do epp presentation 5

7/23/2019 Do Epp Presentation 5

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1

DESIGN OF EXPERIMENTS by

R. C. Baker

How to gain ! year" o# e$%erien&e inone "'ort week(



Ro)e o# DOE in Pro&e"" I*%ro+e*ent

, DOE i" a #or*a) *at'e*ati&a) *et'o- #or"y"te*ati&a))y %)anning an- &on-&ting "&ienti#i&

"t-ie" t'at &'ange e$%eri*enta) +ariab)e"

toget'er in or-er to -eter*ine t'eir e##e&t o# a

gi+en re"%on"e.

, DOE *ake" &ontro))e- &'ange" to in%t

+ariab)e" in or-er to gain *a$i** a*ont" o#

in#or*ation on &a"e an- e##e&t re)ation"'i%"

wit' a *ini** "a*%)e "i/e.



0


, DOE i" *ore e##i&ient t'at a "tan-ar-

a%%roa&' o# &'anging one +ariab)e at a

ti*e2 in or-er to ob"er+e t'e +ariab)e3"

i*%a&t on a gi+en re"%on"e.

, DOE generate" in#or*ation on t'e e##e&t

+ario" #a&tor" 'a+e on a re"%on"e +ariab)ean- in "o*e &a"e" *ay be ab)e to -eter*ine

o%ti*a) "etting" #or t'o"e #a&tor".



4


, DOE en&orage" brain"tor*ing2 a&ti+itie"

a""o&iate- wit' -i"&""ing key #a&tor" t'at *ay

a##e&t a gi+en re"%on"e an- a))ow" t'e

e$%eri*enter to i-enti#y t'e key2 #a&tor" #or#tre "t-ie".

, DOE i" rea-i)y "%%orte- by n*ero" "tati"ti&a)"o#tware %a&kage" a+ai)ab)e on t'e *arket.



5

B6SIC STEPS IN DOE

, For e)e*ent" a""o&iate- wit' DOE7

, 1. T'e -e"ign o# t'e e$%eri*ent8

, . T'e &o))e&tion o# t'e -ata8

, 0. T'e "tati"ti&a) ana)y"i" o# t'e -ata8 an-

, 4. T'e &on&)"ion" rea&'e- an-re&o**en-ation" *a-e a" a re")t o# t'e

e$%eri*ent.



9

TERMINO:OG;

, Re%)i&ation < re%etition o# a ba"i&

e$%eri*ent wit'ot &'anging any #a&tor

"etting"8 a))ow" t'e e$%eri*enter to e"ti*ate

t'e e$%eri*enta) error =noi"e> in t'e "y"te*"e- to -eter*ine w'et'er ob"er+e-

-i##eren&e" in t'e -ata are rea)2 or ?"t

noi"e28 a))ow" t'e e$%eri*enter to obtain*ore "tati"ti&a) %ower =abi)ity to i-enti#y

"*a)) e##e&t">



@

TERMINO:OG;

, .Ran-o*i/ation < a "tati"ti&a) too) "e- to *ini*i/e %otentia) n&ontro))ab)e bia"e" in t'e e$%eri*ent by

ran-o*)y a""igning *ateria)8 %eo%)e8 or-er t'at

e$%eri*enta) tria)" are &on-&te-8 or any ot'er#a&tor not n-er t'e &ontro) o# t'e e$%eri*enter.

Re")t" in a+eraging ot2 t'e e##e&t" o# t'e

e$traneo" #a&tor" t'at *ay be %re"ent in or-er to

*ini*i/e t'e ri"k o# t'e"e #a&tor" a##e&ting t'e

e$%eri*enta) re")t".



A

TERMINO:OG;

, B)o&king < te&'nie "e- to in&rea"e t'e %re&i"ion o# an e$%eri*ent by breaking t'e

e$%eri*ent into 'o*ogeneo" "eg*ent"

=b)o&k"> in or-er to &ontro) any %otentia)

b)o&k to b)o&k +ariabi)ity =*)ti%)e )ot" o#

raw *ateria)8 "e+era) "'i#t"8 "e+era)

*a&'ine"8 "e+era) in"%e&tor">. 6ny e##e&t"

on t'e e$%eri*enta) re")t" a" a re")t o# t'e b)o&king #a&tor wi)) be i-enti#ie- an-

*ini*i/e-.



TERMINO:OG;

, Con#on-ing 6 &on&e%t t'at ba"i&a))y *ean" t'at

*)ti%)e e##e&t" are tie- toget'er into one %arente##e&t an- &annot be "e%arate-. For e$a*%)e8

, 1. Two %eo%)e #)i%%ing two -i##erent &oin" wo)-

re")t in t'e e##e&t o# t'e %er"on an- t'e e##e&t o#

t'e &oin to be &on#on-e-

, . 6" e$%eri*ent" get )arge8 'ig'er or-er

intera&tion" =-i"&""e- )ater> are &on#on-e- wit'

)ower or-er intera&tion" or *ain e##e&t.



1!

TERMINO:OG;

, Fa&tor" < e$%eri*enta) #a&tor" orin-e%en-ent +ariab)e" =&ontino" or

-i"&rete> an in+e"tigator *ani%)ate" to

&a%tre any &'ange" in t'e ot%t o# t'e

%ro&e"". Ot'er #a&tor" o# &on&ern are t'o"e

t'at are n&ontro))ab)e an- t'o"e w'i&' are

&ontro))ab)e bt 'e)- &on"tant -ring t'e

e$%eri*enta) rn".



11

TERMINO:OG;

, Re"%on"e" < -e%en-ent +ariab)e *ea"re-to -e"&ribe t'e ot%t o# t'e %ro&e"".

, Treat*ent Co*bination" =rn> <e$%eri*enta) tria) w'ere a)) #a&tor" are "et

at a "%e&i#ie- )e+e).



1

TERMINO:OG;

, Fi$e- E##e&t" Mo-e) I# t'e treat*ent)e+e)" are "%e&i#i&a))y &'o"en by t'ee$%eri*enter8 t'en &on&)"ion" rea&'e-wi)) on)y a%%)y to t'o"e )e+e)".

, Ran-o* E##e&t" Mo-e) < I# t'e treat*ent)e+e)" are ran-o*)y &'o"en #ro* a %o%)ation o# *any %o""ib)e treat*ent

)e+e)"8 t'en &on&)"ion" rea&'e- &an bee$ten-e- to a)) treat*ent )e+e)" in t'e %o%)ation.



