Six Sigma Lecture Notes

8/19/2019 Six Sigma Lecture Notes

1/84

SIX SIGMASIX SIGMA

A STRATEGY FOR PERFORMANCEEXCELLENCE

A STRATEGY FOR PERFORMANCEEXCELLENCE


2/84

SIX SIGMASIX SIGMA

99.9% is already VERY GOOD

But what could happen at a quality level of 99.9% i.e.! "### pp$!

in our everyday lives a&out '.(σ

)

• More than 3000 newborns accidentally falling from the hands of nurses or doctors each year

• 4000 wrong medical prescriptions each year

• 400 letters per hour which never arrive at their destinatio

• Two long or short landings at American airports ea

ch day

How good is good enough?


3/84

SIX SIGMASIX SIGMAHo

w can we get theseresults

• 13 wrong drug prescriptions per year

• 10 newborn babies dropped bydoctors/nurses per year

• Two short or long landings per year in all

the airports in the U.S.• One lost article of mail per hour


4/84

SIX SIGMASIX SIGMA

The answer is:

Six Sigma


5/84

SIX SIGMASIX SIGMA

A ision and !hilosophical commitmentto our consumers to offer the highest "uality#

lowest cost products

A $etric that demonstrates "uality le%els at

&&.&&&'( performance for products andprocesss

A )enchmar* of our product and processcapability for comparison to +best in class,

A practical application of statistical Tools

and $ethods to help us measure# analy-e#impro%e# and control our process

W

hat is Six Sigma


6/84

SIX SIGMASIX SIGMASix Si

gma as a Philosoph

Internal &ExternalFailureCosts

Prevention & Appraisal

Costs

Old Belief 4σ C

o s t s

Internal &ExternalFailure Costs

Prevention & Appraisal

Costs

New Belief C o s

t s

4σ

5σ

6σ

Quality

Quality

Old Belief

i!" #ualit$ % i!" Cost

New Belief i!" #ualit$ % ow Cost

σ is a 'easure of "ow 'u("variation exists in a pro(ess


7/84

SIX SIGMASIX SIGMA! Si gma "s# $ Sigma

The 3 sigma Company The 6 sigma Company

• Speds !"#$"% of sales dolla&so 'ost of failu&e

• Speds "% of sales dolla&s o'ost of failu&e

• Relies o ispe'tio to fid

defe'ts

• Relies o 'apa(le p&o'ess t)at

do*t p&odu'e defe'ts• +oes ot )a,e a dis'ipliedapp&oa') to -at)e& ad aaly.edata

• /se Measu&e0 Aaly.e0 12p&o,e0Cot&ol ad Measu&e0 Aaly.e0+esi-

• Be')2a&3s t)e2sel,esa-aist t)ei& 'o2petitio

• Be')2a&3s t)e2sel,esa-aist t)e (est i t)e wo&ld

• Belie,es 44% is -ood eou-) • Belie,es 44% is ua''epta(le

• +efie CTQs ite&ally • +efies CTQs e5te&ally


8/84

SIX SIGMASIX SIGMA%ocus: The &nd 'ser

• Custo2e&6 1te&al o& E5te&al • Cosu2e&6 T)e Ed /se&

t)e 78oi'e of t)e Cosu2e&9 :Cosu2e& Cue;

2ust (e t&aslated ito

t)e 78oi'e of t)e E-iee&9 :Te')i'al Re


9/84

SIX SIGMASIX SIGMASix Sigma as a Metric

C E ! "

# E $

1

)( 2

−

−= ∑

n

x xi

σ

!igma % σ % $eviation & !'uare root of variance (

* + * ( * , * ' * - * . * " # " . - ' , ( +

Axis graduated in Sigma

(/.+ %

9,.', %

99.+- %

99.99-+ %

99.9999'- %

99.999999/ %

result0 -"+-## pp$ outside

deviation

',,## pp$

+## pp$

(- pp$

#.,+ pp$

#.## pp$

&etween 1 2 * "σ

&etween 1 2 * σ

&etween 1 2 * -σ

&etween 1 2 * 'σ

&etween 1 2 * ,σ

&etween 1 2 * (σ

σ %


10/84

SIX SIGMASIX SIGMA3sigma !rocess

/centered

p 2 1.0p* 2 1.0

#'00 ppm

)pe( &i'its


11/84


/shifted 0.4 std. de%.

