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DESIGN OF EXPERIMENTS
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Role of DOE in Process Improvement
DOE is a formal matematical meto! fors"stematicall" plannin# an! con!$ctin# scientific
st$!ies tat can#e e%perimental varia&les
to#eter in or!er to !etermine teir effect of a
#iven response'
DOE ma(es controlle! can#es to inp$t
varia&les in or!er to #ain ma%im$m amo$nts of
information on ca$se an! effect relationsips
)it a minim$m sample si*e'
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Role of DOE in Process Improvement
DOE is more efficient tat a stan!ar!
approac of can#in# ,one varia&le at a
time- in or!er to o&serve te varia&le.s
impact on a #iven response'
DOE #enerates information on te effect
vario$s factors ave on a response varia&lean! in some cases ma" &e a&le to !etermine
optimal settin#s for tose factors'
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Role of DOE in Process Improvement
DOE enco$ra#es ,&rainstormin#- activities
associate! )it !isc$ssin# (e" factors tat ma"
affect a #iven response an! allo)s te
e%perimenter to i!entif" te ,(e"- factors forf$t$re st$!ies'
DOE is rea!il" s$pporte! &" n$mero$s statisticalsoft)are pac(a#es availa&le on te mar(et'
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SI3 STEPS IN DOE
Fo$r elements associate! )it DOE4
1' Te !esi#n of te e%periment5
2' Te collection of te !ata5
+' Te statistical anal"sis of te !ata5 an!
/' Te concl$sions reace! an!recommen!ations ma!e as a res$lt of te
e%periment'
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TERMINO7OG8
Replication 9 repetition of a &asic
e%periment )ito$t can#in# an" factor
settin#s5 allo)s te e%perimenter to estimate
te e%perimental error :noise; in te s"stem$se! to !etermine )eter o&serve!
!ifferences in te !ata are ,real- or ,
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TERMINO7OG8
'Ran!omi*ation 9 a statistical tool $se! to minimi*epotential $ncontrolla&le &iases in te e%periment &"
ran!oml" assi#nin# material5 people5 or!er tat
e%perimental trials are con!$cte!5 or an" oterfactor not $n!er te control of te e%perimenter'
Res$lts in ,avera#in# o$t- te effects of te
e%traneo$s factors tat ma" &e present in or!er to
minimi*e te ris( of tese factors affectin# te
e%perimental res$lts'
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TERMINO7OG8
loc(in# 9 tecni?$e $se! to increase teprecision of an e%periment &" &rea(in# te
e%periment into omo#eneo$s se#ments
:&loc(s; in or!er to control an" potential
&loc( to &loc( varia&ilit" :m$ltiple lots of
ra) material5 several sifts5 several
macines5 several inspectors;' n" effects
on te e%perimental res$lts as a res$lt of te&loc(in# factor )ill &e i!entifie! an!
minimi*e!'
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TERMINO7OG8
3onfo$n!in# A concept tat &asicall" means tat
m$ltiple effects are tie! to#eter into one parenteffect an! cannot &e separate!' For e%ample5
1' T)o people flippin# t)o !ifferent coins )o$l!
res$lt in te effect of te person an! te effect of
te coin to &e confo$n!e!
2' s e%periments #et lar#e5 i#er or!er
interactions :!isc$sse! later; are confo$n!e! )it
lo)er or!er interactions or main effect'
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1B
TERMINO7OG8
Factors 9 e%perimental factors orin!epen!ent varia&les :contin$o$s or
!iscrete; an investi#ator manip$lates to
capt$re an" can#es in te o$tp$t of te
process' Oter factors of concern are tose
tat are $ncontrolla&le an! tose )ic are
controlla&le &$t el! constant !$rin# te
e%perimental r$ns'
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TERMINO7OG8
Responses 9 !epen!ent varia&le meas$re!to !escri&e te o$tp$t of te process'
Treatment 3om&inations :r$n; 9e%perimental trial )ere all factors are set
at a specifie! level'
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TERMINO7OG8
Fi%e! Effects Mo!el A If te treatmentlevels are specificall" cosen &" tee%perimenter5 ten concl$sions reace!)ill onl" appl" to tose levels'
Ran!om Effects Mo!el 9 If te treatmentlevels are ran!oml" cosen from apop$lation of man" possi&le treatment
levels5 ten concl$sions reace! can &ee%ten!e! to all treatment levels in tepop$lation'
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P7NNING DOE
Ever"one involve! in te e%periment so$l!ave a clear i!ea in a!vance of e%actl" )at
is to &e st$!ie!5 te o&
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P7NNING DOE
Select a responseC!epen!ent varia&le:varia⩽ tat )ill provi!e information
a&o$t te pro&lem $n!er st$!" an! te
propose! meas$rement meto! for tisresponse varia&le5 incl$!in# an
$n!erstan!in# of te meas$rement s"stem
varia&ilit"
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P7NNING DOE
Select te in!epen!ent varia&lesCfactors:?$antitative or ?$alitative; to &e
investi#ate! in te e%periment5 te n$m&er
of levels for eac factor5 an! te levels ofeac factor cosen eiter specificall" :fi%e!
