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Design of Experiment chapter 5
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Chapter 5^
Design & Analysis of Experiments8E 2012 Montgomery
Chapter 5^
Design & Analysis of Experiments8E 2012 Montgomery
Chapter 5^
Design & Analysis of Experiments8E 2012 Montgomery
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)?
Chapter 5^
Design & Analysis of Experiments8E 2012 Montgomery
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
+^
−^ −^
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breakdown:^1
1
1 (^
1)(^ 1)
(^
T^
A^ B
AB
E
SS^ SS
SS^
SS^
SS
df abn^
a^
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a^ b
ab n
=^ +
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−^ =^
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−^ −
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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
(^188146104) Life Chapter 5^
Design & Analysis of Experiments8E 2012 Montgomery 15 70 B: Tem perature
125 62 20
22 22 22
Design & Analysis of Experiments8E 2012 Montgomery
Design & Analysis of Experiments8E 2012 Montgomery
Design & Analysis of Experiments8E 2012 Montgomery