p 2 1.0p* 2 0.533

ppm 2 6#77

/about .'sigma

)pe( &i'its


12/84



p 2 1.0p* 2 0.66'

ppm 2 #'5

/about .5sigma

)pe( &i'its


13/84



p 2 1.0p* 2 0.4

ppm 2 66#511

/about 1.53sigma

)pe( &i'its


14/84

SIX SIGMASIX SIGMA(on)*iner +ecrease

*

+

4

5

6

+,-.5+/

66.-00

6.*0,

*++

+14

σ !!$

P&o'ess

Capa(ility

+efe'ts pe& Millio

Oppo&tuities

* Includes 1.5 σ shift

Fo'usi- o σ &e


15/84

SIX SIGMASIX SIGMASix Sigma as a Tool

P&o'ess Mappi- Tole&a'e Aalysis

St&u'tu&e T&ee Co2poets Sea&')

Pa&eto Aalysis =ypot)esis Testi-

Gau-e R > R Re-&essio

Ratioal Su(-&oupi- +OE

Baselii- SPC

May fa2ilia&


16/84

SIX SIGMASIX SIGMASix Sigma as a Method

To -et &esults0 s)ould we fo'us ou& (e)a,io& o t)e Y o& X

• 8 •91:9n

•;ependent •


17/84

SIX SIGMASIX SIGMA A Traditional "iew

• Output Varia&les

3ana4e the outputs.

5ales Growth

3ar6et 5hare

7rofita&ility


18/84

SIX SIGMASIX SIGMA A (on)Traditional "iew

• Output Varia&les

• 8nput Varia&les

3ana4e the inputs respond to the outputs.

5ales Growth

3ar6et 5hare

7rofita&ility

:usto$er 5atisfaction

7roduct ;uality

On*


19/84

SIX SIGMASIX SIGMA+ist inguish ,"ital %ew-.rom ,Tri/ial Man-

8 % 2ependent 3ariale Output. 2efe(t> % Independent 3ariales Potential Cause>? % Independent 3ariale Criti(al Cause

+efie t)e P&o(le2 ? +efe't State2et

% f x0

7. x*. x

+. x

4

7. x51 1 1 8

n9

!rocess

!arameters

:aterial

:et"ods

People

Environ'ent

Output

:a("ine

:easure'ents


20/84

SIX SIGMASIX SIGMAStr ateg 0 Phase )

P)ase

$easure@hat

Analy-e@here# @hen# @hy


21/84

SIX SIGMASIX SIGMASix Si gma 1rgani2ation


22/84

SIX SIGMASIX SIGMA A 3lac4 3elt has56 and will5

Leade&s)ip

S t a t i

s t i '

a l 0

Q u a l i t y

S 3 i l l

1 t e & p

e & s o

a l S

3 i l l

+&i,i- t)e /se

T ) e e w

o f S

i 5

S i - 2 a

M e t o

& i -

http://www.mot.com/


23/84

SIX SIGMASIX SIGMA3l ac4 3elt Training

Tas3

Ti2e oCosulti-?

T&aii-

Meto&i- RelatedP&oe'ts

#reen$elt

%tili&e'tatistical( )ualitytechniue

2+5Find onene, green-elt

2 ( year

$lac$elt

/ead use

oftechniueandcommunic0ate ne,ones

5+1T,o green-elts

4 ( year

"aster$lac$elt

Consulting( "entoring( Training

+1Fie $lac$elts

1 ( year


24/84

SIX SIGMASIX SIGMA:ore 5tatistical 56ills :ore 5i= 5i4$a ;uality 56ills :ore 8nterpersonal 56i

GBM Statistical Software (JMP, Minitab)

MIN101GBM AIEG QMS GBM Commnication (oral, writ

AEC722, DDI121

GBM !merical an" Gra#$ical %ec$ni&es

MIN101, IBM548GBM QS '

