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Design of Experiment chapter 5, Study notes of Statistics

Design of Experiment chapter 5

Typology: Study notes

2019/2020

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Chapter 5 Design & Analysis of Experiments
8E 2012 Montgomery
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Chapter 5^

Design & Analysis of Experiments8E 2012 Montgomery

Design of Engineering Experiments– Introduction to Factorials • Text reference, Chapter 5 • General principles

of factorial experiments

•^ The^

two-factor factorial

with fixed effects

Chapter 5^

Design & Analysis of Experiments8E 2012 Montgomery

•^ The^

two-factor factorial

with fixed effects

• The^

ANOVA

for factorials

• Extensions to more than two factors •^ Quantitative

and^ qualitative

factors –

response curves and surfaces

The Case of Interaction:

Chapter 5^

Design & Analysis of Experiments8E 2012 Montgomery

A^ y^ y^ +^ −^ A^ A B^ y^ y +^ − B^ B AB

+^

=^ −^

=^

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Regression Model & The Associated Response Surface^ Chapter 5

Design & Analysis of Experiments8E 2012 Montgomery

The least squares fit isˆ 35.^

10.^ 5.^ 0.^

35.5^ 10.

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Example 5.1 The Battery Life Experiment

Text reference pg. 187 Chapter 5^

Design & Analysis of Experiments8E 2012 Montgomery A^ = Material type;

B^ = Temperature (A

quantitative

variable)

1.^ What

effects^ do material type & temperature have on life?

2.^ Is there a choice of material that would give long life

regardless of

temperature

(a^ robust

product)?

The General Two-FactorFactorial Experiment

Chapter 5^

Design & Analysis of Experiments8E 2012 Montgomery

a^ levels of factor

A ;^ b^ levels of factor

B ;^ n^ replicates

This is a

completely randomized design

Extension of the ANOVA to Factorials(Fixed Effects Case) – pg. 189

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Chapter 5^

Design & Analysis of Experiments8E 2012 Montgomery

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ANOVA Table – Fixed Effects Case Chapter 5

Design & Analysis of Experiments8E 2012 Montgomery JMP and Design-Expert

will perform the computations

Text gives details of

manual computing

(ugh!) – see pp.

192

Design-Expert Output – Example 5.1 Chapter 5^

Design & Analysis of Experiments8E 2012 Montgomery

Residual Analysis – Example 5.1 Chapter 5

Design & Analysis of Experiments8E 2012 Montgomery

Interaction Plot DE S IG N-E X P E RT P l o tL i fe X = B : T e m p e ratu reY = A : M a te ri a l^ A 1 A 1^ A 2 A 2^ A 3 A 3

Interaction Graph^ A: Material

(^188146104) Life Chapter 5^

Design & Analysis of Experiments8E 2012 Montgomery 15 70 B: Tem perature

125 62 20

22 22 22

Quantitative and Qualitative Factors • The basic ANOVA procedure treats every factor as if itwere^ qualitative • Sometimes an experiment will involve both

quantitative

and^ qualitative

factors, such as in Example 5.

•^ This can be accounted for in the analysis to produce Chapter 5^

Design & Analysis of Experiments8E 2012 Montgomery

•^ This can be accounted for in the analysis to produce^ regression models

for the quantitative factors at each level

(or combination of levels) of the qualitative factors• These^ response curves

and/or^ response surfaces

are often

a considerable aid in practical interpretation of the results

Quantitative and Qualitative Factors Chapter 5^

Design & Analysis of Experiments8E 2012 Montgomery

Regression Model Summary of Results Chapter 5^

Design & Analysis of Experiments8E 2012 Montgomery