Ch 5 Factorial Design

CH. 5FACTORIAL DESIGN

I N T R O D U C T I O N

• Factorial design is an important method to determine the effects of MULTIPLE variables on a response/output.

• Traditionally, experiments are designed to determine the effect of ONE variable upon ONE response/output.

https://controls.engin.umich.edu/wiki/index.php/Design_of_experiments_via_factorial_designs


Tensile Strengt

h

Cooling Rate

%CAlloying Elemen

ts

Heating Temp

Heat Transfer Rate

Temp Diff

Physical Prop.

Fluid Velocity

Heat Transfer Area

Which variable is more important than others?

• R.A. Fisher showed that there are advantages by combining the study of multiple variables in the same factorial experiment. Factorial design can reduce the number of experiments one has to perform by studying multiple factors simultaneously.

• Additionally, it can be used to find both main effects (from each independent factor) and interaction effects (when both factors must be used to explain the outcome).



• Factorial design is a useful method to design experiments in both laboratory and industrial settings.

• Because factorial design can lead to a large number of trials, which can become expensive and time-consuming, factorial design is best used for a small number of variables with few states (1 to 3).



A 23 FACTORIAL DESIGN: PILOT PLANT INVESTIGATION

• This experiment employed a 23 factorial experimental design with two quantitative factors—temperature T and concentration C—and a single qualitative factor—type of catalyst K.

• Each data value recorded is for the response yield y averaged over two duplicate runs.

CALCULATION OF MAIN EFFECTS



INTERACTION EFFECTS

I N T E R A C T I O N E F F E C T S

I N T E R A C T I O N E F F E C T S

A L G O R I T M A YAT E S

• To calculate – The main effects (e.g. main effect 1, main effect 2,

etc.)– The interaction effects (12, 13, 23, 123, etc.)

STANDARD ERROR FOR EFFECTS

effect

effect

VSE

sN

V

24

Repl-1 Repl-2 Varians59 61 274 70 850 58 3269 67 250 54 881 85 846 44 279 81 2

SUM-s^2= 64Average-SUM-s^2= 8

V(effect)= 2SE = 1,41

Yield

S TA N D A R D E R R O R

• Standard error = standard of deviation.

nsSE2

15,1323,136628,472

nsSE

http://hatta2stat.wordpress.com/2011/05/21/standar-error/



EXAMPLE-2

EXAMPLE-3

FACTORIAL DESIGN WITH REPLICATION RUNS

• Checked by ANOVA.• Comparing variation between treatment (ST )

and variation within treatment (SR ).• Conclusion..?

12

1

2

kSs

yynS

TT

k

tttT

COMPARING TWO TREATMENTS

• Checked by Fisher Test and Student Test.• Conclusion..?

25,972

min

2max ss

21

1121

5,97

nnsxxt

tt

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Ch 5 Factorial Design