Chapter 15 2 k Factorial Experiments and Fractions

  • Slides: 63
Download presentation
Chapter 15 2 k Factorial Experiments and Fractions Copyright © 2010 Pearson Addison-Wesley. All

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

Section 15. 2 The 2 k Factorial: Calculation of Effects and Analysis of Variance

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 22 Factorial Experiment Copyright © 2010 Pearson Addison-Wesley. All rights

Table 15. 1 A 22 Factorial Experiment Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4

Figure 15. 1 Response suggesting apparent interaction Copyright © 2010 Pearson Addison-Wesley. All rights

Figure 15. 1 Response suggesting apparent interaction Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 5

Table 15. 2 22 Factorial with No Interaction Copyright © 2010 Pearson Addison-Wesley. All

Table 15. 2 22 Factorial with No Interaction Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 6

Table 15. 3 22 Factorial with Interaction Copyright © 2010 Pearson Addison-Wesley. All rights

Table 15. 3 22 Factorial with Interaction Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 7

Figure 15. 2 Interaction plot for data of Table 15. 2 Copyright © 2010

Figure 15. 2 Interaction plot for data of Table 15. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 8

Figure 15. 3 Interaction plot for data of Table 15. 3 Copyright © 2010

Figure 15. 3 Interaction plot for data of Table 15. 3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 9

Table 15. 4 Signs for Contrasts in a 22 Factorial Experiments Copyright © 2010

Table 15. 4 Signs for Contrasts in a 22 Factorial Experiments Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 10

Table 15. 5 Signs for Contrasts in a 23 Factorial Experiment Copyright © 2010

Table 15. 5 Signs for Contrasts in a 23 Factorial Experiment Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 11

Figure 15. 4 Geometric view of 23 Copyright © 2010 Pearson Addison-Wesley. All rights

Figure 15. 4 Geometric view of 23 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 12

Section 15. 3 Nonreplicated 2 k Factorial Experiment Copyright © 2010 Pearson Addison-Wesley. All

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.

Table 15. 6 Data for Case Study 15. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14

Figure 15. 5 Normal quantile-quantile plot of effects for Case Study 15. 1 Copyright

Figure 15. 5 Normal quantile-quantile plot of effects for Case Study 15. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15

Table 15. 7 Illustration of Two. Factor Interaction Copyright © 2010 Pearson Addison-Wesley. All

Table 15. 7 Illustration of Two. Factor Interaction Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 16

Figure 15. 6 Interaction plot for Case Study 15. 1 Copyright © 2010 Pearson

Figure 15. 6 Interaction plot for Case Study 15. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 17

Figure 15. 7 SAS printout for data of Case Study 15. 1 Copyright ©

Figure 15. 7 SAS printout for data of Case Study 15. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 18

Figure 15. 8 ANOVA table for Exercise 15. 3 Copyright © 2010 Pearson Addison-Wesley.

Figure 15. 8 ANOVA table for Exercise 15. 3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 19

Section 15. 4 Factorial Experiments in a Regression Setting Copyright © 2010 Pearson Addison-Wesley.

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

Table 15. 8 Data for Example 15. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 21

Figure 15. 9 SAS printout for data of Case Study 15. 2 Copyright ©

Figure 15. 9 SAS printout for data of Case Study 15. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. continued on next slide 22

Figure 15. 9 SAS printout for data of Case Study 15. 2 (cont’d) Copyright

Figure 15. 9 SAS printout for data of Case Study 15. 2 (cont’d) Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 23

Section 15. 5 The Orthogonal Design Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 15. 5 The Orthogonal Design Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 15. 10 a Geometric presentation of contrast for the 23 factorial design Copyright

Figure 15. 10 a Geometric presentation of contrast for the 23 factorial design Copyright © 2010 Pearson Addison-Wesley. All rights reserved. continued on next slide 25

Figure 15. 10 b Geometric presentation of contrast for the 23 factorial design (cont’d)

Figure 15. 10 b Geometric presentation of contrast for the 23 factorial design (cont’d) Copyright © 2010 Pearson Addison-Wesley. All rights reserved. continued on next slide 26

Figure 15. 10 c Geometric presentation of contrast for the 23 factorial design (cont’d)

Figure 15. 10 c Geometric presentation of contrast for the 23 factorial design (cont’d) Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 27

Figure 15. 11 A 22 design with center runs Copyright © 2010 Pearson Addison-Wesley.

