copyright © 2010 pearson addison-wesley. all rights reserved. chapter 15 2 k factorial experiments...

Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Chapter 15

2k Factorial Experiments and Fractions


Section 15.1

Introduction


Section 15.2

The 2k Factorial: Calculation of Effects and Analysis of Variance

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 4

Table 15.1 A 22 Factorial Experiment


Figure 15.1 Response suggesting apparent interaction


Table 15.2 22 Factorial with No Interaction


Table 15.3 22 Factorial with Interaction


Figure 15.2 Interaction plot for data of Table 15.2


Figure 15.3 Interaction plot for data of Table15.3


Table 15.4 Signs for Contrasts in a 22 Factorial Experiments


Table 15.5 Signs for Contrasts in a 23 Factorial Experiment


Figure 15.4 Geometric view of 23


Section 15.3

Nonreplicated 2k Factorial Experiment


Table 15.6 Data for Case Study 15.1


Figure 15.5 Normal quantile-quantile plot of effects for Case Study 15.1


Table 15.7 Illustration of Two-Factor Interaction


Figure 15.6 Interaction plot for Case Study 15.1


Figure 15.7 SAS printout for data of Case Study 15.1


Figure 15.8 ANOVA table for Exercise 15.3


Section 15.4

Factorial Experiments in a Regression Setting


Table 15.8 Data for Example 15.2


Figure 15.9 SAS printout for data of Case Study 15.2

continued on next slide


Figure 15.9 SAS printout for data of Case Study 15.2 (cont’d)


Section 15.5

The Orthogonal Design


Figure 15.10a Geometric presentation of contrast for the 23 factorial design



Figure 15.10b Geometric presentation of contrast for the 23 factorial design (cont’d)



Figure 15.10c Geometric presentation of contrast for the 23 factorial design (cont’d)


Figure 15.11 A 22 design with center runs


Figure 15.12 22 factorial with 5 center runs


Figure 15.13 22 factorial with runs at (0,0)


Figure 15.14 Graph Exercise 15.17


Section 15.6

Fractional Factorial Experiments


Table 15.9 Contrasts for the Seven Available Effects for a 23 Factorial Experiment


Figure 15.15 The fractions of the 23 factorial

1

2


Table 15.10 Construction of the Two 23 -1 Designs


Table 15.11 Construction of the Two 24-1 Designs


Table 15.12 A 26-2 Design


Section 15.7

Analysis of Fractional Factorial Experiments


Table 15.13 Signs for Contrasts in a Half-Replicate of a 23 Factorial Experiments


Table 15.14 Data for Example 15.6


Table 15.15 Analysis of Variance for the Data of a Half-Replicate of a 25 Factorial Experiment


Section 15.8

Higher Fractions and Screening Designs


Definition 15.1


Section 15.9

Construction of Resolution III and IV Designs with 8,16,and 32 Design Points


Table 15.16 Some Resolution III, IV, V, VI and VII 2k-p Designs


Section 15.10

Other Two-Level Resolutions III Designs; The Plackett-Burman Designs


Section 15.11

Introduction to Response Surface Methodology


Table 15.17 Central Composite Design for Example 15.8


Figure 15.16 Central composite design for Example 15.8


Figure 15.17 Plot for the response surface prediction conversion for Example 15.8


Figure 15.18 Contour plot of predicted conversion for Example 15.8


Section 15.12

Robust Parameter Design


Definition 15.2


Table 15.18 Design for Example 15.9


Table 15.19 Control Factors for Case Study 15.3


Table 15.20 Noise Factors for Case Study 15.3


Table 15.21 Crossed Arrays and Response Values for Case Study 15.3


Figure 15.19 Plot showing the influence of factors on the mean response


Figure 15.20 Mean and standard deviation for Case Study 15.4


Table 15.22 Experimental Data in a Crossed Array


Figure 15.21 Interaction plots for the data in Table 15.22


Figure 15.22 Interaction plots for the data in Exercise 15.31


Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

Section 15.13

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