do epp presentation 5
TRANSCRIPT
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DESIGN OF EXPERIMENTS by
R. C. Baker
How to gain ! year" o# e$%erien&e inone "'ort week(
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Ro)e o# DOE in Pro&e"" I*%ro+e*ent
, DOE i" a #or*a) *at'e*ati&a) *et'o- #or"y"te*ati&a))y %)anning an- &on-&ting "&ienti#i&
"t-ie" t'at &'ange e$%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$i** a*ont" o#
in#or*ation on &a"e an- e##e&t re)ation"'i%"
wit' a *ini** "a*%)e "i/e.
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Ro)e o# DOE in Pro&e"" I*%ro+e*ent
, DOE i" *ore e##i&ient t'at a "tan-ar-
a%%roa&' o# &'anging one +ariab)e at a
ti*e2 in or-er to ob"er+e t'e +ariab)e3"
i*%a&t on a gi+en re"%on"e.
, DOE generate" in#or*ation on t'e e##e&t
+ario" #a&tor" 'a+e on a re"%on"e +ariab)ean- in "o*e &a"e" *ay be ab)e to -eter*ine
o%ti*a) "etting" #or t'o"e #a&tor".
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Ro)e o# DOE in Pro&e"" I*%ro+e*ent
, DOE en&orage" brain"tor*ing2 a&ti+itie"
a""o&iate- wit' -i"&""ing key #a&tor" t'at *ay
a##e&t a gi+en re"%on"e an- a))ow" t'e
e$%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.
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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.
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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">
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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$%eri*enta) re")t".
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TERMINO:OG;
, B)o&king < te&'nie "e- to in&rea"e t'e %re&i"ion o# an e$%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-.
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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.
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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".
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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$%eri*enta) tria) w'ere a)) #a&tor" are "et
at a "%e&i#ie- )e+e).
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TERMINO:OG;
, Fi$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.
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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$%eri*ent8 t'e e"tion" one 'o%e" toan"wer an- t'e re")t" anti&i%ate-
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P:6NNING 6 DOE
, Se)e&t a re"%on"e-e%en-ent +ariab)e=+ariab)e"> t'at wi)) %ro+i-e in#or*ation
abot t'e %rob)e* n-er "t-y an- t'e
%ro%o"e- *ea"re*ent *et'o- #or t'i"re"%on"e +ariab)e8 in&)-ing an
n-er"tan-ing o# t'e *ea"re*ent "y"te*
+ariabi)ity
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P:6NNING 6 DOE
, Se)e&t t'e in-e%en-ent +ariab)e"#a&tor"=antitati+e or a)itati+e> to be
in+e"tigate- in t'e e$%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$e-
e##e&t" *o-e)> or ran-o*)y =ran-o* e##e&t"
*o-e)>.
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P:6NNING 6 DOE
, C'oo"e an a%%ro%riate e$%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$%eri*ent
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P:6NNING 6 DOE
, Per#or* t'e e$%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$%eri*enta) en+iron*ent a" %o""ib)e.
How t'e -ata are to be &o))e&te- i" a &riti&a)
"tage in DOE
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P:6NNING 6 DOE
, 6na)y/e t'e -ata "ing t'e a%%ro%riate"tati"ti&a) *o-e) in"ring t'at attention i"
%ai- to &'e&king t'e *o-e) a&&ra&y by
+a)i-ating n-er)ying a""*%tion"a""o&iate- wit' t'e *o-e). Be )ibera) in t'e
ti)i/ation o# a)) too)"8 in&)-ing gra%'i&a)
te&'nie"8 a+ai)ab)e in t'e "tati"ti&a)"o#tware %a&kage to in"re t'at a *a$i**
a*ont o# in#or*ation i" generate-
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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$%eri*ent"
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SIMP:E COMP6R6TIE EXPERIMENTS
, Sing)e Mean Hy%ot'e"i" Te"t
, Di##eren&e in Mean" Hy%ot'e"i" Te"t wit'
Ea) arian&e"
, Di##eren&e in Mean" Hy%ot'e"i" Te"t wit'nea) arian&e"
, Di##eren&e in arian&e" Hy%ot'e"i" Te"t
, Paire- Di##eren&e in Mean Hy%ot'e"i" Te"t
, One ay 6na)y"i" o# arian&e
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CRITIC6: ISSES 6SSOCI6TED ITH
SIMP:E COMP6R6TIE EXPERIMENTS
, How :arge a Sa*%)e S'o)- e Take
, 'y Doe" t'e Sa*%)e Si/e Matter
6nyway
, 'at Jin- o# Prote&tion Do e Ha+e
6""o&iate- wit' Re?e&ting Goo-2 St##
, 'at Jin- o# Prote&tion Do e Ha+e
6""o&iate- wit' 6&&e%ting Ba-2 St##
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Sing)e Mean Hy%ot'e"i" Te"t
, 6#ter a %ro-&tion rn o# 1 o/. bott)e"8&on&ern i" e$%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
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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.