AEC279GBM %eam acilitation

DDI170

GBM Statistical Process Control

AEC506, AEC661, AEC662, AEC663GBM Cstomer Satisfaction

SSG100, TCS100GBM Coac$in* an" Mentorin*

LDR380, PER119

GBM Process Ca#abilit+

AEC661, AEC662, SCP201GBM Si Ste#s to Si Si*ma

SSG100, SSG102CDGBM Mana*in* C$an*e

MGT564, MGT124, PDE5

GBM Com#arati-e %ests

MIN101, SPC201GBM Concrrent En*ineerin* BM .ea"ers$i#

MGT561, MGT562, DDI1

GBM Anal+sis of /ariance (A!0/A)

ENG998, AEC603GBM %CS

TCS100 BM %eam il"in*

MGT560, MGT562, EC72

GBM Measrement S+stem Anal+sis

AEC663GBM S+stemic A##roac$ to Problem

Sol-in*

QUA392

M Instrctional%eac$in*

MT132

GBM 3esi*n of E#eriments (e4*4 ll,

ractional, %a*c$i 3esi*ns)

ENG998, QUA389

GBM %eam 0riente" Problem Sol-in*

(53, 63, 7P) M Mana*in* Pro8ects

AEC471, MGT839

GBM 9e*ression (e4*4 linear, nonlinear) BM Qalit+ S+stem 9e-iew

QUA590

GBM Statistical Process C$aracteri:ation

Strate*ies an" %ec$ni&es

ENG227

BM %eam Problem Sol-in* !on;

Manfactrin*

CES103 BM Statistical Inference

MIN101, SPC201 BM 3esi*n for Manfactrabilit+

ENG123, ENG123CD

BM Confi"ence Inter-als

MIN101, SPC201 BM inancialEconomic Qalit+ Isses

BM Probabilit+ Conce#ts an"

3istribtions

SPC201

M Qalit+ nction 3e#lo+ment

QUA200A, QUA200B, QUA200C

BM 9es#onse Srface Met$o"s

QUA393 M %otal Qalit+ Mana*ement

BM Screenin* 30E

QUA391 M enc$mar


25/84

SIX SIGMASIX SIGMA7orporate 7ommitment

:otorola is (o''itted to developin! t"ese leaders@

e provide t"ese people wit" extensive trainin! in statisti(aland interpersonal tools. silled !uidan(e and 'ana!e'entsupport@

On(e t"eir develop'ent "as a("ieved a level wort"$ ofre(o!nition. we even "ave a ter' for t"ose ex(eptionalindividuals

Si5 Si-2a Bla'3 Belts

C"ris Dalvin

http://www.mot.com/


26/84

SIX SIGMASIX SIGMA7orporate 7ommitment87ont9d

• :otto

#ualit$ is our =o

Custo'er satisfa(tion is our dut$

Custo'er lo$alt$ is our future

http://www.mot.com/


27/84

SIX SIGMASIX SIGMA3arrier 3rea4through Plan

".##

"#.##

"##.##

>9'

D 7 3 O p

( 5i4$a

58G3?

>9, >9( >9+

(

,.(,,.(

,.,

,.'

,.-

3Y9, 3Y9( 3Y9+ 3Y9/

Pareto, rainstormin*, C=E, -C

53, 63, %CS %eams, SPC

30E, 3M, PC

9enewlac< elt Pro*ram (Internal Motorola)

lac< elt Pro*ram (Eternal S##liers)

Proliferation of Master lac< elts

http://www.mot.com/


28/84

SIX SIGMASIX SIGMA1ther 7ompanies ha/e 3lac43elts Program

• GE $as -er+ sccessfll+ institte" t$is #ro*ram > ?, traine" lac< elts b+ @E 1''6

> 1, traine" lac< elts b+ @E 2

> @o $a-enBt mc$ ftre at GE nless t$e+ are selecte" to become lac< elts; Jac< Delc$

• o"a< $as institte" t$is #ro*ram > CE0 an" C00 "ri-en #rocess > %rainin* incl"es bot$ written an" oral eams

> Minimm re&irementsF a colle*e e"cation, basic statistics, #resentation s IM ; A