effects mo!el; or ran!oml" :ran!om effects
mo!el;'
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P7NNING DOE
3oose an appropriate e%perimental !esi#n
:relativel" simple !esi#n an! anal"sis meto!s are
almost al)a"s &est; tat )ill allo) "o$r e%perimental
?$estions to &e ans)ere! once te !ata is collecte!
an! anal"*e!5 (eepin# in min! tra!eoffs &et)eenstatistical po)er an! economic efficienc"' t tis
point in time it is #enerall" $sef$l to sim$late te
st$!" &" #eneratin# an! anal"*in# artificial !ata to
ins$re tat e%perimental ?$estions can &e ans)ere!
as a res$lt of con!$ctin# "o$r e%periment
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P7NNING DOE
Perform te e%periment :collect !ata;pa"in# partic$lar attention s$c tin#s as
ran!omi*ation an! meas$rement s"stem
acc$rac"5 )ile maintainin# as $niform ane%perimental environment as possi&le'
o) te !ata are to &e collecte! is a critical
sta#e in DOE
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P7NNING DOE
nal"*e te !ata $sin# te appropriatestatistical mo!el ins$rin# tat attention is
pai! to cec(in# te mo!el acc$rac" &"
vali!atin# $n!erl"in# ass$mptionsassociate! )it te mo!el' e li&eral in te
$tili*ation of all tools5 incl$!in# #rapical
tecni?$es5 availa&le in te statisticalsoft)are pac(a#e to ins$re tat a ma%im$m
amo$nt of information is #enerate!
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P7NNING DOE
ase! on te res$lts of te anal"sis5 !ra)concl$sionsCinferences a&o$t te res$lts5
interpret te p"sical meanin# of tese
res$lts5 !etermine te practical si#nificanceof te fin!in#s5 an! ma(e recommen!ations
for a co$rse of action incl$!in# f$rter
e%periments
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2B
SIMP7E 3OMPRTIE EXPERIMENTS
Sin#le Mean "potesis Test
Difference in Means "potesis Test )it
E?$al ariances
Difference in Means "potesis Test )itne?$al ariances
Difference in ariances "potesis Test
Paire! Difference in Mean "potesis Test
One a" nal"sis of ariance
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3RITI37 ISSES SSO3ITED IT
SIMP7E 3OMPRTIE EXPERIMENTS
o) 7ar#e a Sample So$l! e Ta(eH
" Does te Sample Si*e Matter
n")a"H
at in! of Protection Do e ave
ssociate! )it Re
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Sin#le Mean "potesis Test
fter a pro!$ction r$n of 12 o*' &ottles5concern is e%presse! a&o$t te possi&ilit" tat
te avera#e fill is too lo)'
o4 J 12
a4 KL 12
level of si#nificance J J 'B0 sample si*e J @
SPE3 FOR TE MEN4 12 '1
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Sin#le Mean "potesis Test
Sample mean J 11'@
Sample stan!ar! !eviation J B'10
Sample si*e J @
3omp$te! t statistic J A2'B PAal$e J B'B>B0162
3ON37SION4 Since PAal$e L 'B05 "o$
fail to re
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Sin#le Mean "potesis Test Po)er 3$rve
Po)er 3$rvealpa J B'B05 si#ma J B'10
Tr$e Mean
Po)er
11'> 11'@ 12 12'1 12'2B
B'2
B'/
B'6
B'>
1
Si l M i T P
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Sin#le Mean "potesis Test Po)er
3$rve A Different Sample Si*es
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DIFFEREN3E IN MENS A E7
RIN3ES
o4 1= 2
a4 1 2
level of si#nificance J J 'B0
sample si*es &ot J 10
ss$mption4 1J 2
Sample means J 11'> an! 12'1
Sample stan!ar! !eviations J B'1 an! B'2