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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
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Sing)e Mean Hy%ot'e"i" Te"t Power Cr+e
Si ) M H ' i T P
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Sing)e Mean Hy%ot'e"i" Te"t Power
Cr+e Di##erent Sa*%)e Si/e"
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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
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DIFFERENCE IN ME6NS E6: 6RI6NCES
Can yo -ete&t t'i" -i##eren&e
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DIFFERENCE IN ME6NS E6:
6RI6NCES
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DIFFERENCE IN ME6NS nE6:
6RI6NCES
, Sa*e a" t'e Ea) arian&e2 &a"e e$&e%t
t'e +arian&e" are not a""*e- ea).
, How -o yo know i# it i" rea"onab)e to
a""*e t'at +arian&e" are ea) OR
nea)
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DIFFERENCE IN 6RI6NCE
H;POTHESIS TEST
, Sa*e e$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.
DIFFERENCE IN 6RI6NCE
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DIFFERENCE IN 6RI6NCE
H;POTHESIS TEST
Can yo -ete&t t'i" -i##eren&e
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00
DIFFERENCE IN 6RI6NCE
H;POTHESIS TEST POER CRE
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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.
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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
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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
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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$!
SINCE NEED:E ME6NS 6RE NOT 6::
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0A
SINCE NEED:E ME6NS 6RE NOT 6::
E6:8 HICH ONES 6RE DIFFERENT
, M)ti%)e Range Te"t" #or @ Nee-)e" Met'o/ !0. percent SD
,ol2) ,ount Mean 3omogeneous 4roups
--------------------------------------------------------------------------------
5( ) 11.(#" 6
5) ) 11.!#11 6 51 ) 11.!#)( 6
5" ) 11.!#($ 6
5$ ) 11.!!01 6
50 ) 11.!!0$ 6
5% ) 1).11 6
IS6: COMP6RISON OF @
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0
IS6: COMP6RISON OF @
NEED:ES
N1
N
N0
N4
N5
N9
N@
Bo$an-H'i"ker P)ot
11.5 11.@ 11. 1.1 1.0
Co)1
C o )
k
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4!
F6CTORI6: =k > DESIGNS
, E$%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>.
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41
F6CTORI6: =k > DESIGNS
, 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$%eri*enta) tria)" are rn in a ran-o*or-er8 et&.>
, T'e "a) nor*a)ity a""*%tion" are
"ati"#ie-.
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4
F6CTORI6: =k > DESIGNS
, Parti&)ar)y "e#) in t'e ear)y "tage" o#e$%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$%eri*ent &o))e&t" -ata at a)) %o""ib)e
&o*bination" o# #a&tor )e+e)">.
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40
F6CTORI6: =k > DESIGNS
, 6" k get" )arge8 t'e "a*%)e "i/e wi))in&rea"e e$%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
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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 $1 (1 #3
4 %&'% %&'% #4 4 (1 (1 #4
)*n*ra!&+*, S*tt&n s rt%o ona! S*tt&n s
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45
F6CTORI6: =k > DESIGNS =k K >
, E"ti*ating *ain e##e&t" a""o&iate- wit'
&'anging t'e )e+e) o# ea&' #a&tor #ro* )ow
to 'ig'. T'i" i" t'e e"ti*ate- e##e&t on t'e
re"%on"e +ariab)e a""o&iate- wit' &'anging
#a&tor 6 or B #ro* t'eir )ow to 'ig' +a)e".
>=
>= 014 y y y y Effect A Factor
+−
+=
>=
>= 140 y y y y Effect B Factor
+−
+=
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49
F6CTORI6: =k > DESIGNS =k K >7
GR6PHIC6: OTPT, Neit'er #a&tor 6 nor Fa&tor B 'a+e an e##e&t
on t'e re"%on"e +ariab)e.
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4@
F6CTORI6: =k > DESIGNS =k K >7
GR6PHIC6: OTPT
, Fa&tor 6 'a" an e##e&t on t'e re"%on"e
+ariab)e8 bt Fa&tor B -oe" not.
