲面作用。

30. &SixAdvanced Statistics_DOE129 The 2 2 Factorial Design

31. &SixAdvanced Statistics_DOE130 The Calculation (I) Effects Contrast

32. &SixAdvanced Statistics_DOE131 Sum of Square Errors The Calculation (II)

33. &SixAdvanced Statistics_DOE132 The AVONA Table

34. &SixAdvanced Statistics_DOE133 The Regression Model Since the effect of AB is not significant, the regression model would be The estimates of these coefficients are Why?

35. &SixAdvanced Statistics_DOE134 The Residuals Residuals at x 1 =1 and x 2 = -1 Computer Output

36. &SixAdvanced Statistics_DOE135 2 3 因子階層設計

37. &SixAdvanced Statistics_DOE136 2 3 因子階層設計 _ 符號表

38. &SixAdvanced Statistics_DOE137 計算 各因子之 Contrast =  (Sign)  (Treatment Combination ) Contrast A = -(1)+a-b+ab-c+ac-bc+abc Contrast B = -(1)-a+b+ab-c-ac+bc+abc Contrast AB = 各因子之效用 Effect = Contrast / (n  2 k-1 ) 各因子之 Sum of Square = Contrast / (n  2 k ) SS A = {-(1)+a-b+ab-c+ac-bc+abc} 2 / 8n

39. &SixAdvanced Statistics_DOE138 Example for 2 3 Design A: 速度 B: 切割深度 C: 切刀角度

40. &SixAdvanced Statistics_DOE139 計算 _Example 各因子之效用 各因子之 Sum of Square SS A = {-(1)+a-b+ab-c+ac-bc+abc} 2 / 8n = (27) 2 / (8  2) = 45.5625

41. &SixAdvanced Statistics_DOE140 ANOVA 表 _Example

42. &SixAdvanced Statistics_DOE141 Example for 2 4 Design

43. &SixAdvanced Statistics_DOE142 2 4 因子階層設計 _ 符號表 請完成請完成

44. &SixAdvanced Statistics_DOE143 ANOVA 表 _Example

45. &SixAdvanced Statistics_DOE144 AD 交互作用與迴歸函數

46. &SixAdvanced Statistics_DOE145 2 k Design with Center Points 增加預估曲線作用之能力 不破壞設計之平衡性 (Balanced Design) 只需增加少數幾個實驗

47. &SixAdvanced Statistics_DOE146 Example

48. &SixAdvanced Statistics_DOE147 ANOVA 表 _Example

49. &SixAdvanced Statistics_DOE148 2 k 因子實驗之區隔化與混雜化 2 2 factorial design with Blocking

50. &SixAdvanced Statistics_DOE149 The ANOVA

51. &SixAdvanced Statistics_DOE150 Confounding( 混雜化 ) 受限於資源（時間、金錢、人力等），無法再每一個 區隔皆有完整的因子實驗。 Confounding is a design technique for arranging a complete factorial design in blocks, where the block size is smaller than the number of treatment combinations in one replicate. It causes information about certain treatment effects (usually high-order interactions) to be indistinguishable from, or confounded with, blocks.

52. &SixAdvanced Statistics_DOE151 Confounding in 2 blocks Effect AB confounded with block.

53. &SixAdvanced Statistics_DOE152 The 2 3 Design Confounded(I)

54. &SixAdvanced Statistics_DOE153 The 2 3 Design Confounded(II) The Degrees of Freedom

55. &SixAdvanced Statistics_DOE154 The 2 3 Design Confounded(III) Replications => n = 4.

56. &SixAdvanced Statistics_DOE155 The 2 3 Design Confounded(IV) Replications => n = 4.

57. &SixAdvanced Statistics_DOE156 An Example

58. &SixAdvanced Statistics_DOE157 The ANOVA

59. &SixAdvanced Statistics_DOE158 Confounding in 4 blocks ADE and BCE are confounded, in addition, ABCD is also confounded. Why? Suggested Blocking => pp. 298, Table 7-8.