10

P:6NNING 6 DOE

, E+eryone in+o)+e- in t'e e$%eri*ent "'o)-'a+e a &)ear i-ea in a-+an&e o# e$a&t)y w'at

i" to be "t-ie-8 t'e ob?e&ti+e" o# t'e

e$%eri*ent8 t'e e"tion" one 'o%e" toan"wer an- t'e re")t" anti&i%ate-



14

P:6NNING 6 DOE

, Se)e&t a re"%on"e-e%en-ent +ariab)e=+ariab)e"> t'at wi)) %ro+i-e in#or*ation

abot t'e %rob)e* n-er "t-y an- t'e

%ro%o"e- *ea"re*ent *et'o- #or t'i"re"%on"e +ariab)e8 in&)-ing an

n-er"tan-ing o# t'e *ea"re*ent "y"te*

+ariabi)ity



15

P:6NNING 6 DOE

, Se)e&t t'e in-e%en-ent +ariab)e"#a&tor"=antitati+e or a)itati+e> to be

in+e"tigate- in t'e e$%eri*ent8 t'e n*ber

o# )e+e)" #or ea&' #a&tor8 an- t'e )e+e)" o#ea&' #a&tor &'o"en eit'er "%e&i#i&a))y =#i$e-

e##e&t" *o-e)> or ran-o*)y =ran-o* e##e&t"

*o-e)>.



19

P:6NNING 6 DOE

, C'oo"e an a%%ro%riate e$%eri*enta) -e"ign

=re)ati+e)y "i*%)e -e"ign an- ana)y"i" *et'o-" are

a)*o"t a)way" be"t> t'at wi)) a))ow yor e$%eri*enta)

e"tion" to be an"were- on&e t'e -ata i" &o))e&te-

an- ana)y/e-8 kee%ing in *in- tra-eo##" between"tati"ti&a) %ower an- e&ono*i& e##i&ien&y. 6t t'i"

%oint in ti*e it i" genera))y "e#) to "i*)ate t'e

"t-y by generating an- ana)y/ing arti#i&ia) -ata to

in"re t'at e$%eri*enta) e"tion" &an be an"were-

a" a re")t o# &on-&ting yor e$%eri*ent



1@

P:6NNING 6 DOE

, Per#or* t'e e$%eri*ent =&o))e&t -ata> %aying %arti&)ar attention "&' t'ing" a"

ran-o*i/ation an- *ea"re*ent "y"te*

a&&ra&y8 w'i)e *aintaining a" ni#or* ane$%eri*enta) en+iron*ent a" %o""ib)e.

How t'e -ata are to be &o))e&te- i" a &riti&a)

"tage in DOE



1A

P:6NNING 6 DOE

, 6na)y/e t'e -ata "ing t'e a%%ro%riate"tati"ti&a) *o-e) in"ring t'at attention i"

%ai- to &'e&king t'e *o-e) a&&ra&y by

+a)i-ating n-er)ying a""*%tion"a""o&iate- wit' t'e *o-e). Be )ibera) in t'e

ti)i/ation o# a)) too)"8 in&)-ing gra%'i&a)

te&'nie"8 a+ai)ab)e in t'e "tati"ti&a)"o#tware %a&kage to in"re t'at a *a$i**

a*ont o# in#or*ation i" generate-



1

P:6NNING 6 DOE

, Ba"e- on t'e re")t" o# t'e ana)y"i"8 -raw&on&)"ion"in#eren&e" abot t'e re")t"8

inter%ret t'e %'y"i&a) *eaning o# t'e"e

re")t"8 -eter*ine t'e %ra&ti&a) "igni#i&an&eo# t'e #in-ing"8 an- *ake re&o**en-ation"

#or a &or"e o# a&tion in&)-ing #rt'er

e$%eri*ent"



!

SIMP:E COMP6R6TIE EXPERIMENTS

, Sing)e Mean Hy%ot'e"i" Te"t

, Di##eren&e in Mean" Hy%ot'e"i" Te"t wit'

Ea) arian&e"

, Di##eren&e in Mean" Hy%ot'e"i" Te"t wit'nea) arian&e"

, Di##eren&e in arian&e" Hy%ot'e"i" Te"t

, Paire- Di##eren&e in Mean Hy%ot'e"i" Te"t

, One ay 6na)y"i" o# arian&e



1

CRITIC6: ISSES 6SSOCI6TED ITH

SIMP:E COMP6R6TIE EXPERIMENTS

, How :arge a Sa*%)e S'o)- e Take

, 'y Doe" t'e Sa*%)e Si/e Matter

6nyway

, 'at Jin- o# Prote&tion Do e Ha+e

6""o&iate- wit' Re?e&ting Goo-2 St##

, 'at Jin- o# Prote&tion Do e Ha+e

6""o&iate- wit' 6&&e%ting Ba-2 St##



Sing)e Mean Hy%ot'e"i" Te"t

, 6#ter a %ro-&tion rn o# 1 o/. bott)e"8&on&ern i" e$%re""e- abot t'e %o""ibi)ity t'at

t'e a+erage #i)) i" too )ow.

, Ho7 µ K 1

, Ha7 µ L 1

, )e+e) o# "igni#i&an&e K α K .!5, "a*%)e "i/e K

, SPEC FOR THE ME6N7 1 .1



0

Sing)e Mean Hy%ot'e"i" Te"t

, Sa*%)e *ean K 11.

, Sa*%)e "tan-ar- -e+iation K !.15

, Sa*%)e "i/e K

, Co*%te- t "tati"ti& K .!, Pa)e K !.!A!519

, CONC:SION7 Sin&e Pa)e .!58 yo

#ai) to re?e&t 'y%ot'e"i" an- "'i% %ro-&t.



4

Sing)e Mean Hy%ot'e"i" Te"t Power Cr+e

Power Cr+ea)%'a K !.!58 "ig*a K !.15

Tre Mean

P o w e r

11.A 11. 1 1.1 1.!

!.

!.4

!.9

!.A

1



5

Sing)e Mean Hy%ot'e"i" Te"t Power Cr+e

Si ) M H ' i T P



9

Sing)e Mean Hy%ot'e"i" Te"t Power

Cr+e Di##erent Sa*%)e Si/e"



@

DIFFERENCE IN ME6NS E6:

6RI6NCES

, Ho7 µ1 = µ2

, Ha7 µ1 <> µ2

, )e+e) o# "igni#i&an&e K α K .!5

, "a*%)e "i/e" bot' K 15

, 6""*%tion7 σ1 K σ2 ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗

, Sa*%)e *ean" K 11.A an- 1.1

, Sa*%)e "tan-ar- -e+iation" K !.1 an- !.

, Sa*%)e "i/e" K 15 an- 15



A

DIFFERENCE IN ME6NS E6: 6RI6NCES

Can yo -ete&t t'i" -i##eren&e



DIFFERENCE IN ME6NS E6:

6RI6NCES



0!

DIFFERENCE IN ME6NS nE6:

6RI6NCES

, Sa*e a" t'e Ea) arian&e2 &a"e e$&e%t

t'e +arian&e" are not a""*e- ea).

, How -o yo know i# it i" rea"onab)e to

a""*e t'at +arian&e" are ea) OR

nea)



01

DIFFERENCE IN 6RI6NCE

H;POTHESIS TEST

, Sa*e e$a*%)e a" Di##eren&e in Mean7

, Sa*%)e "tan-ar- -e+iation" K !.1 an- !.

