Chapter 5 Design & Analysis of Experiments
8E 2012 Montgomery
1
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community
Ask the community for help and clear up your study doubts
University Rankings
Discover the best universities in your country according to Docsity users
Free resources
Our save-the-student-ebooks!
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Design of Experiment chapter 5
Typology: Study notes
2019/2020
1 / 29
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Design of Experiment chapter 5 and more Study notes Statistics in PDF only on Docsity!
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
+^
=^ −^
=^
−^
+^
=^ −^
=^
−^
+^
=^
−^
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.
y^
x^ x
x x y^
x^
x^
x x^
x^
x
β^ β^
β^ β
ε
=^ +^
+^ +
=^ +
≅^ +
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
...^
..^ ...^
..^ ...
.^ ..^
..^ ...^
(^
)^
(^ )
(^
) (^
)^
(^
)
a^ b^ n^
a^
b
ijk^
i^
j
i^ j^ k^
i^
j a^ b^
a^ b^ n ij^ i^
j^
ijk^ ij
y^ y^
bn^ y^
y^ an
y^
y
n^ y
y^
y^ y^
y^ y
=^ =^ =^
=^
−^ =^
−^ +^
−
+^
−^ −^
+^ +^
−
∑∑∑
∑^
∑ ∑∑^
∑∑∑
Chapter 5^
Design & Analysis of Experiments8E 2012 Montgomery
.^ ..^
..^ ...^
(^
)^
(^
)
ij^ i^
j^
ijk^ ij
i^ j^
i^ j^ k
n^ y
y^
y^ y^
y^ y
=^ =^
=^ =^ =
+^
−^ −^
+^ +^
−
∑∑^
∑∑∑
breakdown:^1
1
1 (^
1)(^ 1)
(^
T^
A^ B
AB
E
SS^ SS
SS^
SS^
SS
df abn^
a^
b^
a^ b
ab n
=^ +
+^
−^ =^
−^ +^
−^ +^
−^ −
+^
−
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