Sample si*es J 10 an! 10
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DIFFEREN3E IN MENS A E7 RIN3ES
3an "o$ !etect tis !ifferenceH
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DIFFEREN3E IN MENS A E7
RIN3ES
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DIFFEREN3E IN MENS A $nE7
RIN3ES
Same as te ,E?$al ariance- case e%cept
te variances are not ass$me! e?$al'
o) !o "o$ (no) if it is reasona&le to
ass$me tat variances are e?$al OR
$ne?$alH
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DIFFEREN3E IN RIN3E
8POTESIS TEST
Same e%ample as Difference in Mean4
Sample stan!ar! !eviations J B'1 an! B'2
Sample si*es J 10 an! 10
N$ll "potesis4 ratio of variances J 1'B
lternative4 not e?$al
3omp$te! F statistic J B'20
PAal$e J B'B1/BB=1
Re
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DIFFEREN3E IN RIN3E
8POTESIS TEST
3an "o$ !etect tis !ifferenceH
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DIFFEREN3E IN RIN3E
8POTESIS TEST APOER 3RE
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PIRED DIFFEREN3E IN MENS
8POTESIS TEST
T)o !ifferent inspectors eac meas$re 1Bparts on te same piece of test e?$ipment'
N$ll "potesis4 DIFFEREN3E IN MENS
J B'B lternative4 not e?$al
3omp$te! t statistic J A1'22=B2
PAal$e J B'20B@//
Do not re
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PIRED DIFFEREN3E IN MENS
8POTESIS TEST A POER 3RE
Po)er 3$rve
alpa J B'B05 si#ma J +'>66
Difference in Means
Po)er
A0 A/ A+ A2 A1 B 1 2 + / 0
B
B'2
B'/
B'6
B'>
1
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ONE 8 N78SIS OF RIN3E
se! to test "potesis tat te means of
several pop$lations are e?$al'
E%ample4 Pro!$ction line as = fill nee!les an!"o$ )is to assess )eter or not te avera#e
fill is te same for all = nee!les'
E%periment4 sample 2B fills from eac of te @nee!les an! test at 0 level of si#n'
o4 1J 2 =3= 4 = 5 =6= 7
RES7TS4 N78SIS OF RIN3E
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RES7TS4 N78SIS OF RIN3E
T7E
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$!
SIN3E NEED7E MENS RE NOT 77
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SIN3E NEED7E MENS RE NOT 77
E75 I3 ONES RE DIFFERENTH
M$ltiple Ran#e Tests for = Nee!lesMet'o/ !0. percent SD
,ol2) ,ount Mean 3omogeneous 4roups
--------------------------------------------------------------------------------
5( ) 11.(#" 6
5) ) 11.!#11 651 ) 11.!#)( 6
5" ) 11.!#($ 6
5$ ) 11.!!01 6
50 ) 11.!!0$ 6
5% ) 1).11 6
IS7 3OMPRISON OF =
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IS7 3OMPRISON OF =
NEED7ES
N1
N2
N+
N/
N0
N6
N=
o%Aan!AGis(er Plot
11'0 11'= 11'@ 12'1 12'+
3olQ1
3olQ2
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F3TORI7 :2(; DESIGNS
E%periments involvin# several factors : ( J
of factors; )ere it is necessar" to st$!"
te
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F3TORI7 :2(; DESIGNS
Factors are ass$me! to &e fi%e! :fi%e!effects mo!el;
Desi#ns are completel" ran!omi*e!
:e%perimental trials are r$n in a ran!omor!er5 etc';
Te $s$al normalit" ass$mptions are
satisfie!'
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F3TORI7 :2(; DESIGNS
Partic$larl" $sef$l in te earl" sta#es ofe%perimental )or( )en "o$ are li(el" to
ave man" factors &ein# investi#ate! an!
