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Unformatted text preview: 2k  Factorial Design
Special case of multifactor DOE v Each factor has only 2 levels: ‘On’ and ‘Off’ (or)
‘High’ and ‘Low’ (or) simply denoted as ‘+’ and ‘’
v Very useful in preliminary analysis v • can ‘‘weed’’ out unimportant factors • allows initial study of interactions Can’t explore a wide range – but gives
directions
v 9/19/11 School of Chemical 11 2k  Factorial Design
Factor
A Factor Factor Factor
A
B
C
# Exp
=2 + Factor
A
+
 + +    9/19/11 + +  +  + +   +  +    # Exp
=4  + + +  Factor
B + +  +   # Exp with k
factors = 2k
School of Chemical 22 # Exp
=8 22  Factorial Design
 (1) n – observations at each
treatment
a – total of observations at
‘a’
b – total of observations at
‘b’
ab –
9/19/11 total of observations Chemical
School of at  ‘a’ + ‘b’ + ‘a’   ‘ab’ Symb
ol
(1) + ‘b’ Factor Factor
A
B + ‘ab’ Main effect
of AA: y A  = a + ab y +2n Main effect
of BB: y B  = b + ab y +2n Interaction
effect AB: (1) + ab =
2n 33 b + (1)
2n
a + (1)
2n
a+b
2n 22  Factorial Design
With change in A, the
mean response changes. =>
Factor A has an effect.
v Mean
Response B
B
1
2 A
1 9/19/11 A
2 At another value of B, with
change
in A, the mean
response changes
although
from a different initial
value
to different
final value. =>
Factor B has an effect.
v Factors A and B do not
interact. Irrespective of B
value, A seems to
affect the
response in the same
manner
v School of Chemical 44 22  Factorial Design A
1 A
2 Factor A has an
effect
v B
B
1
2 Mean
Response Mean
Response B
B
1
2 A
1 A
2 Factor A does not have
an effect
v v Factor B does not v v No interaction v 9/19/11 Factor B does
No interaction School of Chemical 55 22  Factorial Design A
1 A
2 Factor A has an
effect
v v Factor B does There is AB
interaction
v 9/19/11 B
B
1
2 Mean
Response Mean
Response B
B
1
2 A
1 A
2 Factor A does not have
an effect
v Factor B does not v However, there is AB
interaction
v School of Chemical 66 ...
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This note was uploaded on 09/19/2011 for the course CHE 320 taught by Professor Harris during the Spring '10 term at Purdue.
 Spring '10
 Harris

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