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Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Chapter 15
2k Factorial Experiments and Fractions
Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 15.2
The 2k Factorial: Calculation of Effects and Analysis of Variance
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Table 15.1 A 22 Factorial Experiment
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Figure 15.1 Response suggesting apparent interaction
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Table 15.2 22 Factorial with No Interaction
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Table 15.3 22 Factorial with Interaction
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Figure 15.2 Interaction plot for data of Table 15.2
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Figure 15.3 Interaction plot for data of Table15.3
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Table 15.4 Signs for Contrasts in a 22 Factorial Experiments
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Table 15.5 Signs for Contrasts in a 23 Factorial Experiment
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Figure 15.4 Geometric view of 23
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Section 15.3
Nonreplicated 2k Factorial Experiment
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Table 15.6 Data for Case Study 15.1
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Figure 15.5 Normal quantile-quantile plot of effects for Case Study 15.1
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Table 15.7 Illustration of Two-Factor Interaction
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Figure 15.6 Interaction plot for Case Study 15.1
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Figure 15.7 SAS printout for data of Case Study 15.1
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Figure 15.8 ANOVA table for Exercise 15.3
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Section 15.4
Factorial Experiments in a Regression Setting
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Table 15.8 Data for Example 15.2
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Figure 15.9 SAS printout for data of Case Study 15.2
continued on next slide
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Figure 15.9 SAS printout for data of Case Study 15.2 (cont’d)
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Figure 15.10a Geometric presentation of contrast for the 23 factorial design
continued on next slide
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Figure 15.10b Geometric presentation of contrast for the 23 factorial design (cont’d)
continued on next slide
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Figure 15.10c Geometric presentation of contrast for the 23 factorial design (cont’d)
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Figure 15.11 A 22 design with center runs
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Figure 15.12 22 factorial with 5 center runs
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Figure 15.13 22 factorial with runs at (0,0)
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Figure 15.14 Graph Exercise 15.17
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Section 15.6
Fractional Factorial Experiments
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Table 15.9 Contrasts for the Seven Available Effects for a 23 Factorial Experiment
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Figure 15.15 The fractions of the 23 factorial
1
2
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Table 15.10 Construction of the Two 23 -1 Designs
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Table 15.11 Construction of the Two 24-1 Designs
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Section 15.7
Analysis of Fractional Factorial Experiments
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Table 15.13 Signs for Contrasts in a Half-Replicate of a 23 Factorial Experiments
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Table 15.14 Data for Example 15.6
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Table 15.15 Analysis of Variance for the Data of a Half-Replicate of a 25 Factorial Experiment
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Section 15.8
Higher Fractions and Screening Designs
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Section 15.9
Construction of Resolution III and IV Designs with 8,16,and 32 Design Points
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Table 15.16 Some Resolution III, IV, V, VI and VII 2k-p Designs
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Section 15.10
Other Two-Level Resolutions III Designs; The Plackett-Burman Designs
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Section 15.11
Introduction to Response Surface Methodology
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Table 15.17 Central Composite Design for Example 15.8
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Figure 15.16 Central composite design for Example 15.8
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Figure 15.17 Plot for the response surface prediction conversion for Example 15.8
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Figure 15.18 Contour plot of predicted conversion for Example 15.8
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Table 15.18 Design for Example 15.9
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Table 15.19 Control Factors for Case Study 15.3
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Table 15.20 Noise Factors for Case Study 15.3
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Table 15.21 Crossed Arrays and Response Values for Case Study 15.3
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Figure 15.19 Plot showing the influence of factors on the mean response
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Figure 15.20 Mean and standard deviation for Case Study 15.4
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Table 15.22 Experimental Data in a Crossed Array
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Figure 15.21 Interaction plots for the data in Table 15.22
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Figure 15.22 Interaction plots for the data in Exercise 15.31