, Sa*%)e "i/e" K 15 an- 15

,

, N)) Hy%ot'e"i"7 ratio o# +arian&e" K 1.!

, 6)ternati+e7 not ea)

, Co*%te- F "tati"ti& K !.5

, Pa)e K !.!14!!@1

, Re?e&t t'e n)) 'y%ot'e"i" #or a)%'a K !.!5.




0


H;POTHESIS TEST

Can yo -ete&t t'i" -i##eren&e



00


H;POTHESIS TEST POER CRE



04

P6IRED DIFFERENCE IN ME6NS

H;POTHESIS TEST

, Two -i##erent in"%e&tor" ea&' *ea"re 1! %art" on t'e "a*e %ie&e o# te"t ei%*ent.

, N)) 'y%ot'e"i"7 DIFFERENCE IN ME6NS

K !.!, 6)ternati+e7 not ea)

, Co*%te- t "tati"ti& K 1.@!

, Pa)e K !.5!44

, Do not re?e&t t'e n)) 'y%ot'e"i" #or a)%'a K

!.!5.



05

P6IRED DIFFERENCE IN ME6NS

H;POTHESIS TEST POER CRE

Power Cr+e

a)%'a K !.!58 "ig*a K 0.A99

Di##eren&e in Mean"

P o w e r

5 4 0 1 ! 1 0 4 5

!

!.

!.4

!.9

!.A

1



09

ONE 6; 6N6:;SIS OF 6RI6NCE

, "e- to te"t 'y%ot'e"i" t'at t'e *ean" o#

"e+era) %o%)ation" are ea).

, E$a*%)e7 Pro-&tion )ine 'a" @ #i)) nee-)e" an-yo wi"' to a""e"" w'et'er or not t'e a+erage

#i)) i" t'e "a*e #or a)) @ nee-)e".

, E$%eri*ent7 "a*%)e ! #i))" #ro* ea&' o# t'e nee-)e" an- te"t at 5Q )e+e) o# "ign.

, Ho7 µ1 K µ2 = µ3= µ4 = µ5 = µ6 = µ7

RES:TS7 6N6:;SIS OF 6RI6NCE



0@

RES:TS7 6N6:;SIS OF 6RI6NCE

T6B:E

Analysis of Variance

---------------------------------------------------------------------------

Source Sum of Squares Df Mean Square F-Ratio P-Val

---------------------------------------------------------------------------

Between groups 1.11! " .1#$$"% 1#."" .

it'in groups 1.$(1( 1$$ .!#)#$(---------------------------------------------------------------------------

*otal +,orr. ).%($" 1$!

SINCE NEED:E ME6NS 6RE NOT 6::



0A

SINCE NEED:E ME6NS 6RE NOT 6::

E6:8 HICH ONES 6RE DIFFERENT

, M)ti%)e Range Te"t" #or @ Nee-)e" Met'o/ !0. percent SD

,ol2) ,ount Mean 3omogeneous 4roups

--------------------------------------------------------------------------------

5( ) 11.(#" 6

5) ) 11.!#11 6 51 ) 11.!#)( 6

5" ) 11.!#($ 6

5$ ) 11.!!01 6

50 ) 11.!!0$ 6

5% ) 1).11 6

IS6: COMP6RISON OF @



0

IS6: COMP6RISON OF @

NEED:ES

N1

N

N0

N4

N5

N9

N@

Bo$an-H'i"ker P)ot

11.5 11.@ 11. 1.1 1.0

Co)1

C o )

k



4!

F6CTORI6: =k > DESIGNS

, E$%eri*ent" in+o)+ing "e+era) #a&tor" = k K

o# #a&tor"> w'ere it i" ne&e""ary to "t-y

t'e ?oint e##e&t o# t'e"e #a&tor" on a "%e&i#i&

re"%on"e.

, Ea&' o# t'e #a&tor" are "et at two )e+e)" =a

)ow2 )e+e) an- a 'ig'2 )e+e)> w'i&' *ay

be a)itati+e =*a&'ine 6*a&'ine B8 #an

on#an o##> or antitati+e =te*%eratreA!!te*%eratre !!8 )ine "%ee- 4!!! %er

'or)ine "%ee- 5!!! %er 'or>.



41


, Fa&tor" are a""*e- to be #i$e- =#i$e-e##e&t" *o-e)>

, De"ign" are &o*%)ete)y ran-o*i/e-

=e$%eri*enta) tria)" are rn in a ran-o*or-er8 et&.>

, T'e "a) nor*a)ity a""*%tion" are

"ati"#ie-.



4


, Parti&)ar)y "e#) in t'e ear)y "tage" o#e$%eri*enta) work w'en yo are )ike)y to

'a+e *any #a&tor" being in+e"tigate- an-

yo want to *ini*i/e t'e n*ber o#treat*ent &o*bination" ="a*%)e "i/e> bt8 at

t'e "a*e ti*e8 "t-y a)) k #a&tor" in a

&o*%)ete #a&toria) arrange*ent =t'e

e$%eri*ent &o))e&t" -ata at a)) %o""ib)e

&o*bination" o# #a&tor )e+e)">.



40


, 6" k get" )arge8 t'e "a*%)e "i/e wi))in&rea"e e$%onentia))y. I# e$%eri*ent i"

re%)i&ate-8 t'e rn" again in&rea"e".

k # of runs2 4

3 8

4 16

5 32

6 64

7 128

8 256

9 512

10 1024



44

F6CTORI6: =k > DESIGNS =k K >

, Two #a&tor" "et at two )e+e)" =nor*a))y

re#erre- to a" )ow an- 'ig'> wo)- re")t int'e #o))owing -e"ign w'ere ea&' )e+e) o#

#a&tor 6 i" %aire- wit' ea&' )e+e) o# #a&tor

B.

RUN Factor A Factor B RESPNSE RUN Factor A Factor B RESPNSE

1 !o" !o" #1 1 $1 $1 #1

2 %&'% !o" #2 2 (1 $1 #2

3 !o" %&'% #3 3 $1 (1 #3

4 %&'% %&'% #4 4 (1 (1 #4

)*n*ra!&+*, S*tt&n s rt%o ona! S*tt&n s



45


, E"ti*ating *ain e##e&t" a""o&iate- wit'

&'anging t'e )e+e) o# ea&' #a&tor #ro* )ow

to 'ig'. T'i" i" t'e e"ti*ate- e##e&t on t'e

re"%on"e +ariab)e a""o&iate- wit' &'anging

#a&tor 6 or B #ro* t'eir )ow to 'ig' +a)e".

>=

>= 014 y y y y Effect A Factor

+−

+=

>=

>= 140 y y y y Effect B Factor

+−

+=



49

F6CTORI6: =k > DESIGNS =k K >7

GR6PHIC6: OTPT, Neit'er #a&tor 6 nor Fa&tor B 'a+e an e##e&t

on t'e re"%on"e +ariab)e.



