Design of Experiments

Chapter 5

Design & Analysis of Experiments

1

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Design of Engineering Experiments – Introduction to Factorials • • • • •

Text ext ref refer eren ence ce,, Cha Chapt pter er 5 General principles of factorial experiments The two-factor factorial with fixed effects The ANOVA for factorials Exte Extensi nsions ons to more more than than two two fact factors ors









Some Basic Definitions

Definition of a factor effect: The change in the mean response when the factor is changed from low to high A

40 + 52

20 + 30

21









The Case of Interaction:

A = y A

+

−

yA

−

=

50 + 12

−

20 + 40

=

1









Regression Model & The Associated Response Surface









The Effect of Interaction on the Response Surface











Example 5.1 The Battery Life Experiment Text reference pg. 187











The General Two-Factor Factorial Experiment





















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

b

n

∑∑∑

( yijk − y... ) = bn 2

a

∑

( yi .. − y... ) + an 2

b

∑

( y. j . − y... ) 2











ANOVA Table – Fixed Effects Case





































Design-Expert Output – Example 5.1

































































































Design of Experiments

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