Probability statistics for engineers and scientists 9th by walpole myers chapter 15

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Chapter 15

Experiments

and Fractions

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Section 15.1

Introduction

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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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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

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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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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Section 15.5

The Orthogonal Design

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Figure 15.10a Geometric presentation

of contrast for the 23 factorial design

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Figure 15.10b Geometric presentation

(cont’d)

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Figure 15.10c Geometric presentation

(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

12

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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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Table 15.12 A 26-2 Design

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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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Definition 15.1

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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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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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Section 15.12

Robust

Parameter

Design

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Definition 15.2

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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

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Potential

Misconceptions and Hazards;

Relationship to

Material in Other Chapters

Section 15.13

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