4@


GR6PHIC6: OTPT

, Fa&tor 6 'a" an e##e&t on t'e re"%on"e

+ariab)e8 bt Fa&tor B -oe" not.

= k> =k >



4A


GR6PHIC6: OTPT

, Fa&tor 6 an- Fa&tor B 'a+e an e##e&t on t'e

re"%on"e +ariab)e.




4

F6CTORI6: = > DESIGNS =k >7

GR6PHIC6: OTPT

,Fa&tor B 'a" an e##e&t on t'e re"%on"e +ariab)e8 bt on)y i##a&tor 6 i" "et at t'e Hig'2 )e+e). T'i" i" called

interaction an- it ba"i&a))y *ean" t'at t'e e##e&t one #a&tor

'a" on a re"%on"e i" -e%en-ent on t'e )e+e) yo "et ot'er

#a&tor" at. Intera&tion" &an be *a?or %rob)e*" in a DOE i#

yo #ai) to a&&ont #or t'e intera&tion w'en -e"igning yore$%eri*ent.



5!

EX6MP:E7


, 6 *i&robio)ogi"t i" intere"te- in t'e e##e&t

o# two -i##erent &)tre *e-i*" *e-i* 1

=)ow> an- *e-i* ='ig'>U an- two-i##erent ti*e" 1! 'or" =)ow> an- ! 'or"

='ig'>U on t'e growt' rate o# a %arti&)ar

CF.

EX6MP:E7



51

EX6MP:E7


, Sin&e two #a&tor" are o# intere"t8 k K8 an-we wo)- nee- t'e #o))owing #or rn"

re")ting in

RUN -*,&u. /&.* )ro"t% Rat*

1 !o" !o" 17

2 %&'% !o" 15

3 !o" %&'% 38

4 %&'% %&'% 39

)*n*ra!&+*, S*tt&n's

EX6MP:E7



5

EX6MP:E7


, E"ti*ate" #or t'e *e-i* anti*ee##e&t" are

, Me-i* e##e&t K =150>U < =1@ 0A>U K !.5

, Ti*e e##e&t K =0A0>U < =1@ 15>U K.5

EX6MP:E7



50

EX6MP:E7


EX6MP:E7



54

EX6MP:E7


, 6 "tati"ti&a) ana)y"i" "ing t'e a%%ro%riate"tati"ti&a) *o-e) wo)- re")t in t'e

#o))owing in#or*ation. Fa&tor 6 =*e-i*>

an- Fa&tor B =ti*e>*ype 777 Sums of Squares

------------------------------------------------------------------------------------

Source Sum of Squares Df Mean Square F-Ratio P-Value

------------------------------------------------------------------------------------

FA,*8R A .)0 1 .)0 .11 .(!0)

FA,*8R B 0".)0 1 0".)0 ))0. .%)%

Resiual ).)0 1 ).)0------------------------------------------------------------------------------------

*otal +correcte 0#.(0 $

All F-ratios are 9ase on t'e resiual mean square error.

EX6MP:E7



55

EX6MP:E7

CONC:SIONS

, In "tati"ti&a) )angage8 one wo)- &on&)-et'at #a&tor 6 =*e-i*> i" not "tati"ti&a))y

"igni#i&ant at a 5Q )e+e) o# "igni#i&an&e

"in&e t'e %+a)e i" greater t'an 5Q =!.!5>8

bt #a&tor B =ti*e> i" "tati"ti&a))y "igni#i&ant

at a 5 Q )e+e) o# "igni#i&an&e "in&e t'i" %

+a)e i" )e"" t'an 5Q.

EX6MP:E7



59

EX6MP:E7

CONC:SIONS

, In )ay*an ter*"8 t'i" *ean" t'at we 'a+eno e+i-en&e t'at wo)- a))ow " to

&on&)-e t'at t'e *e-i* "e- 'a" an e##e&t

on t'e growt' rate8 a)t'og' it *ay we))

'a+e an e##e&t =or &on&)"ion wa"

in&orre&t>.



5@

EX6MP:E7

CONC:SIONS, 6--itiona))y8 we 'a+e e+i-en&e t'at wo)-

a))ow " to &on&)-e t'at ti*e -oe" 'a+e an

e##e&t on t'e growt' rate8 a)t'og' it *aywe)) not 'a+e an e##e&t =or &on&)"ion wa"

in&orre&t>.



5A

EX6MP:E7

CONC:SIONS

, In genera) we &ontro) t'e )ike)i'oo- o#

rea&'ing t'e"e in&orre&t &on&)"ion" by t'e

"e)e&tion o# t'e )e+e) o# "igni#i&an&e #or t'ete"t an- t'e a*ont o# -ata &o))e&te-

="a*%)e "i/e>.

k DESIGNS =k >



5

k DESIGNS =k >

, 6" t'e n*ber o# #a&tor" in&rea"e8 t'e

n*ber o# rn" nee-e- to &o*%)ete a

&o*%)ete #a&toria) e$%eri*ent wi)) in&rea"e

-ra*ati&a))y. T'e #o))owing k -e"ign

)ayot -e%i&t t'e n*ber o# rn" nee-e- #or+a)e" o# k #ro* to 5. For e$a*%)e8 w'en

k K 58 it wi)) take 0 e$%eri*enta) rn" #or

t'e &o*%)ete #a&toria) e$%eri*ent.

k DESIGNS =k >



9!

RUNS

1 $1 $1 $1 $1 $1

2 (1 $1 $1 $1 $13 $1 (1 $1 $1 $1

4 (1 (1 $1 $1 $1

5 $1 $1 (1 $1 $1

6 (1 $1 (1 $1 $1

7 $1 (1 (1 $1 $1

8 (1 (1 (1 $1 $1

9 $1 $1 $1 (1 $1

10 (1 $1 $1 (1 $1

11 $1 (1 $1 (1 $1

12 (1 (1 $1 (1 $113 $1 $1 (1 (1 $1

14 (1 $1 (1 (1 $1

15 $1 (1 (1 (1 $1

16 (1 (1 (1 (1 $1

17 $1 $1 $1 $1 (1

18 (1 $1 $1 $1 (1

19 $1 (1 $1 $1 (1

20 (1 (1 $1 $1 (1

21 $1 $1 (1 $1 (1

22 (1 $1 (1 $1 (123 $1 (1 (1 $1 (1

24 (1 (1 (1 $1 (1

25 $1 $1 $1 (1 (1

26 (1 $1 $1 (1 (1

27 $1 (1 $1 (1 (1

28 (1 (1 $1 (1 (1

29 $1 $1 (1 (1 (1

30 (1 $1 (1 (1 (1

31 $1 (1 (1 (1 (1

32 (1 (1 (1 (1 (1

2k Desi n La outs k = 2-5

k = 2

k = 3

k = 4

k = 5



91

Intera&tion" #or k De"ign" =k K 0>

, Intera&tion" between +ario" #a&tor" &an be e"ti*ate- #or -i##erent -e"ign" abo+e

by *)ti%)ying t'e a%%ro%riate &o)*n"

toget'er an- t'en "btra&ting t'e a+eragere"%on"e #or t'e )ow" #ro* t'e a+erage

re"%on"e #or t'e 'ig'".