> !a-istar ; Citiban


29/84

SIX SIGMASIX SIGMA

Measu&eMeasu&e

C"ara(teri?e Pro(ess

nderstand Pro(essE,aluateE,aluate

I'prove and 3erif$ Pro(ess

12p&o,e12p&o,e

:aintain New Pro(essCot&ol Cot&ol


30/84

SIX SIGMASIX SIGMA

;efine

!roblem

;efine

!roblemUnderstand

!rocess

Understand

!rocessollect

;ata

ollect

;ata!rocess

!erformance

!rocess

!erformance

Pro(ess Capailit$

< CpGCp< ;un C"arts

nderstand Prole'Control orCapailit$9

2ata H$pes

< 2efe(tives< 2efe(ts< Continuous

:easure'ent)$ste's Evaluation:)E9

2efine Pro(ess<

Pro(ess :appin! istori(al

Perfor'an(e Brainstor'

Potential 2efe(tCauses

2efe(t

)tate'ent Pro=e(t

Doals

/de&stad t)e P&o'ess ad Potetial 12pa't /de&stad t)e P&o'ess ad Potetial 12pa't

$easure !hase


31/84

SIX SIGMASIX SIGMA

Ceduce

omplaints

int./e>t.

Ceduce

ostCeduce

;efects

P&o(le2 +efiitios eed to (e (ased o


32/84


33/84

SIX SIGMASIX SIGMA

H i ' e

ow do we *now our processD

Process Ma#

istorical 3ata

is$bone


34/84

SIX SIGMASIX SIGMA

CAT


35/84


36/84

SIX SIGMASIX SIGMA

Visualizing the Causes

σ st σs$ift K

σtotal

Time )

Time *

Time 3

Time 4

+ithin ,roup

•Called σ short term &σst(

•"ur potential - the bestwe can be

• The s reported by all .sigma companies

• The trivial many


37/84

SIX SIGMASIX SIGMA

Visualizing the Causes

/etween ,roups

σ st σs$ift K σtotal

Time )

Time *

Time 3

Time 4

•Called σshift &truly ameasurement in sigmas ofhow far the mean has shifted(

•ndicates our process control• The vital few


38/84

SIX SIGMASIX SIGMA

Assi!nale Cause• Outside influen(es

• Bla( noise

• Potentiall$ (ontrollale• ow t"e pro(ess is a(tuall$ perfor'in!

over ti'e

is$bone


39/84

SIX SIGMASIX SIGMA

Co''on Cause 3ariation• 3ariation present in ever$ pro(ess

• Not (ontrollale

• H"e est t"e pro(ess (an e wit"in t"epresent te("nolo!$

;ata within subgroups G.st will contain only ommon ause

ariation

;ata within subgroups G.st will contain only ommon ause

ariation

SIX SIGMA


40/84

SIX SIGMASIX SIGMA

σ2Hotal K σ2Part


41/84

SIX SIGMASIX SIGMA

To ude&stad w)e&e you wat to (e0

you eed to 3ow )ow to -et t)e&e,

To ude&stad w)e&e you wat to (e0

you eed to 3ow )ow to -et t)e&e,

$ap the !rocess$ap the !rocess

$easure the !rocess$easure the !rocess

,,

Understand the !roblem

,8, 2 function of %ariables ,>,

82f>

Understand the !roblem

,8, 2 function of %ariables ,>,

82f>

S S GSIX SIGMA


42/84

SIX SIGMASIX SIGMA

Measu&eMeasu&e


nderstand Pro(essE,aluateE,aluate


12p&o,e12p&o,e

:aintain New Pro(essCot&ol Cot&ol

SIX SIGMASIX SIGMA


43/84

SIX SIGMASIX SIGMA

In man+ cases, t$e "ata sam#le can be transforme" so t$at it is a##roimatel+ normal4

or eam#le, s&are roots, lo*arit$ms, an" reci#rocals often ta


44/84

SIX SIGMASIX SIGMA

D$at "o we !ee"L

LSL /SL LSL /SL

LSL /SL

ff0Target /o, ariation=i-) Potetial +efe'ts

Good Cp (ut Bad Cp3

n Target 7igh ariation

=i-) Potetial +efe'ts

No so -ood Cp ad Cp3

n0Target /o, ariation

Low Potetial +efe'ts

Good Cp ad Cp3

3ariation redu(tion and pro(ess

(enterin! (reate pro(esses wit"less potential for defe(ts1 H"e (on(ept of defe(t redu(tionapplies to ABB pro(esses not =ust'anufa(turin!9