= k> =k >
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4A
F6CTORI6: =k > DESIGNS =k K >7
GR6PHIC6: OTPT
, Fa&tor 6 an- Fa&tor B 'a+e an e##e&t on t'e
re"%on"e +ariab)e.
F6CTORI6: =k > DESIGNS =k K >7
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4
F6CTORI6: = > DESIGNS =k >7
GR6PHIC6: OTPT
,Fa&tor B 'a" an e##e&t on t'e re"%on"e +ariab)e8 bt on)y i##a&tor 6 i" "et at t'e Hig'2 )e+e). T'i" i" called
interaction an- it ba"i&a))y *ean" t'at t'e e##e&t one #a&tor
'a" on a re"%on"e i" -e%en-ent on t'e )e+e) yo "et ot'er
#a&tor" at. Intera&tion" &an be *a?or %rob)e*" in a DOE i#
yo #ai) to a&&ont #or t'e intera&tion w'en -e"igning yore$%eri*ent.
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5!
EX6MP:E7
F6CTORI6: =k > DESIGNS =k K >
, 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
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51
EX6MP:E7
F6CTORI6: =k > DESIGNS =k K >
, 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
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5
EX6MP:E7
F6CTORI6: =k > DESIGNS =k K >
, E"ti*ate" #or t'e *e-i* an- ti*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
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50
EX6MP:E7
F6CTORI6: =k > DESIGNS =k K >
EX6MP:E7
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54
EX6MP:E7
F6CTORI6: =k > DESIGNS =k K >
, 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
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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
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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>.
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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>.
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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 >
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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 >
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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
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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'".
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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 $1
(1 (1 (1 1 1 1 1
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90
k DESIGNS =k >
, On&e t'e e##e&t #or a)) #a&tor" an-
intera&tion" are -eter*ine-8 yo are ab)e to
-e+e)o% a %re-i&tion *o-e) to e"ti*ate t'ere"%on"e #or "%e&i#i& +a)e" o# t'e #a&tor".
In genera)8 we wi)) -o t'i" wit' "tati"ti&a)
"o#tware8 bt #or t'e"e -e"ign"8 yo &an -oit by 'an- &a)&)ation" i# yo wi"'.
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94
k DESIGNS =k >
, For e$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>
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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
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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
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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
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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
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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 $1
(1 (1 (1 1 1 1 1
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@!
Prob)e*" t'at Intera&tion" Ca"e(
, Intera&tion" < I# intera&tion" e$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$%eri*ent wit' #or rn" an- t'ree #a&tor"
re")ting in t'e #o))owing -ata7
Prob)e*" t'at Intera&tion" Ca"e(
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@1
Prob)e*" t'at Intera&tion" Ca"e(
, Fa&tor 6 E##e&t K !
, Fa&tor B E##e&t K !, Fa&tor C E##e&t K 5
, In t'i" e$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.
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@
Prob)e*" t'at Intera&tion" Ca"e(
Intera&tion P)ot
F6CTOR 6
5
9
@
A
1!
R E S P O N S E
1 1
F6CTOR B1
1
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@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
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@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
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@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
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@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$%eri*enta) rn"8 w'ere
n i" a *)ti%)e o# 4 = o# rn" wi)) be 48 A8
18 198 V>. Sin&e n *ay be ite )arge8
yo &an "t-y a )arge n*ber o# #a&tor"
wit' *o-erate)y "*a)) "a*%)e "i/e". =n K
1!! *ean" yo &an "t-y #a&tor" wit'1!! rn">
Ot'er De"ign I""e"
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@@
Ot'er De"ign I""e"
, May want to &o))e&t -ata at &enter %oint" to
e"ti*ate non)inear re"%on"e"
, More t'an two )e+e)" o# a #a&tor < no
%rob)e* =*)ti)e+e) #a&toria)>
, 'at -o yo -o i# yo want to bi)- a non
)inear *o-e) to o%ti*i/e2 t'e re"%on"e.