"o$ )ant to minimi*e te n$m&er oftreatment com&inations :sample si*e; &$t5 at
te same time5 st$!" all ( factors in a
complete factorial arran#ement :te
e%periment collects !ata at all possi&le
com&inations of factor levels;'
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F3TORI7 :2(; DESIGNS
s ( #ets lar#e5 te sample si*e )illincrease e%ponentiall"' If e%periment is
replicate!5 te r$ns a#ain increases'
k # of runs2 4
3 8
4 16
5 32
6 64
7 128
8 256
9 512
10 1024
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F3TORI7 :2(; DESIGNS :( J 2;
T)o factors set at t)o levels :normall"
referre! to as lo) an! i#; )o$l! res$lt inte follo)in# !esi#n )ere eac level of
factor is paire! )it eac level of factor
'
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 $1 (1 #3
4 %&'% %&'% #4 4 (1 (1 #4
)*n*ra!&+*, S*tt&n s rt%o ona! S*tt&n s
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F3TORI7 :2(; DESIGNS :( J 2;
Estimatin# main effects associate! )it
can#in# te level of eac factor from lo)
to i#' Tis is te estimate! effect on te
response varia&le associate! )it can#in#
factor or from teir lo) to i# val$es'
2
;:
2
;: +1/2 yyyyEffectAFactor +
+
=
2
;:
2
;: 21/+ yyyyEffectBFactor +
+
=
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/0
F3TORI7 :2(; DESIGNS :( J 2;4
GRPI37 OTPT Neiter factor nor Factor ave an effect
on te response varia&le'
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F3TORI7 :2(; DESIGNS :( J 2;4
GRPI37 OTPT
Factor as an effect on te response
varia&le5 &$t Factor !oes not'
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F3TORI7 :2(; DESIGNS :( J 2;4
GRPI37 OTPT
Factor an! Factor ave an effect on te
response varia&le'
F3TORI7 :2(; DESIGNS :( J 2;4
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F3TORI7 :2 ; DESIGNS :( 2;4
GRPI37 OTPT
Factor as an effect on te response varia&le5 &$t onl" iffactor is set at te ,i#- level' Tis is called
interactionan! it &asicall" means tat te effect one factor
as on a response is !epen!ent on te level "o$ set oter
factors at' Interactions can &e ma
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EXMP7E4
F3TORI7 :2(; DESIGNS :( J 2;
micro&iolo#ist is intereste! in te effect
of t)o !ifferent c$lt$re me!i$ms me!i$m 1
:lo); an! me!i$m 2 :i#; an! t)o!ifferent times 1B o$rs :lo); an! 2B o$rs
:i#; on te #ro)t rate of a partic$lar
3F $#s'
EXMP7E4
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EXMP7E4
F3TORI7 :2(; DESIGNS :( J 2;
Since t)o factors are of interest5 ( J25 an!)e )o$l! nee! te follo)in# fo$r r$ns
res$ltin# in
RUN -*,&u. /&.* )ro"t% Rat*
1 !o" !o" 17
2 %&'% !o" 15
3 !o" %&'% 38
4 %&'% %&'% 39
)*n*ra!&+*, S*tt&n's
EXMP7E4
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EXMP7E4
F3TORI7 :2(; DESIGNS :( J 2;
Estimates for te me!i$m an! timeeffects are
Me!i$m effect J :10+@;C2 9 :1= +>;C2 J AB'0
Time effect J :+>+@;C2 9 :1= 10;C2 J22'0
EXMP7E4
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EXMP7E4
F3TORI7 :2(; DESIGNS :( J 2;
EXMP7E4
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EXMP7E4
F3TORI7 :2(; DESIGNS :( J 2;
statistical anal"sis $sin# te appropriatestatistical mo!el )o$l! res$lt in te
follo)in# information' Factor :me!i$m;
an! Factor :time;*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.
EXMP7E4
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EXMP7E4
3ON37SIONS
In statistical lan#$a#e5 one )o$l! concl$!etat factor :me!i$m; is not statisticall"
si#nificant at a 0 level of si#nificance
since te pAval$e is #reater tan 0 :B'B0;5
&$t factor :time; is statisticall" si#nificant
at a 0 level of si#nificance since tis pA
val$e is less tan 0'
EXMP7E4
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EXMP7E4
3ON37SIONS
In la"man terms5 tis means tat )e aveno evi!ence tat )o$l! allo) $s to
concl$!e tat te me!i$m $se! as an effect
on te #ro)t rate5 alto$# it ma" )ell
ave an effect :o$r concl$sion )as
incorrect;'
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EXMP7E4
3ON37SIONS !!itionall"5 )e ave evi!ence tat )o$l!
allo) $s to concl$!e tat time !oes ave an
effect on te #ro)t rate5 alto$# it ma")ell not ave an effect :o$r concl$sion )as
incorrect;'
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EXMP7E4
3ON37SIONS
In #eneral )e control te li(elioo! of
reacin# tese incorrect concl$sions &" te
selection of te level of si#nificance for tetest an! te amo$nt of !ata collecte!
