FactorialDesign2k

# FactorialDesign2k - 2k Factorial Design Special case of...

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Unformatted text preview: 2k - Factorial Design Special case of multi-factor 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.

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FactorialDesign2k - 2k Factorial Design Special case of...

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