<p> Chapter 8. Two-Level Fractional Factorial Designs</p><p>Example 1. Five factors for an IC were investigated for improving the process yield. : aperture setting (small, large) exposure time ( below nominal, above nominal) development time (s, s) mask dimension (small, large) etch time ( min, min) </p><p>(i)Create factorial design using a design with .</p><p>1</p><p>(ii)Suppose that the experiment is performed in the run order so as to obtain the following data. </p><p>(iii)Fit a full model. </p><p>2</p><p>효과의 정규 확률도 (반응: yield, α = 0.05)</p><p>99 효과 유형 유의하지 않음 95 B 유의함</p><p>90 A 요인 이름 C 80 A A AB B B 70 C C 60 율 D D 50 분 E E 40 백 30 20</p><p>10 5</p><p>1 0 5 10 15 20 25 30 35 효과 Lenth의 PSE = 0.9375</p><p>(iv)Fit a reduced model. </p><p>3</p><p>(v)Plot the interaction between A and B.</p><p> yield에 대한 주효과도 적합 평균 A B C 50</p><p>40 균 평</p><p>의 30 d l e i y</p><p>20</p><p>10 -1 1 -1 1 -1 1</p><p>When B= -1, there is not much difference between the effect of A. However, if B=1, then A=1 has a much higher yield than A=-1. To get the maximum yield, we would use A=1 and B=1. From the main effect plot, C=1 gives a higher yield than C=-1.</p><p>(vi)Provide the contour plot.</p><p>4 yield 대 B, A의 등고선도 1.0 yield < 20 20 – 30 30 – 40 0.5 40 – 50 50 – 60 > 60</p><p>고정 값 C 1</p><p>B 0.0</p><p>-0.5</p><p>-1.0 -1.0 -0.5 0.0 0.5 1.0 A</p><p>Example 2. A quality improvement team uses a designed experiment to study the injection molding process so that shrinkage can be reduced. Six factors are considered: mold temperature screw speed </p><p> cycle time gate size holding pressure (i)Create factorial design using a . </p><p>5 (ii)Suppose that you get the following data after experiments. Enter the data in column C11</p><p>(iii)Test hypotheses</p><p>6</p><p>효과의 정규 확률도 (반응: 수축정도, α = 0.05)</p><p>99 효과 유형 유의하지 않음 95 B 유의함</p><p>90 A 요인 이름 AB 80 A 성형온도 B 나사속도 70 C 지속시간 60 율 D 사이클시간 50 분 E 게이트크기 40 백 F 지속압력 30 20</p><p>10 ABF 5 AD</p><p>1 0 10 20 30 40 효과 Lenth의 PSE = 0.9375</p><p>(iv)Find the reduced model.</p><p>7</p><p>Example 3. Design with I=ACE and I=BDE. </p><p>Example 4. A human performance analyst is conducting an experiment to study eye focus time and has built an apparatus in which several factors can be controlled during the test. : sharpness of vision 8 : distance from target to eye : target shape : illumination level : target size : target density : subject (i) Design </p><p>(ii)Suppose that you get the following data after experiments. Enter the data in column C12</p><p>9 (iii)Test hypotheses</p><p>효과의 정규 확률도 (반응: response, α = 0.05) 99 효과 유형 유의하지 않음 95 유의함 B 90 요인 이름 80 A A D B B 70 A C C 60 율 D D 50 분 E E 40 백 F F 30 G G 20</p><p>10 5</p><p>1 0 10 20 30 40 효과 Lenth의 PSE = 0.675</p><p>Plot shows that A, B, D effects are significant. However, is aliased with is aliased with and is aliased with . Therefore, it is not known if A,D, AD are significant or if A,B,D are significant. </p><p>(iv)To separate the main effects and the two-factor interactions, we use the full fold over design </p><p>Case 1. Adjust the current design.</p><p>10</p><p>11 효과의 정규 확률도 (반응: response, α = 0.05)</p><p>99 효과 유형 유의하지 않음 95 B 유의함</p><p>90 D 요인 이름 80 BD A A B B 70 C C 60 율 D D 50 분 E E 40 백 F F 30 G G 20</p><p>10 5 AF</p><p>1 0 10 20 30 40 효과 Lenth의 PSE = 0.75</p><p>Suppose that we do not consider the block effect in the model.</p><p>12 효과의 정규 확률도 (반응: response, α = 0.05)</p><p>99 효과 유형 유의하지 않음 95 B 유의함</p><p>90 D 요인 이름 BD 80 A A B B 70 C C 60 율 D D 50 분 E E 40 백 F F 30 G G 20</p><p>10 5</p><p>1 0 10 20 30 40 효과 Lenth의 PSE = 1.21875</p><p>Case 2. A new design is used. </p><p>13</p><p>(i)Suppose that you get the following data after experiments. Enter the data in column C12</p><p>(ii)Test hypotheses</p><p>14</p><p>효과의 정규 확률도 (반응: response, α = 0.05)</p><p>99 효과 유형 유의하지 않음 95 B 유의함</p><p>90 D 요인 이름 BD 80 A A B B 70 C C 60 율 D D 50 분 E E 40 백 F F 30 G G 20</p><p>10 5</p><p>1 0 10 20 30 40 효과 Lenth의 PSE = 1.21875</p><p>15</p>