Figure 15. 11 A 22 design with center runs Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 28

Figure 15. 12 22 factorial with 5 center runs Copyright © 2010 Pearson Addison-Wesley.

Figure 15. 12 22 factorial with 5 center runs Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 29

Figure 15. 13 22 factorial with runs at (0, 0) Copyright © 2010 Pearson

Figure 15. 13 22 factorial with runs at (0, 0) Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 30

Figure 15. 14 Graph Exercise 15. 17 Copyright © 2010 Pearson Addison-Wesley. All rights

Figure 15. 14 Graph Exercise 15. 17 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 31

Section 15. 6 Fractional Factorial Experiments 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 23 Factorial Experiment

Table 15. 9 Contrasts for the Seven Available Effects for a 23 Factorial Experiment Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 33

Figure 15. 15 The the 23 factorial Copyright © 2010 Pearson Addison-Wesley. All rights

Figure 15. 15 The the 23 factorial Copyright © 2010 Pearson Addison-Wesley. All rights reserved. fractions of 34

Table 15. 10 Construction of the Two 23 -1 Designs Copyright © 2010 Pearson

Table 15. 10 Construction of the Two 23 -1 Designs Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 35

Table 15. 11 Construction of the Two 24 -1 Designs Copyright © 2010 Pearson

Table 15. 11 Construction of the Two 24 -1 Designs Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 36

Table 15. 12 A 26 -2 Design Copyright © 2010 Pearson Addison-Wesley. All rights

Table 15. 12 A 26 -2 Design Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 37

Section 15. 7 Analysis of Fractional Factorial Experiments Copyright © 2010 Pearson Addison-Wesley. All

Section 15. 7 Analysis of Fractional Factorial Experiments Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 15. 13 Signs for Contrasts in a Half. Replicate of a 23 Factorial

Table 15. 13 Signs for Contrasts in a Half. Replicate of a 23 Factorial Experiments Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 39

Table 15. 14 Data for Example 15. 6 Copyright © 2010 Pearson Addison-Wesley. All

Table 15. 14 Data for Example 15. 6 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 40

Table 15. 15 Analysis of Variance for the Data of a Half-Replicate of a

Table 15. 15 Analysis of Variance for the Data of a Half-Replicate of a 25 Factorial Experiment Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 41

Section 15. 8 Higher Fractions and Screening Designs Copyright © 2010 Pearson Addison-Wesley. All

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. 43

Definition 15. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 43

Section 15. 9 Construction of Resolution III and IV Designs with 8, 16, and

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 15. 16 Some Resolution III, IV, V, VI and VII 2 k-p Designs

Table 15. 16 Some Resolution III, IV, V, VI and VII 2 k-p Designs Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 45

Section 15. 10 Other Two-Level Resolutions III Designs; The Plackett-Burman Designs Copyright © 2010

Section 15. 10 Other Two-Level Resolutions III Designs; The Plackett-Burman Designs Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 15. 11 Introduction to Response Surface Methodology Copyright © 2010 Pearson Addison-Wesley. All

Section 15. 11 Introduction to Response Surface Methodology Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 15. 17 Central Composite Design for Example 15. 8 Copyright © 2010 Pearson

Table 15. 17 Central Composite Design for Example 15. 8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 48

Figure 15. 16 Central composite design for Example 15. 8 Copyright © 2010 Pearson

Figure 15. 16 Central composite design for Example 15. 8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 49

Figure 15. 17 Plot for the response surface prediction conversion for Example 15. 8

Figure 15. 17 Plot for the response surface prediction conversion for Example 15. 8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 50

Figure 15. 18 Contour plot of predicted conversion for Example 15. 8 Copyright ©

Figure 15. 18 Contour plot of predicted conversion for Example 15. 8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 51

Section 15. 12 Robust Parameter Design Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 15. 12 Robust Parameter Design Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Definition 15. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 53

Definition 15. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 53

Table 15. 18 Design for Example 15. 9 Copyright © 2010 Pearson Addison-Wesley. All

Table 15. 18 Design for Example 15. 9 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 54

Table 15. 19 Control Factors for Case Study 15. 3 Copyright © 2010 Pearson

Table 15. 19 Control Factors for Case Study 15. 3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 55

Table 15. 20 Noise Factors for Case Study 15. 3 Copyright © 2010 Pearson

Table 15. 20 Noise Factors for Case Study 15. 3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 56

