Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Chapter 15 2 k Factorial Experiments and Fractions

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.1 Introduction

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.2 The 2 k Factorial: Calculation of Effects and Analysis of Variance

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table 15.1 A 2 2 Factorial Experiment

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.1 Response suggesting apparent interaction

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Factorial with No Interaction

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Factorial with Interaction

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.2 Interaction plot for data of Table 15.2

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.3 Interaction plot for data of Table15.3

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table 15.4 Signs for Contrasts in a 2 2 Factorial Experiments

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table 15.5 Signs for Contrasts in a 2 3 Factorial Experiment

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.4 Geometric view of 2 3

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.3 Nonreplicated 2 k Factorial Experiment

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table 15.6 Data for Case Study 15.1

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.5 Normal quantile-quantile plot of effects for Case Study 15.1

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table 15.7 Illustration of Two- Factor Interaction

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.6 Interaction plot for Case Study 15.1

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.7 SAS printout for data of Case Study 15.1

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.8 ANOVA table for Exercise 15.3

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.4 Factorial Experiments in a Regression Setting

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table 15.8 Data for Example 15.2

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.9 SAS printout for data of Case Study 15.2 continued on next slide

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.9 SAS printout for data of Case Study 15.2 (cont’d)

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.5 The Orthogonal Design

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.10a Geometric presentation of contrast for the 23 factorial design continued on next slide

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.10b Geometric presentation of contrast for the 23 factorial design (cont’d) continued on next slide

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure 15.10c Geometric presentation of contrast for the 23 factorial design (cont’d)

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure A 2 2 design with center runs

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure factorial with 5 center runs

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure factorial with runs at (0,0)

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure Graph Exercise 15.17

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.6 Fractional Factorial Experiments

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table 15.9 Contrasts for the Seven Available Effects for a 2 3 Factorial Experiment

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure The fractions of the 2 3 factorial

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Construction of the Two Designs

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Construction of the Two Designs

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table A Design

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.7 Analysis of Fractional Factorial Experiments

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Signs for Contrasts in a Half- Replicate of a 2 3 Factorial Experiments

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Data for Example 15.6

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Analysis of Variance for the Data of a Half-Replicate of a 2 5 Factorial Experiment

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.8 Higher Fractions and Screening Designs

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Definition 15.1

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.9 Construction of Resolution III and IV Designs with 8,16,and 32 Design Points

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Some Resolution III, IV, V, VI and VII 2 k-p Designs

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section Other Two-Level Resolutions III Designs; The Plackett-Burman Designs

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section Introduction to Response Surface Methodology

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Central Composite Design for Example 15.8

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure Central composite design for Example 15.8

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure Plot for the response surface prediction conversion for Example 15.8

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure Contour plot of predicted conversion for Example 15.8

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section Robust Parameter Design

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Definition 15.2

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Design for Example 15.9

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Control Factors for Case Study 15.3

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Noise Factors for Case Study 15.3

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Crossed Arrays and Response Values for Case Study 15.3

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure Plot showing the influence of factors on the mean response

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure Mean and standard deviation for Case Study 15.4

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Table Experimental Data in a Crossed Array

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure Interaction plots for the data in Table 15.22

Copyright © 2010 Pearson Addison-Wesley. All rights reserved Figure Interaction plots for the data in Exercise 15.31

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Potential Misconceptions and Hazards; Relationship to Material in Other Chapters Section 15.13