='it a target8 *a$i*i/e8 or *ini*i/e> <
&a))e- re"%on"e "r#a&e *o-e)ing
Ot'er De"ign I""e"
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@A
Ot'er De"ign I""e"
, 'at -o yo -o i# t'e #a&tor" )e+e)" are
&ategori&a) an- not 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
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@
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
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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 $1 1
0 1 1
0 0 0
Re"%on"e Sr#a&e De"ign" < Centra)
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A1
% g
Co*%o"ite
, De"ign &)a""7 Re"%on"e Sr#a&e, De"ign na*e7 Centra) &o*%o"ite b)o&ke- &be"tar
, N*ber o# e$%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"
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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 $176383
0 0 176383
M)ti)e+e) Fa&toria) De"ign"
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A0
M)ti)e+e) Fa&toria) De"ign", De"ign &)a""7 M)ti)e+e) Fa&toria)
, N*ber o# e$%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 @ 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"
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A4
Ne"te- De"ign
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A5
g, De"ign &)a""7 arian&e Co*%onent"
, N*ber o# e$%eri*enta) #a&tor"7 0
, N*ber o# re"%on"e"7 1
, N*ber o# rn"7 @
, Ran-o*i/e-7 No
Fa&tor" :e+e)" nit"
, , Fa&tor6 0
, Fa&torB 0
, Fa&torC 0
;o 'a+e &reate- a +arian&e &o*%onent" -e"ign w'i&' wi))e"ti*ate t'e &ontribtion o# 0 #a&tor" to o+era)) %ro&e""+ariabi)ity. T'e -e"ign i" 'ierar&'i&a)8 wit' ea&' #a&torne"te- in t'e #a&tor abo+e it. 6 tota) o# @ *ea"re*ent"are reire-.
Ne"te- De"ign
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A9
Ne"te- De"ign
Re"%on"e Sr#a&e De"ign" < Bo$Be'nken
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A@
EX6MP:E REC6P, De"ign &)a""7 Re"%on"e Sr#a&e
, De"ign na*e7 Bo$Be'nken -e"ign
, Ba"e De"ign
,
, N*ber o# e$%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! 0! ;e", Fa&torB 0! 9! ;e"
, Fa&torC 4! 9! ;e"
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AA
Re"%on"e Sr#a&e De"ign" < Bo$Be'nken
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A
Re"%on"e Sr#a&e De"ign" < Bo$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
Re"%on"e Sr#a&e De"ign" < Bo$Be'nken
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!
% gRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>
Example: std. dev. of noise = 0
RUN F1 F2 F3 0
1 10 45 60 11800
2 30 45 40 8800
3 20 30 40 8400
4 10 30 50 9300
5 20 45 50 9400
6 30 60 50 8300
7 20 45 50 9400
8 30 45 60 10800
9 20 45 50 9400
10 20 60 40 8400
11 10 45 40 9800
12 30 30 50 11300
13 20 60 60 10400
14 10 60 50 12300
15 20 30 60 10400
Re"%on"e Sr#a&e De"ign" < Bo$
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1
% g
Be'nkenRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>
Example: std. dev. of noise = 0
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
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Re"%on"e Sr#a&e De"ign" < Bo$Be'nkenRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>
Example: std. dev. of noise = 0
Optimie Response
-----------------
!oa": #A$%#%&' 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
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0
Re"%on"e Sr#a&e De"ign" < Bo$Be'nkenRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>
Example: std. dev. of noise = 0
R S # D i B B ' k
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4
Re"%on"e Sr#a&e De"ign" < Bo$Be'nkenRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>
Example: std. dev. of noise = 100
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
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5
Re"%on"e Sr#a&e De"ign" < Bo$Be'nkenRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>
Example: std. dev. of noise = 100
Regression coeffs. for Var_*
----------------------------------------------------------------------
constant = 2*12.
A:Factor_A = *+.
B:Factor_B = 200.0+C:Factor_C = *.
AA = 9.09
AB = -9.11+
AC = -0.02
BB = 0.11222
BC = -0.*11++
CC = 1.10
Re"%on"e Sr#a&e De"ign" Bo$ Be'nken
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9
Re"%on"e Sr#a&e De"ign" < Bo$Be'nkenRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>
Example: std. dev. of noise = 100
Stan-ar-i/e- Pareto C'art #or arR0
Stan-ar-i/e- e##e&t
! 1! ! 0! 4!
6CBB
B7Fa&torRB
BC
CC
67Fa&torR6
66C7Fa&torRC
6B
Re"%on"e Sr#a&e De"ign" Bo$ Be'nken
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@
Re"%on"e Sr#a&e De"ign" < Bo$Be'nkenRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>
Example: std. dev. of noise = 100
Contor" o# E"ti*ate- Re"%on"e Sr#a&e
Fa&torCK9!.!
Fa&tor6
F a & t o rR B
ar0
0!!.!
5!!.!@!!.!