9

Intera&tion" #or k De"ign" =k K 0>

a b c ab ac bc abc

$1 $1 $1 1 1 1 $1

(1 $1 $1 $1 $1 1 1

$1 (1 $1 $1 1 $1 1

(1 (1 $1 1 $1 $1 $1

$1 $1 (0 1 $1 $1 1

(1 $1 (1 $1 1 $1 $1$1 (1 (1 $1 $1 1 $1

(1 (1 (1 1 1 1 1



90

k DESIGNS =k >

, On&e t'e e##e&t #or a)) #a&tor" an-

intera&tion" are -eter*ine-8 yo are ab)e to

-e+e)o% a %re-i&tion *o-e) to e"ti*ate t'ere"%on"e #or "%e&i#i& +a)e" o# t'e #a&tor".

In genera)8 we wi)) -o t'i" wit' "tati"ti&a)

"o#tware8 bt #or t'e"e -e"ign"8 yo &an -oit by 'an- &a)&)ation" i# yo wi"'.



94

k DESIGNS =k >

, For e$a*%)e8 i# t'ere are no "igni#i&ant intera&tion"

%re"ent8 yo &an e"ti*ate a re"%on"e by t'e

#o))owing #or*)a. =#or antitati+e #a&tor" on)y>



95

ONE F6CTOR EX6MP:E

, Si*%)e one #a&tor2 e$a*%)e w'ere t'e

#a&tor i" t'e n*ber o# 'or" a "t-ent

"t-ie" #or an e$a* =:O K 1! HRS8HIGH K ! HRS> an- t'e re"%on"e +ariab)e

i" t'eir gra-e. E"ti*ate t'e *o-e) #or

%re-i&tion a "t-ent" gra-e a" a #n&tion o#t'e n*ber o# 'or" t'ey "t-y.

ONE F6CTOR EX6MP:E



99

P)ot o# Fitte- Mo-e)

HRS STGD;

G R 6 D E

1! 1 14 19 1A !

55

95

@5

A5

5

ONE F6CTOR EX6MP:E



9@

ONE F6CTOR EX6MP:E

, T'e ot%t "'ow" t'e re")t" o# #itting agenera) )inear *o-e) to -e"&ribe t'e

re)ation"'i% between GR6DE an- HRS

STD;. T'e eation o# t'e #itte- genera)

*o-e) i"

, GR6DE K .0 0.1 =HRS STD;>

, T'e #itte- ort'ogona) *o-e) i"

, GR6DE K @5 15 =SC6:ED HRS>

T : ) S i D i



9A

Two :e+e) S&reening De"ign" , S%%o"e t'at yor brain"tor*ing "e""ion

re")te- in @ #a&tor" t'at +ario" %eo%)et'ink *ig't2 'a+e an e##e&t on a re"%on"e.6 #)) #a&toria) -e"ign wo)- reire @ K1A e$%eri*enta) rn" wit'ot re%)i&ation.

T'e %r%o"e o# "&reening -e"ign" i" tore-&e =i-enti#y> t'e n*ber o# #a&tor"-own to t'e *a?or2 ro)e %)ayer" wit' a

*ini*a) n*ber o# e$%eri*enta) rn". Oneway to -o t'i" i" to "e t'e 0 #)) #a&toria)-e"ign an- "e intera&tion &o)*n" #or#a&tor".

Note t'at



9

Note t'at

6ny #a&tor - e##e&t i" now &on#on-e- wit' t'e ab

intera&tion

6ny #a&tor e e##e&t i" now &on#on-e- wit' t'e a&

intera&tion

et&.

'at i" t'e -e intera&tion &on#on-e- wit'a b c d = ab e = ac f = bc g = abc

$1 $1 $1 1 1 1 $1

(1 $1 $1 $1 $1 1 1

$1 (1 $1 $1 1 $1 1

(1 (1 $1 1 $1 $1 $1

$1 $1 ( 1 $1 $1 1

(1 $1 (1 $1 1 $1 $1

$1 (1 (1 $1 $1 1 $1

(1 (1 (1 1 1 1 1



@!

Prob)e*" t'at Intera&tion" Ca"e(

, Intera&tion" < I# intera&tion" e$i"t an- yo #ai) to

a&&ont #or t'i"8 yo *ay rea&' erroneo"

&on&)"ion". S%%o"e t'at yo %)an an

e$%eri*ent wit' #or rn" an- t'ree #a&tor"

re")ting in t'e #o))owing -ata7




@1


, Fa&tor 6 E##e&t K !

, Fa&tor B E##e&t K !, Fa&tor C E##e&t K 5

, In t'i" e$a*%)e8 i# yo were a""*ing t'at

)arger i" better2 t'en yo wo)- "et Fa&torC at t'e 'ig' )e+e)2 an- it a%%ear" to *akeno -i##eren&e w'ere yo "et #a&tor" 6 an- B.In t'i" &a"e t'ere i" a #a&tor 6 intera&tion

wit' #a&tor B an- t'i" intera&tion i"&on#on-e- wit' t'e #a&tor C e##e&t.



@


Intera&tion P)ot

F6CTOR 6

5

9

@

A

1!

R E S P O N S E

1 1

F6CTOR B1

1



@0

Re"o)tion o# a De"ign

, T'e abo+e -e"ign wo)- be &a))e- a

re"o)tion III -e"ign be&a"e *ain e##e&t"

are a)ia"e- =&on#on-e-> wit' two #a&torintera&tion".

Re"o)tion o# a De"ign



@4

g

, Re"o)tion III De"ign" < No *ain e##e&t" area)ia"e- wit' any ot'er *ain e##e&t BT "o*e =ora))> *ain e##e&t" are a)ia"e- wit' two wayintera&tion"

, Re"o)tion I De"ign" < No *ain e##e&t" area)ia"e- wit' any ot'er *ain e##e&t OR two #a&torintera&tion8 BT two #a&tor intera&tion" *ay bea)ia"e- wit' ot'er two #a&tor intera&tion"

, Re"o)tion De"ign" < No *ain e##e&t OR two#a&tor intera&tion i" a)ia"e- wit' any ot'er *aine##e&t or two #a&tor intera&tion8 BT two #a&torintera&tion" are a)ia"e- wit' t'ree #a&torintera&tion".

C S i D i



@5

Co**on S&reening De"ign"

, Fra&tiona) Fa&toria) De"ign" < t'e tota)n*ber o# e$%eri*enta) rn" *"t be a

%ower o# =48 A8 198 08 948 V>. I# yo

be)ie+e #ir"t or-er intera&tion" are "*a))

&o*%are- to *ain e##e&t"8 t'en yo &o)-

&'oo"e a re"o)tion III -e"ign. W"t

re*e*ber t'at i# yo 'a+e *a?or

intera&tion"8 it &an *e"" % yor "&reeninge$%eri*ent.

