23 1 n n Five 23 Design 23

23 -1設計 n n &Five 23 Design 分成兩個23 -1 Designs。 符號表(一) DOE Class 90 a 4

部分階層設計之產生器(Generator) n &Five ABC稱為此部份階層之產生器(Generator)。 DOE Class 90 a 5

23 -1 對比差異與平均效應 n n &Five Contrast. A = abc+a-b-c Contrast. AB = abc+c-a-b Contrast. B = abc+b-a-c Contrast. AC = abc+b-a-c Contrast. C = abc+c-a-b Contrast. BC = abc+a-b-c AEA = 1/2(abc+a-b-c) = AEBC AEB = 1/2(abc+b-a-c) = AEAC AEC = 1/2(abc+c-a-b) = AEAB DOE Class 90 a 8

23 -1 Design (I=-ABC)下之Aliases n 在 23 -1 Design (I=-ABC)下之Aliases為 l`A A-BC l`B B-AC l`C C-AB n &Five WHY? DOE Class 90 a 10

&Five DOE Class 90 a 14

Aliases for the Example A = A(ABCD) = A 2 BCD = BCD B = B(ABCD) = AB 2 CD = ACD C = C(ABCD) = ABC 2 D = ABD D = D(ABCD) = ABCD 2 = ABC AB = AC = BC = n n l. A A+BCD l. B B+ACD l. C C+ABD l. D D+ABC l. AB AB+CD l. AC AC+BD l. BC BC+AD n 所以，24 -1 Design (I=ABCD)之解析度為Ⅳ。 n Computer Output &Five DOE Class 90 a 18

&Five DOE Class 90 a 20

&Five DOE Class 90 a 21

&Five DOE Class 90 a 22

Conclusion for the Example 扣除一因子 扣除二因子 &Five DOE Class 90 a 23

&Five DOE Class 90 a 24

26 -2 Design 符號表 &Five DOE Class 90 a 26

26 -2 Design (I = ABCE = BCDF=ADEF) 之Aliases n n &Five A = BCE = DEF = ABCDF B = ACE = CDF = ABDEF C = E = F = AB = BC = ABD = 完整之Aliases結構如下頁。 DOE Class 90 a 27

&Five DOE Class 90 a 28

26 -2 Design之計算 n 26 -2 Design (I = ABCE = BCDF=ADEF) 共有16次實驗，16 -1=15 個自由度，可用以估算 6個主因子作用及多數 2因子交互作用。 n 其計算如下： Contrast. A = ae+abf+acf+abce+adef+abd+acd+abcdef -(1)-bef-cef-bc-df-bde-cde-bcdf 平均效應： AEA = Contrast. A / 8 SSA = Contrast. A 2 / 16 n 其他因子之計算同此方法。 &Five DOE Class 90 a 29

&Five DOE Class 90 a 31

&Five DOE Class 90 a 32

一般 2 k-p Design n 需要p個產生器(Generators)。 n n n 每一作用(Effect)有2 p個Aliases。 n n n &Five 24 -1 Design (I=ABCD) 26 -2 Design (I = ABCE = BCDF) 23 -1 Design (I=ABC)中，l. A A+BC 26 -2 Design (I = ABCE = BCDF) 中，l. A A+BCE+DEF+ABCDF 只允許 2 k-p-1個作用(及其Aliases)被估算出來。 DOE Class 90 a 33

在 2 k-p中使用區隔化(Blocking) n &Five 26 -2 Design (I = ABCE = BCDF) 中，用ABD作區隔化： DOE Class 90 a 34

&Five DOE Class 90 a 35

&Five DOE Class 90 a 36

&Five DOE Class 90 a 37

&Five DOE Class 90 a 38

&Five DOE Class 90 a 40

常用之 2 k-p Design &Five DOE Class 90 a 41

32 Design &Five DOE Class 90 a 45

&Five DOE Class 90 a 47

&Five DOE Class 90 a 50

&Five DOE Class 90 a 51

&Five DOE Class 90 a 52