:sample si*e;'
2( DESIGNS :( L 2;
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2(DESIGNS :( L 2;
s te n$m&er of factors increase5 te
n$m&er of r$ns nee!e! to complete a
complete factorial e%periment )ill increase
!ramaticall"' Te follo)in# 2( !esi#n
la"o$t !epict te n$m&er of r$ns nee!e! forval$es of ( from 2 to 0' For e%ample5 )en
( J 05 it )ill ta(e 20 J +2 e%perimental r$ns
for te complete factorial e%periment'
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Interactions for 2( Desi#ns :( J +;
Interactions &et)een vario$s factors can&e estimate! for !ifferent !esi#ns a&ove
&" m$ltipl"in# te appropriate col$mns
to#eter an! ten s$&tractin# te avera#eresponse for te lo)s from te avera#e
response for te i#s'
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6B
Interactions for 2( Desi#ns :( J +;
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 $1
(1 (1 (1 1 1 1 1
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2(DESIGNS :( L 2;
Once te effect for all factors an!
interactions are !etermine!5 "o$ are a&le to
!evelop a pre!iction mo!el to estimate teresponse for specific val$es of te factors'
In #eneral5 )e )ill !o tis )it statistical
soft)are5 &$t for tese !esi#ns5 "o$ can !oit &" an! calc$lations if "o$ )is'
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2(DESIGNS :( L 2;
For e%ample5 if tere are no si#nificant interactions
present5 "o$ can estimate a response &" te
follo)in# form$la' :for ?$antitative factors onl";
ONE F3TOR EXMP7E
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ONE F3TOR EXMP7E
Plot of Fitte! Mo!el
RS STD8
GR2DE
1B 12 1/ 16 1> 2B
00
60
=0
>0
@0
ONE F3TOR EXMP7E
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ONE F3TOR EXMP7E
Te o$tp$t so)s te res$lts of fittin# a#eneral linear mo!el to !escri&e te
relationsip &et)een GRDE an! RS
STD8' Te e?$ation of te fitte! #eneral
mo!el is
GRDE J 2@'+ +'1 :RS STD8;
Te fitte! orto#onal mo!el is
GRDE J =0 10 :S37ED RS;
T 7 l S i D i
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60
T)o 7evel Screenin# Desi#ns S$ppose tat "o$r &rainstormin# session
res$lte! in = factors tat vario$s peopletin( ,mi#t- ave an effect on a response' f$ll factorial !esi#n )o$l! re?$ire 2=J12> e%perimental r$ns )ito$t replication'
Te p$rpose of screenin# !esi#ns is tore!$ce :i!entif"; te n$m&er of factors!o)n to te ,ma
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Note tat
n" factor ! effect is no) confo$n!e! )it te a&interaction
n" factor e effect is no) confo$n!e! )it te ac
interaction
etc'
at is te !e interaction confo$n!e! )itHHHHHHHHa 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 (0 1 $1 $1 1
(1 $1 (1 $1 1 $1 $1
$1 (1 (1 $1 $1 1 $1
(1 (1 (1 1 1 1 1
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Pro&lems tat Interactions 3a$seU
Interactions 9 If interactions e%ist an! "o$ fail to
acco$nt for tis5 "o$ ma" reac erroneo$s
concl$sions' S$ppose tat "o$ plan an
e%periment )it fo$r r$ns an! tree factors
res$ltin# in te follo)in# !ata4
Pro&lems tat Interactions 3a$seU
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Pro&lems tat Interactions 3a$seU
Factor Effect J B
Factor Effect J B
In tis e%ample5 if "o$ )ere ass$min# tat
,smaller is &etter- ten it appears to ma(e
no !ifference )ere "o$ set factors an! 'If "o$ )ere to set factor at te lo) val$e
an! factor at te lo) val$e5 "o$r response
varia&le )o$l! &e lar#er tan !esire!' In tiscase tere is a factor interaction )it
factor '
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6@
Pro&lems tat Interactions 3a$seU
Interaction Plot
F3TOR
0
6
=
>
@
1B
RESPONSE
A1 1
F3TOR A1
1
Resol$tion of a Desi#n
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=B
#
Resol$tion III Desi#ns 9 No main effects arealiase! )it an" oter main effect T some :orall; main effects are aliase! )it t)o )a"interactions
Resol$tion I Desi#ns 9 No main effects arealiase! )it an" oter main effect OR t)o factorinteraction5 T t)o factor interactions ma" &ealiase! )it oter t)o factor interactions
Resol$tion Desi#ns 9 No main effect OR t)o
factor interaction is aliase! )it an" oter maineffect or t)o factor interaction5 T t)o factorinteractions are aliase! )it tree factorinteractions'
i i
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=1
3ommon Screenin# Desi#ns
Fractional Factorial Desi#ns 9 te totaln$m&er of e%perimental r$ns m$st &e a
po)er of 2 :/5 >5 165 +25 6/5 V;' If "o$
&elieve first or!er interactions are small
compare! to main effects5 ten "o$ co$l!