C S i D i



@9

Co**on S&reening De"ign"

, P)a&kettBr*an De"ign" < Two )e+e)8re"o)tion III -e"ign" "e- to "t-y % to

n1 #a&tor" in n e$%eri*enta) rn"8 w'ere

n i" a *)ti%)e o# 4 = o# rn" wi)) be 48 A8

18 198 V>. Sin&e n *ay be ite )arge8

yo &an "t-y a )arge n*ber o# #a&tor"

wit' *o-erate)y "*a)) "a*%)e "i/e". =n K

1!! *ean" yo &an "t-y #a&tor" wit'1!! rn">

Ot'er De"ign I""e"



@@

Ot'er De"ign I""e"

, May want to &o))e&t -ata at &enter %oint" to

e"ti*ate non)inear re"%on"e"

, More t'an two )e+e)" o# a #a&tor < no

%rob)e* =*)ti)e+e) #a&toria)>

, 'at -o yo -o i# yo want to bi)- a non

)inear *o-e) to o%ti*i/e2 t'e re"%on"e.

='it a target8 *a$i*i/e8 or *ini*i/e> <

&a))e- re"%on"e "r#a&e *o-e)ing

Ot'er De"ign I""e"



@A

Ot'er De"ign I""e"

, 'at -o yo -o i# t'e #a&tor" )e+e)" are

&ategori&a) annot antitati+e8 or "o*e are&ategori&a) an- "o*e are antitati+e

, 'at -o yo -o i# t'e "tr&tre o# yo

e$%eri*ent i" ne"te-2 T'e"e are &a))e-'eirar&'i&a) -e"ign" an- wi)) a))ow yo to

%artition t'e tota) +ariabi)ity a*ong t'e

-i##erent )e+e)" o# t'e -e"ign =&a))e-+arian&e &o*%onent">

Re"%on"e Sr#a&e De"ign" < Bo$Be'nken7



@

Re"%on"e Sr#a&e De"ign" Bo$ Be'nken7

6#ter "&reening -e"ign" i-enti#y *a?or #a&tor" <Ne$t "te%.

, De"ign &)a""7 Re"%on"e Sr#a&e

, De"ign na*e7 Bo$Be'nken -e"ign

, Ba"e De"ign

,

, N*ber o# e$%eri*enta) #a&tor"7 0 N*ber o# b)o&k"7 1

, N*ber o# re"%on"e"7 1, N*ber o# rn"7 15 Error -egree" o# #ree-o*7 5

, Ran-o*i/e-7 No

, Fa&tor" :ow Hig' nit" Contino"

, , Fa&tor6 1.! 1.! ;e"

, Fa&torB 1.! 1.! ;e"

, Fa&torC 1.! 1.! ;e"

Re"%on"e Sr#a&e De"ign" < Bo$Be'nken



A!

Re"%on"e Sr#a&e De"ign" Bo$ Be'nken

FA/R A FA/R B FA/R

0 0 0

$1 $1 0

1 $1 0

$1 1 0

1 1 0

$1 0 $1

1 0 $1

0 0 0

$1 0 1

1 0 1

0 $1 $1

0 1 $1

0 $1 1

0 1 1

0 0 0

Re"%on"e Sr#a&e De"ign" < Centra)



A1

% g

Co*%o"ite

, De"ign &)a""7 Re"%on"e Sr#a&e, De"ign na*e7 Centra) &o*%o"ite b)o&ke- &be"tar

, N*ber o# e$%eri*enta) #a&tor"7 0 N*ber o# b)o&k"7

, N*ber o# re"%on"e"7 1

, N*ber o# rn"7 19 Error -egree" o# #ree-o*7 5

, Ran-o*i/e-7 No

, Fa&tor" :ow Hig' nit"Contino"

, , Fa&tor6 1.! 1.! ;e"

, Fa&torB 1.! 1.! ;e"

, Fa&torC 1.! 1.! ;e"



A

Re"%on"e Sr#a&e De"ign" < Centra)

Co*%o"iteFA/R A FA/R B FA/R

$1 $1 $1

1 $1 $1

$1 1 $1

1 1 $1

0 0 0

$1 $1 1

1 $1 1

$1 1 1

1 1 1

$176383 0 0

176383 0 0

0 $176383 0

0 0 0

0 176383 0

0 0 $176383

0 0 176383

M)ti)e+e) Fa&toria) De"ign"



A0

M)ti)e+e) Fa&toria) De"ign", De"ign &)a""7 M)ti)e+e) Fa&toria)



, N*ber o# rn"7 @ Error -egree" o# #ree-o*7 1@

, Ran-o*i/e-7 No

, Fa&tor" :ow Hig' :e+e)" nit"

,

, Fa&tor6 1.! 1.! 0

, Fa&torB 1.! 1.! 0

, Fa&torC 1.! 1.! 0

M)ti)e+e) Fa&toria) De"ign"



A4

Ne"te- De"ign



A5

g, De"ign &)a""7 arian&e Co*%onent"

, N*ber o# e$%eri*enta) #a&tor"7 0


, N*ber o# rn"7 @

, Ran-o*i/e-7 No

Fa&tor" :e+e)" nit"

, , Fa&tor6 0

, Fa&torB 0

, Fa&torC 0

;o 'a+e &reate- a +arian&e &o*%onent" -e"ign w'i&' wi))e"ti*ate t'e &ontribtion o# 0 #a&tor" to o+era)) %ro&e""+ariabi)ity. T'e -e"ign i" 'ierar&'i&a)8 wit' ea&' #a&torne"te- in t'e #a&tor abo+e it. 6 tota) o# @ *ea"re*ent"are reire-.

Ne"te- De"ign



A9

Ne"te- De"ign




A@

EX6MP:E REC6P, De"ign &)a""7 Re"%on"e Sr#a&e

, De"ign na*e7 Bo$Be'nken -e"ign

, Ba"e De"ign

,



, N*ber o# rn"7 15 Error -egree" o# #ree-o*7 5, Ran-o*i/e-7 No

, Fa&tor" :ow Hig' nit" Contino"

,

, Fa&tor6 1! 0! ;e", Fa&torB 0! 9! ;e"

, Fa&torC 4! 9! ;e"



AA




A

Re"%on"e Sr#a&e De"ign" < Bo$Be'nkenRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>

RUN F1 F2 F3

1 10 45 60

2 30 45 40

3 20 30 40

4 10 30 50

5 20 45 50

6 30 60 50

7 20 45 50

8 30 45 60

9 20 45 50

10 20 60 40

11 10 45 40

12 30 30 50

13 20 60 60

14 10 60 50

15 20 30 60




!

% gRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>

Example: std. dev. of noise = 0

RUN F1 F2 F3 0

1 10 45 60 11800

2 30 45 40 8800

3 20 30 40 8400

4 10 30 50 9300

5 20 45 50 9400

6 30 60 50 8300

7 20 45 50 9400

8 30 45 60 10800

9 20 45 50 9400

10 20 60 40 8400

11 10 45 40 9800

12 30 30 50 11300

13 20 60 60 10400

14 10 60 50 12300

15 20 30 60 10400

Re"%on"e Sr#a&e De"ign" < Bo$



1

% g

Be'nkenRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>


Regression coeffs. for Var_1

------------------------------------------------------------

constant = 0.0

A:Factor_A = 40.0

B:Factor_B = 200.0

C:Factor_C = 100.0

AA = 9.0

AB = -10.0

AC = 0.0

BB = 0.0BC = 0.0

CC = 0.0

R S # D i B B ' k





Optimie Response

-----------------

!oa": #A$%#%&' Var_1

Optim(m )a"(e = 1*2+1.4

Factor ,o ig/ Optim(m

-----------------------------------------------------------------------

Factor_A 10.0 *0.0 10.101

Factor_B *0.0 +0.0 +0.0Factor_C 40.0 +0.0 +0.0

R S # D i B B ' k



0



R S # D i B B ' k



4



RUN F1 F2 F3 100

1 10 45 60 11825

2 30 45 40 8781

3 20 30 40 8413

4 10 30 50 9216

5 20 45 50 9288

6 30 60 50 8261

7 20 45 50 9329

8 30 45 60 10855

9 20 45 50 9205

10 20 60 40 8538

11 10 45 40 9718

12 30 30 50 11308

13 20 60 60 10316

14 10 60 50 12056

15 20 30 60 10378

R S # D i B B ' k



5



Regression coeffs. for Var_*

----------------------------------------------------------------------

constant = 2*12.

A:Factor_A = *+.

B:Factor_B = 200.0+C:Factor_C = *.

AA = 9.09

AB = -9.11+

AC = -0.02

BB = 0.11222

BC = -0.*11++

CC = 1.10




9



Stan-ar-i/e- Pareto C'art #or arR0

Stan-ar-i/e- e##e&t

! 1! ! 0! 4!

6CBB

B7Fa&torRB

BC

CC

67Fa&torR6

66C7Fa&torRC

6B




@



Contor" o# E"ti*ate- Re"%on"e Sr#a&e

Fa&torCK9!.!

Fa&tor6

F a & t o rR B

ar0

0!!.!

5!!.!@!!.!

!!.!

1!1!!.!

1!0!!.!

1!5!!.!

1!@!!.!

1!!!.!

111!!.!

110!!.!

115!!.!

11@!!.!

1! 14 1A 9 0!

0!

05

4!

45

5!55

9!




A



, O%ti*i/e Re"%on"e

,

, Goa)7 *a$i*i/e ;

, O%ti** +a)e K 1010.4

, Fa&tor :ow Hig' O%ti**

,

, Fa&tor6 1!.! 0!.! 1!.1!09

, Fa&torB 0!.! 9!.! 9!.!

, Fa&torC 4!.! 9!.! 9!.!

R S # D i T' : ) F t i ) D i =00>



Re"%on"e Sr#a&e De"ign" < T'ree :e+e) Fa&toria) De"ign =00>

RE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>


RUN F1 F2 F3 100

1 10 30 40 8270

2 20 30 40 8272

3 30 30 40 10324

4 10 45 40 9928

5 20 45 40 8520

6 30 45 40 8973

7 10 60 40 11082

8 20 60 40 8377

9 30 60 40 7410

10 10 30 50 9191

11 20 30 50 9331

12 30 30 50 11131

13 10 45 50 10615

Re"%on"e S r#a&e De"ign" T'ree :e e) Fa&toria) De"ign =00>



1!!




RUN F1 F2 F3 100

14 20 45 50 9302

15 30 45 50 9723

16 10 60 50 12088

17 20 60 50 9343

18 30 60 50 8260

19 10 30 60 10313

20 20 30 60 10363

21 30 30 60 12267

22 10 45 60 11763

23 20 45 60 10534

24 30 45 60 10791

25 10 60 60 13281

26 20 60 60 10349

27 30 60 60 9497

Re"%on"e Sr#a&e De"ign" T'ree :e+e) Fa&toria) De"ign =00>



1!1




Regression coeffs. for 3

----------------------------------------------------------------------

constant = 2.0

A:Factor_A = *+.02B:Factor_B = 212.0+

C:Factor_C = -*1.0*0+

AA = .9**

AB = -9.***

AC = -0.190**

BB = -0.2*04

BC = 0.100+

CC = 1.*0***




1!




, O%ti*i/e Re"%on"e

,

, Goa)7 *a$i*i/e ;

, O%ti** +a)e K 100!.9


,

, Fa&tor6 1!.! 0!.! 1!.!

, Fa&torB 0!.! 9!.! 9!.!

, Fa&torC 4!.! 9!.! 9!.!




1!0




E"ti*ate- Re"%on"e Sr#a&eFa&torCK9!.!

Fa&tor6

Fa&torB

;

1! 14 1A 9 0! 0! 054! 45

5! 559!

4!!

1!4!!

114!!

14!!

104!!




1!4





Fa&torBK9!.!

Fa&tor6

F a & t o rR C

;

A!!.!

A9!!.!!!!.!

4!!.!

A!!.!

1!!!.!

1!9!!.!

11!!!.!

114!!.!11A!!.!

1!!.!

19!!.!

1! 14 1A 9 0!

4!

44

4A

5

59

9!

C:6SSROOM EXERCISE



1!5

, STDENT INC:6SS EXPERIMENT7

Co))e&t -ata #or e$%eri*ent to -eter*ine#a&tor "etting" =two #a&tor"> to 'it a target

re"%on"e ="%ot on wa))>.

, Fa&tor 6 < 'eig't o# "'aker =)ow an- 'ig'>, Fa&tor B < )o&ation o# "'aker =&)o"e to

'an- an- &)o"e to wa))>

, De"ign e$%eri*ent < wo)- "gge"t"e+era) re%)i&ation"

C:6SSROOM EXERCISE



1!9

, Con-&t E$%eri*ent < "t-ent 'o)-" 0 #oot

%in t'e tai) on t'e -onkey2 "ti&k an-atte*%t" to 'it t'e target. 6n ob"er+er wi))

a""i"t to *ark t'e 'it on t'e target.

, Co))e&t -ata < "t-ent" take -ata 'o*e #orweek an- &o*e ba&k wit' w'at yo wo)-

re&o**en- 6ND w'y.

, ;O TE:: THE C:6SS HO TO P:6;THE G6ME TO IN2.

C:6SSROOM EXERCISE



1!@

C:6SSROOM EXERCISE



1!A

-ARER

S/

ER/A

PE 1S/ BS 2N BS 3R BS 4/ BS -EAN

S/ANAR

EA/N

$2750 $4500 $4750 $5000 $4250 1021

$12500 $6750 $4625 $4000 $6969 3871

3000 3250 3875 6250 4094 1484

4625 11250 12625 14000 10625 4155

-ARER

S/

: ER/A PE ;AS SE / ;A <-ARER EN F S/

:ER/A PE ;AS SE / AN

ER/APE

:SAN) EE A/E ; N ER/A PE:SAN) EE A/E ) N ER/A PE

C:6SSROOM EXERCISE



1!