3ariation redu(tion and pro(ess(enterin! (reate pro(esses wit"less potential for defe(ts1 H"e (on(ept of defe(t redu(tionapplies to ABB pro(esses not =ust'anufa(turin!9

SIX SIGMASIX SIGMA


45/84

SIX SIGMASIX SIGMA

Eli'inate Hrivial :an$Eli'inate Hrivial :an$ #ualitative Evaluation He("ni(al Expertise Drap"i(al :et"ods )(reenin! 2esi!n of Experi'ents

#ualitative Evaluation He("ni(al Expertise Drap"i(al :et"ods )(reenin! 2esi!n of Experi'ents

Identif$ 3ital FewIdentif$ 3ital Few

Pareto Anal$sis $pot"esis Hestin! ;e!ression 2esi!n of Experi'ents

Pareto Anal$sis $pot"esis Hestin! ;e!ression 2esi!n of Experi'ents#uantif$

Opportunit$

#uantif$

Opportunit$ M ;edu(tion in 3ariation CostG Benefit

M ;edu(tion in 3ariation CostG Benefit

Our FoalH

,s

SIX SIGMASIX SIGMA


46/84

SIX SIGMASIX SIGMA

Graph>Box

plot

12

20

*2

Graph>Box

plot+ithout values

3P

/o5 plots help to see the data distribution

3a+

3P

1

'

1

?

''

'?

1'

1?

''

'?

0#erator

3P

1

'

1

?

''

'?

S$ift

3P

1

'

1

?

''

'?

SIX SIGMASIX SIGMA


47/84

SIX SIGMASIX SIGMA

Statistical Anal+sis

,1,*5,1,*,,1,05,1,0,,1,,5,1,,,

/

6

5

4

+

*

0

,

F r e u e n ( $

,1,*5,1,*,,1,05,1,0,,1,,5,1,,,

+,

*,

0,

,

F r e u e n ( $

Is t"e fa(tor reall$ i'portant

2o we understand t"e i'pa(t fort"e fa(tor

as our i'prove'ent 'ade ani'pa(t

"at is t"e true i'pa(t

$pot"esis Hestin!

;e!ression Anal$sis

5545+5*5055

6,

5,

4,

+,

*,

0,

,

8

5

< % 1

% 1 1

Q5M PI

;e!ression

C o m p a r

e

S a m p

l e M e

a n s

& V a r i a

n c e s

I d e n t i

f y

R e l a t

i o n s h i

p s

E s t a b l

i s h

L i m i t s

Appl$ statisti(s to validate a(tions & i'prove'ents

SIX SIGMASIX SIGMA


48/84

SIX SIGMASIX SIGMA

A6 7oor Control8 7oor 7rocess

/6 Must control the 7rocess better8 Technology is 9ne

C6 7rocess control is good8 bad 7rocess or technology

$6 +orld Class

A /

C $

TEC:";",<

1 2 ? 7 N

goodpoor

*=2*=0

)=2

)=0

0=2 C " T # " ;

shi

ft

Ζ St

poor

good

SIX SIGMASIX SIGMA


49/84

SIX SIGMASIX SIGMA

Con<su'erCue

He("ni(al;euire'ent

Preli'inar$2rawin!G2ataase

Identit$CH#s

Identif$Criti(alPro(ess

Otain 2ata on)i'ilar Pro(ess

Cal(ulate Svalues

;ev ,2rawin!s

Stop

Ad=ustpro(ess &desi!n

0st pie(einspe(tion

Prepilot2ata

Pilot data

Otain data;e("e(JSK levels

Stop Fixpro(ess &desi!n

ST+

SU% 2esi!n Intent$.A.