coose a resol$tion III !esi#n' W$st
remem&er tat if "o$ ave ma
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3ommon Screenin# Desi#ns
Plac(ettA$rman Desi#ns 9 T)o level5resol$tion III !esi#ns $se! to st$!" $p to
nA1 factors in n e%perimental r$ns5 )ere
n is a m$ltiple of / : of r$ns )ill &e /5 >5
125 165 V;' Since n ma" &e ?$ite lar#e5
"o$ can st$!" a lar#e n$m&er of factors
)it mo!eratel" small sample si*es' :n J
1BB means "o$ can st$!" @@ factors )it1BB r$ns;
Oter Desi#n Iss$es
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Oter Desi#n Iss$es
Ma" )ant to collect !ata at center points to
estimate nonAlinear responses
More tan t)o levels of a factor 9 no
pro&lem :m$ltiAlevel factorial;
at !o "o$ !o if "o$ )ant to &$il! a nonA
linear mo!el to ,optimi*e- te response'
:it a tar#et5 ma%imi*e5 or minimi*e; 9
calle! response s$rface mo!elin#
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=/
Response S$rface Desi#ns 9 o%Aen(en
RUN F1 F2 F3 100
1 10 45 60 11825
2 30 45 40 8781
3 20 30 40 8413
4 10 30 50 9216
5 20 45 50 9288
6 30 60 50 8261
7 20 45 50 9329
8 30 45 60 10855
9 20 45 50 9205
10 20 60 40 8538
11 10 45 40 9718
12 30 30 50 11308
13 20 60 60 10316
14 10 60 50 12056
15 20 30 60 10378
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Response S$rface Desi#ns 9 o%Aen(en
Regression coeffs. for Var_3
----------------------------------------------------------------------
constant = 2312.5
A:Factor_A = 36.575
B:Factor_B = 200.067C:Factor_C = 3.85
AA = .0875
AB = -.81167
AC = -0.0825
BB = 0.117222
BC = -0.311667
CC = 1.10875
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Response S$rface Desi#ns 9 o%Aen(en
3onto$rs of Estimate! Response S$rface
FactorQ3J6B'B
FactorQ
FactorQ1
arQ+
@+BB'B
@0BB'B@=BB'B
@@BB'B
1B1BB'B
1B+BB'B
1B0BB'B
1B=BB'B
1B@BB'B
111BB'B
11+BB'B
110BB'B
11=BB'B
1B 1/ 1> 22 26 +B
+B
+0
/B
/0
0B
00
6B
37SSROOM EXER3ISE
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==
37SSROOM EXER3ISE
STDENT INA37SS EXPERIMENT4
3ollect !ata for e%periment to !eterminefactor settin#s :t)o factors; to it a tar#et
response :spot on )all;'
Factor 9 ei#t of sa(er :lo) an! i#;
Factor 9 location of sa(er :close to
an! an! close to )all;
Desi#n e%periment 9 )o$l! s$##est
several replications
37SSROOM EXER3ISE
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37SSROOM EXER3ISE
3on!$ct E%periment 9 st$!ent ol!s + foot
,pin te tail on te !on(e"- stic( an!attempts to it te tar#et' n o&server )ill
assist to mar( te it on te tar#et'
3ollect !ata 9 st$!ents ta(e !ata ome for)ee( an! come &ac( )it )at "o$ )o$l!
recommen! ND )"'
8O TE77 TE 37SS O TO P78TE GME TO ,IN-'
37SSROOM EXER3ISE
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37SSROOM EXER3ISE
37SSROOM EXER3ISE
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>B
37SSROOM EXER3ISE
-ARER
S/
ER/A
PE1S/ BS 2N BS 3R BS 4/ BS -EAN
S/ANAR
EA/N
$2750 $4500 $4750 $5000 $4250 1021
$12500 $6750 $4625 $4000 $6969 3871
3000 3250 3875 6250 4094 1484
4625 11250 12625 14000 10625 4155
-ARER
S/
: ER/A PE ;AS SE / ;A
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3onto$r Plots for Mean an! St!' Dev'