!!.!
1!1!!.!
1!0!!.!
1!5!!.!
1!@!!.!
1!!!.!
111!!.!
110!!.!
115!!.!
11@!!.!
1! 14 1A 9 0!
0!
05
4!
45
5!55
9!
Re"%on"e Sr#a&e De"ign" Bo$ Be'nken
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A
Re"%on"e Sr#a&e De"ign" < Bo$Be'nkenRE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>
Example: std. dev. of noise = 100
, O%ti*i/e Re"%on"e
,
, Goa)7 *a$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>
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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>
Example: std. dev. of noise = 100
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>
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1!!
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>
Example: std. dev. of noise = 100
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>
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1!1
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>
Example: std. dev. of noise = 100
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***
Re"%on"e Sr#a&e De"ign" T'ree :e+e) Fa&toria) De"ign =00>
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1!
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>
Example: std. dev. of noise = 100
, O%ti*i/e Re"%on"e
,
, Goa)7 *a$i*i/e ;
, O%ti** +a)e K 100!.9
, Fa&tor :ow Hig' O%ti**
,
, Fa&tor6 1!.! 0!.! 1!.!
, Fa&torB 0!.! 9!.! 9!.!
, Fa&torC 4!.! 9!.! 9!.!
Re"%on"e Sr#a&e De"ign" T'ree :e+e) Fa&toria) De"ign =00>
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1!0
Re"%on"e Sr#a&e De"ign" < T'ree :e+e) Fa&toria) De"ign =00>
RE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>
Example: std. dev. of noise = 100
E"ti*ate- Re"%on"e Sr#a&eFa&torCK9!.!
Fa&tor6
Fa&torB
;
1! 14 1A 9 0! 0! 054! 45
5! 559!
4!!
1!4!!
114!!
14!!
104!!
Re"%on"e Sr#a&e De"ign" T'ree :e+e) Fa&toria) De"ign =00>
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1!4
Re"%on"e Sr#a&e De"ign" < T'ree :e+e) Fa&toria) De"ign =00>
RE6: MODE:7 ; K 4!F1!!F1!!F01!F1FF1F1 =NOISE>
Example: std. dev. of noise = 100
Contor" o# E"ti*ate- Re"%on"e Sr#a&e
Fa&torBK9!.!
Fa&tor6
F a & t o rR C
;
A!!.!
A9!!.!!!!.!
4!!.!
A!!.!
1!!!.!
1!9!!.!
11!!!.!
114!!.!11A!!.!
1!!.!
19!!.!
1! 14 1A 9 0!
4!
44
4A
5
59
9!
C:6SSROOM EXERCISE
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1!5
, STDENT INC:6SS EXPERIMENT7
Co))e&t -ata #or e$%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$%eri*ent < wo)- "gge"t"e+era) re%)i&ation"
C:6SSROOM EXERCISE
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1!9
, Con-&t E$%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
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1!@
C:6SSROOM EXERCISE
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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
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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
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11!
PIN THE T6I: D6T6 INPT
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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".
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11
ESTIM6TE OF EFFECTS =ME6N HIT>
Pareto C'art #or ME6N
E##e&t
! 0 9 1 15
67M6RJER STICJ
6B
B7ERTIC6: PO:E
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110
ESTIM6TE OF EFFECTS =ME6N HIT>
Main E##e&t" P)ot #or ME6N
M E 6 N
M6RJER STICJ 1.! 1.!
ERTIC6: PO:E1.! 1.!
9
0
!
0
9
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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
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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
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119
CONTOR P:OT OF RESPONSE
=ME6N HIT>
Contor" o# E"ti*ate- Re"%on"e Sr#a&e
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
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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>
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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>
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11
=ME6N HIT>, O%ti*i/e Re"%on"e
,
, Goa)7 *aintain ME6N at !.!
, O%ti** +a)e K !.!
, Fa&tor :ow Hig' O%ti**
,
, M6RJER STICJ 1.! 1.! !.!0011
, ERTIC6: PO:E 1.! 1.! !.10A!0
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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
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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
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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
, Fa&tor :ow Hig' O%ti**
,
, M6RJER STICJ 1.! 1.! 1.!
, ERTIC6: PO:E 1.! 1.! 1.!
INTER6CTION
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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
CONTOR P:OT OF RESPONSE
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14
CONTOR P:OT OF RESPONSE
=STD DE HIT>
Contor" o# E"ti*ate- Re"%on"e Sr#a&e
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
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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
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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+.
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