50/84

SIX SIGMASIX SIGMA

• @" Define the custo$er :ue and technical require$ent we

need to satisfy

:onsu$er :ue0 loc/- &/$inin /"

7referred # " wn " w n " wn " w n " wn " w n t * t t *t " wn " w n t *t " wn # #

En4ineerin43etrics

:usto$er Require$ents : u s t o $ e r A e i 4 h t s

R " # i $ % i # i & '

( L " ) " #

*

T i + "

& , i n - & $ #

#

T , & $ # E # " . & / i . i

& ' U - $ 0 "

R " 1

2 3 4 , /

S ' - & " +

T i + "

& , R " 5 $ i /

6 # , , / - 5 $ . " , . . 7 5 i " 3

S " n - , /

R " - , # 7 &

i , n

R " - 5 , n - "

& i + "

& , 5 , 8 " /

# , - -

9 , # & $ 0 "

P , 8 " /

T i + "

& , - 7 5 5

# ' B $ .

: 7 5

P , 8 " /

% $ . : 7 5 5 , 8 " / . $ 5 $ . i

& ' ( & i + " *

S " n - , /

S " n -

i & i ) i

& '

6 # , , /

L , $ 3

i n 0

T i + "

B " & 8 " " n + $ i n & " n $ n . "

T i + "

% " & 8 " " n " 1 7 i 5 + " n

& / " 5

# $ . " + " n

&

S $ 4 " & ' I n 3 " x

R $ & i n 0

C , -

& , 4 i n ) " -

& + " n

&

C , -

& , 4 + $ i n & " n $ . "

C , -

& , 4 i n -

& $ # # $ & i , n

; " $ / -

i n M $ i n -

& / " $ + + $ /

: " &

1 $-& R"-n-" 9

2 Ln&i+" %$.: "/ -#' 9

L "n)i/n+"n&$# i+$.& 9

? S$" & "/$&" 9

7 M""& "//"i/"+"n&- 9

N L in)"-&+"n& .-& 3

6 ..i"- -+$## #/ -$." 3

5 E$-' &/$" 3

' L /$in .-&- 3

1 L &i+" &i+#"+"n& 3

11 C


51/84

SIX SIGMASIX SIGMA

• O2 3efine t$e tar*et "imensions (!ew "esi*ns) or

#rocess mean (eistin* "esi*n) for all matin* Parts

Ga# Mst e %K411, .S.K41 an" S. K 421

Ga#

SIX SIGMASIX SIGMA


52/84

SIX SIGMASIX SIGMA

(;) (;) (;) (;)

()

)tep V+• Dat"er pro(ess (apailit$ data1

• se a(tual or si'ilar part data to (al(ulate )) oflar!est (ontriutors1

• :a$ use expert data for 'ini'al (ontriutors

• 2o not (al(ulate s fro' (urrent toleran(es

Ga# 9e&irements

µ% K 41

S. K 42

.S. K 41

SIX SIGMASIX SIGMA


53/84

SIX SIGMASIX SIGMA

(;) (;) (;) (;)

()

µ*a#K µ bo > µcbe1 > µcbe2 > µcbe > µcbe?

σ*a# K σ2 bo σ

2cbe1 σ

2cbe2 σ

2cbe σ

2cbe?

)"ort Her'µ*a#K 5.080 > 1.250 > 1.250 > 1.250 > 1.250 = .016

σ*a# K (.001)2 (.001)2 (.001)2 (.001)2 (.001)2 K 422?

on! Her'K 2 2 2 2 2 K

rom #rocessF

A-era*e σst

Cbe 1427 41

o 745 41

s$ift K 14N


54/84

SIX SIGMASIX SIGMA


55/84

SIX SIGMASIX SIGMA

(σ

Ahat Do 8 need to do to i$prove $y Ga$e)

G%%E9


56/84

SIX SIGMASIX SIGMA


57/84

SIX SIGMASIX SIGMA

ee /rand Ma5well :ouse Choc? @ull o uts

+ater !pring Tap

Co>ee Amount ) *

;evel@actor

SIX SIGMASIX SIGMA


58/84

SIX SIGMASIX SIGMA3ain Effects3ain EffectsF Effect of eac$ in"i-i"al factor on res#onse