, HOMEORJ7

, .Deter*ine t'e e##e&t" *arker "ti&k2 an- +erti&a) %o)e2'a+e on t'e mean location of the hit.

, .Deter*ine t'e e##e&t" *arker "ti&k2 an- +erti&a) %o)e2

'a+e on t'e standard deviation of the hit.

,.'i&' #a&tor wo)- yo "ay a##e&t" t'e *ean )o&ation o#t'e 'it2

, .'i&' #a&tor wo)- yo "ay a##e&t" t'e "tan-ar- -e+iation

o# t'e 'it2

, OPTIM6: SETTINGS7 'ere wo)- yo re&o**en- we

)o&ate t'e +erti&a) %o)e2 an- t'e *arker "ti&k2 IF we

wi"' to =a> MINIMIE THE 6RI6BI:IT; OF THE HIT

an- =b> HIT THE T6RGET :OC6TED 6T !2



11!

PIN THE T6I: D6T6 INPT



111

ESTIM6TE OF EFFECTS =ME6N HIT>

, E"ti*ate- e##e&t" #or ME6N

,

, a+erage K !.A@5

, 67M6RJER STICJ K 1.!9, B7ERTIC6: PO:E K 1.9

, 6B K 4.95

,

, No -egree" o# #ree-o* )e#t to e"ti*ate "tan-ar- error".



11


Pareto C'art #or ME6N

E##e&t

! 0 9 1 15

67M6RJER STICJ

6B

B7ERTIC6: PO:E



110


Main E##e&t" P)ot #or ME6N

M E 6 N

M6RJER STICJ 1.! 1.!

ERTIC6: PO:E1.! 1.!

9

0

!

0

9



114

INTER6CTION P:OT =ME6N HIT>

Intera&tion P)ot #or ME6N

M E 6 N

M6RJER STICJ

1.! 1.!

ERTIC6: PO:EK1.!

ERTIC6: PO:EK1.!

ERTIC6: PO:EK1.!

ERTIC6: PO:EK1.!

@

4

1

5

A

11



115

0D P:OT OF RESPONSE =ME6N HIT>

E"ti*ate- Re"%on"e Sr#a&e

M6RJER STICJ

ERTIC6: PO:E

M E 6 N

1 !.9 !. !. !.9 11 !.9

!.!. !.9

1

@

4

1

5

A

11

CONTOR P:OT OF RESPONSE



119


=ME6N HIT>


M6RJER STICJ

F E R T I C 6 : P O : E

ME6N

4.!.!

!.!

.!

4.!

9.!

A.!

1 !.9 !. !. !.9 1

1

!.9

!.

!.

!.9

1

6N6:;SIS OF 6RI6NCE T6B:E



11@

6N6:;SIS OF 6RI6NCE T6B:E

=ME6N HIT>

, 6na)y"i" o# arian&e #or ME6N

,

, Sor&e S* o# Sare" D# Mean Sare FRatio Pa)e

,

, 67M6RJER STICJ 0.90A4 1 0.90A4 !.1@ !.@511, B7ERTIC6: PO:E 19A.15 1 19A.15 @.A9 !.1A1

, Tota) error 1.0!9 1 1.0!9

,

ESTIM6TED :INE6R RESPONSE MODE:=ME6N HIT>



11A

= >

, Regre""ion &oe##". #or ME6N

, , &on"tant K !.A@5

, 67M6RJER STICJ K !.50

, B7ERTIC6: PO:E K 9.4A45

,

, T'e Stat6-+i"or

,

, T'i" %ane -i"%)ay" t'e regre""ion eation w'i&' 'a" been #itte- to

, t'e -ata. T'e eation o# t'e #itte- *o-e) i"

, ME6N K !.A@5 !.50M6RJER STICJ 9.4A45ERTIC6: PO:E

OPTIM6: F6CTOR SETTINGS=ME6N HIT>



11

=ME6N HIT>, O%ti*i/e Re"%on"e

,

, Goa)7 *aintain ME6N at !.!

, O%ti** +a)e K !.!


,

, M6RJER STICJ 1.! 1.! !.!0011

, ERTIC6: PO:E 1.! 1.! !.10A!0



1!

ESTIM6TE OF EFFECTS =STD DE HIT>

, E"ti*ate- e##e&t" #or STD DE

,

, a+erage K .90@5

, 67M6RJER STICJ K .@9!5

, B7ERTIC6: PO:E K !.0@05

, 6B K !.!A5



11

ESTIM6TE OF EFFECTS =STD DE HIT>

, 6na)y"i" o# arian&e #or STD DE

,

, Sor&e S* o# Sare" D# Mean Sare FRatio Pa)e

,

, 67M6RJER STICJ @.9!09 1 @.9!09 51.00 !.!!9, B7ERTIC6: PO:E !.105! 1 !.105! [email protected] !.14@

, Tota) error !.!!A!1!5 1 !.!!A!1!5

,

, Tota) =&orr.> @.@9@A@ 0

OPTIM6: F6CTOR SETTINGS



1

OPTIM6: F6CTOR SETTINGS

=STD DE HIT>

, O%ti*i/e Re"%on"e

,

, Goa)7 minimize STD DE

, O%ti** +a)e K 1.!95@5


,

, M6RJER STICJ 1.! 1.! 1.!

, ERTIC6: PO:E 1.! 1.! 1.!

INTER6CTION



10

INTER6CTION

=STD DE HIT>

Intera&tion P)ot #or STD DE

S T D D E F

M6RJER STICJ

1.! 1.!

ERTIC6: PO:EK1.!

ERTIC6: PO:EK1.!

ERTIC6: PO:EK1.!

ERTIC6: PO:EK1.!

!

1

0

4

5




14


=STD DE HIT>


M6RJER STICJ

F E R T I C 6 : P O : E

STD DE

1.!

1.5

.!

.5

0.!

0.5

4.!

4.5

1 !.9 !. !. !.9 11

!.9

!.

!.

!.9

1

SO H6T3S THE 6NSER



15

SO8 H6T3S THE 6NSER

, I O:D7

, 1. SET THE M6RJER STICJ2 6T :O=C:OSE TO THE 6::>

, . SET THE ERTIC6: PO:E2 6T 66:E TH6T I:: HIT THE T6RGET.

SO H6T3S THE 6NSER



19

SO8 H6T3S THE 6NSER

, FROM REGRESSION FOR ME6N HIT28

SET M6RJER STICJ 6T 128 HIT 6T

!28 6ND SO:E FOR P, HIT K .!A@5 .50MS 9.4A45P

, ! K .A@5 .50=1> 9.4A45P

, Re")ting in, P K .!1 an- MS K 1

Contor P)ot" #or Mean an- St-. De+.

do epp presentation 5

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