Table 15. 21 Crossed Arrays and Response Values for Case Study 15. 3 Copyright

Table 15. 21 Crossed Arrays and Response Values for Case Study 15. 3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 57

Figure 15. 19 Plot showing the influence of factors on the mean response Copyright

Figure 15. 19 Plot showing the influence of factors on the mean response Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 58

Figure 15. 20 Mean and standard deviation for Case Study 15. 4 Copyright ©

Figure 15. 20 Mean and standard deviation for Case Study 15. 4 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 59

Table 15. 22 Experimental Data in a Crossed Array Copyright © 2010 Pearson Addison-Wesley.

Table 15. 22 Experimental Data in a Crossed Array Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 60

Figure 15. 21 Interaction plots for the data in Table 15. 22 Copyright ©

Figure 15. 21 Interaction plots for the data in Table 15. 22 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 61

Figure 15. 22 Interaction plots for the data in Exercise 15. 31 Copyright ©

Figure 15. 22 Interaction plots for the data in Exercise 15. 31 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 62

Section 15. 13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters Copyright

Section 15. 13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

7 2 Factorial Experiments 7 2 Factorial Experiments7 2 Factorial Experiments 7 2 Factorial Experiments
CHAPTER 5 FACTORIAL DESIGNS FACTORIAL ESSENTIALS Factorial designCHAPTER 5 FACTORIAL DESIGNS FACTORIAL ESSENTIALS Factorial design
Recursion Factorial 6 654321 Factorial 75 Factorial 75Recursion Factorial 6 654321 Factorial 75 Factorial 75
ANOVA FACTORIAL DESIGN Factorial design Factorial design anANOVA FACTORIAL DESIGN Factorial design Factorial design an
Factorial Designs Chapter 11 Factorial designs Allow experimentsFactorial Designs Chapter 11 Factorial designs Allow experiments
Factorial Experiments Factorial Design experiment in which moreFactorial Experiments Factorial Design experiment in which more
Chapter 15 2 k Factorial Experiments and FractionsChapter 15 2 k Factorial Experiments and Fractions
Chapter 15 2 k Factorial Experiments and FractionsChapter 15 2 k Factorial Experiments and Fractions
Chapter 15 2 k Factorial Experiments and FractionsChapter 15 2 k Factorial Experiments and Fractions
Chapter 2 Fractions The Meaning of Fractions FractionsChapter 2 Fractions The Meaning of Fractions Fractions
Fractions Percents Expressing Percents as Fractions and FractionsFractions Percents Expressing Percents as Fractions and Fractions
Fractions Fractions and Their Forms Operating Fractions OperatingFractions Fractions and Their Forms Operating Fractions Operating
Multiplying Fractions Multiply fractions including improper fractions andMultiplying Fractions Multiply fractions including improper fractions and
Fractions Equivalent and Simplifying Fractions Multiplying Fractions DividingFractions Equivalent and Simplifying Fractions Multiplying Fractions Dividing
FRACTIONS Fractions have numerators and denominators Fractions representFRACTIONS Fractions have numerators and denominators Fractions represent
TwoLevel Factorial and Fractional Factorial Designs in BlocksTwoLevel Factorial and Fractional Factorial Designs in Blocks
Twolevel Factorial and Fractional Factorial Designs in BlocksTwolevel Factorial and Fractional Factorial Designs in Blocks
Lesson 42 Permutations and combinations factorial A factorialLesson 42 Permutations and combinations factorial A factorial
Fractions Fractions Fractions CATHY JONES Secondary Math InstructionFractions Fractions Fractions CATHY JONES Secondary Math Instruction
Final Jeopardy Fractions Addition Fractions Subtraction Fractions MultiplicationFinal Jeopardy Fractions Addition Fractions Subtraction Fractions Multiplication
Fractions English for teachers Fractions Fractions one halfFractions English for teachers Fractions Fractions one half
Fractions Fractions Fractions CATHY JONES Secondary Math InstructionFractions Fractions Fractions CATHY JONES Secondary Math Instruction
Reciprocal Multiplying Fractions Dividing Fractions QUIZ Multiplying FractionsReciprocal Multiplying Fractions Dividing Fractions QUIZ Multiplying Fractions
Fractions Order fractions fractions of amounts Objectives DayFractions Order fractions fractions of amounts Objectives Day