ean RAB ean RB

% a s t e

242

46

ME

SIX SIGMASIX SIGMA


59/84

SIX SIGMASIX SIGMA

ean RAB

%em# RHB

ean RB

%em# R@B

% a s t e

Interaction

:oncept of 8nteraction:oncept of 8nteraction

SIX SIGMASIX SIGMA


60/84

SIX SIGMASIX SIGMA

D$+ se 3oE LD$+ se 3oE L• S$ift t$e a-era*e of a #rocess4

• 9e"ce t$e -ariation4

• S$ift a-era*e an" re"ce -ariation

1 2

SIX SIGMASIX SIGMA


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SIX SIGMASIX SIGMA

3oE tec$ni&es

• ll actorial4

2? K 1N trials

2 is nmber of le-els

? is nmber of factors

• All combinations are teste"4

• ractional factorial can re"ce nmber of

trials from 1N to 54

SIX SIGMASIX SIGMA


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SIX SIGMASIX SIGMA

3oE tec$ni&es4cont"4

• ractional actorial

• %a*c$i tec$ni&es

• 9es#onse Srface Met$o"olo*ies

• alf fraction

SIX SIGMASIX SIGMA


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SIX SIGMASIX SIGMA

igh Bow

Ad"esion Area ('*9 05 *,

H$pe of Dlue A(r$l ret"an

H"i(ness of Foa' )t$rene H"i( H"in

H"i(ness of o!o H"i( H"in

A'ount of pressure )"ort on!

Pressure appli(ation ti'e )'all Bi!

Pri'er applied es No

Be%elJactor

3ini :ase * F855?F 3O


64/84

SIX SIGMASIX SIGMA

; ;

;

;

;

;

;

;

; ;

;

;

; ;

;

;

1

2

?

7

N

6

5

'45

$esign Array

A C 3 !o Glin* Str

54'

'42

54'

124

1

14'

124N

A Adhesion Area cm

) Type of Flue

Thic*ness of Joam

Styrene

; Thic*ness of Bogo

T

A ) ;

R 416, 515, 5165 515-

< 614- 515- 514+ 515,

Effect %ablation

SIX SIGMASIX SIGMA


65/84

SIX SIGMASIX SIGMA

＋ ; ＋ ; ＋ ; ＋ ;

G l u i n

4 5 t r

e n 4 t h

A"$esion

Area %+#e of Gle %$< of oamSt+rene%$< of lo*o

@actor E>ect 7lot

?4N

N47

747

7475 74N7

74?

7475

7

SIX SIGMASIX SIGMA


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SIX SIGMASIX SIGMA

14 3efine 0b8ecti-e4

24 Select t$e 9es#onse (@)

4 Select t$e factors (Hs)

?4 C$oose t$e factor le-els

74 Select t$e E#erimental 3esi*n

N4 9n E#eriment an" Collect t$e 3ata

64 Anal+:e t$e "ata

54 Conclsions

'4 Perform a confirmation rn4

5


67/84

SIX SIGMASIX SIGMA

4o amount of e5perimentation can

prove me right a single e5periment canprove me wrong4

B=!cience can only ascertain what is8but not what should be8 and outside of

its domain value Dudgments of all ?indsremain necessary=

; Albert Einstein

SIX SIGMASIX SIGMA


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SIX SIGMASIX SIGMA

Measu&eMeasu&e


nderstand Pro(ess

E,aluateE,aluate


12p&o,e12p&o,e

:aintain New Pro(ess

Cot&ol Cot&ol

SIX SIGMASIX SIGMA


69/84

SIX SIGMASIX SIGMA

:OF


70/84

SIX SIGMASIX SIGMA

:OF


71/84

SIX SIGMASIX SIGMA

:OF


72/84

SIX SIGMASIX SIGMA

P;O2CH:ANADE:ENH

O3E;ADOA OF

)OFHA;E

LNOE2DE OFCO:PEHIHO;)

)PE;3I)ION

P;O2CH2E)IDN

P;O2CH:ANADE:ENH

P;O2CH2E)IDN

P;O2CH:ANADE:ENH

INNO3AHION

OHPH

2I;ECHO;O;DANISAHION

INHIHI3E AN)E;)

)PPO;H

:EHO2) HO :ALEEA)IE; FO; )E;)

CA;ACHE;I)HIC)

• Or!ani?in! ideas into 'eanin!ful(ate!ories

• 2ata ;edu(tion1 ar!e nu'ers of ual1

Inputs into 'a=or di'ensions or (ate!ories1

AJJ


73/84

SIX SIGMASIX SIGMA

$ATC


74/84

SIX SIGMASIX SIGMA

A d

d f e a

t u r e s

: a

B e e x

i s t i n ! p r o

d u (

t f a s t

e r

: a

B e e x

i s t i n ! p r o

d u (

t e a s

i e r

t o u s e

& e a v e a s


75/84

SIX SIGMASIX SIGMA

:OF


76/84

SIX SIGMASIX SIGMA

ow do we sele(t t"e (orre(t Control C"art

%+#e

3ata

In"4 Meas4 or

sb*ro#s

!ormall+ "ist4

"ata

Interest in

s""en mean

c$an*es

Gra#$ "efects

of "efecti-es

0#ort4 Area

constant from

sam#le to

sam#le

H, 9m

#, n#

H ; 9 MA, EDMA or

CSM an"9m

C,

Si:e of t$e

sb*ro#

constant

#

If mean is bi*, H an"

9 are effecti-e too

Ir neit$er n nor # are

smallF H ; 9, H ; 9m

are effecti-e

More efecti-e to

"etect *ra"al

c$an*es in lon* term

se H ; 9 c$art wit$

mo"ifie" rles

/ariablesAttribtes

Measrement

of sb*ro#sIn"i-i"als

@es

!o !o

@es

@es

!o

@es

!o

3efects 3efecti-es

SIX SIGMASIX SIGMA


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SIX SIGMASIX SIGMA

SIX SIGMASIX SIGMA


78/84

SIX SIGMASIX SIGMA

Additional 3ariale ased tools01 P;E


79/84

SIX SIGMA

*1 Co''on Causes C"art E:A91•:ean of auto'ated 'anufa(turin! pro(esses drifts e(ause ofin"erent pro(ess fa(tor1 )PC (onsideres pro(ess stati(1•2rift produ(ed $ (o''on (auses1•I'ple'ent a Co''on Cause C"art1

•No (ontrol li'its1 A(tion li'its are pla(ed on ("art1•Co'puted ased on (osts•3iolatin! a(tion li'it does not result in sear(" for spe(ial(ause1 A(tion taen to rin! pro(ess (loser to tar!et value1

•Pro(ess 'ean tra(ed $ E:A

•Benefits•sed w"en pro(ess "as in"erent drift•Provide fore(ast of w"ere next pro(ess 'easure'ent will e1•sed to develop pro(edures for d$na'i( pro(ess (ontrol

•Euation E:A % y8t 9 σ :yt 0 y8t; σ etween , and 0

SIX SIGMASIX SIGMA


80/84

SIX SIGMA

=@$A chart of sand temperature

,

5,

0,,

05,

0 4 / 0 ,

0 +

0 6

0 Q

* *

* 5

* -

Obser%ations

; e g r e e s

)andHe'peratureE:A

Sad Te2pe&atu&e E@MA E&&o&

0*5 0*51,, ,1,,

0*+ 0*51,,


81/84

S S G

Pro=e(t Closure

•I'prove'ent full$ i'ple'ented and pro(ess re


82/84

$otorola CO<

1&5'1&&7 • ;edu(ed in


83/84

Feneral =lectric CO<

1&&41&&5

• Co'pan$ wide savin!s of over W0 Billion1

• Esti'ated annual savin!s to e W616 Billion $ t"e $ear *,,,1

SIX SIGMASIX SIGMA

3i0liograph


84/84

3i0liograph

• Control En!ineerin! On line. 2esi!n for )ix )i!'a Capailit$

"ttpGGwww1(ontrolen!1(o'G. 0QQQ

• Forrest 1 Bre$fo!le III. I'ple'entin! )ix )i!'a. Xo"n iel$ & )ons. In(.0QQQ

• Infinit$ Perfor'an(e )$ste's. )ix )i!'a Overview."ttpGGwww16si!'aworld1(o'GsixYsi!'a1"t'. *,,,

• :otorola In(1. "at is + vs1 6 si!'a."ttpGGwww1:otorola1(o'G:I:)G:)PDG)pe(ialGC:Gsld,001"t'. 0QQ/

• )i!'a oldin!s. In(1. )ix )i!'a Breat"rou!" )trate!$.

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Documents

Six Sigma Lecture Notes