06 Process Capability V16
Transcript of 06 Process Capability V16
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06 Process Capability
Measure ControlImproveAnalyzeDefineRecognize
Six SigmaSix SigmaGreen Belt TrainingGreen Belt Training
2006 American Society for Quality. All Rights Reserved.
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AnalyzeMeasure Page 2 Process Capability, Version 2.1
Define
Define
About This Module
Process Capability
Process Capability is .
!he "ay Si# Sigma measures process performance
A viable and valuable tool for all $reen %elts
&i'ely to be an integral aspect of customerre(uirements
Certain to be a competitive discriminator
Six Sigma, A Quest for Process Perfection Meet Goals an Attac! Variation
"#ata$ile%Cams&aft.mt'"#ata$ile"proccap.mt'"#ata$ile"Poisson Process Capability.mt'
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AnalyzeMeasure Page ( Process Capability, Version 2.1
Define
Define
What We Will earn
Process Capability
). !he %asics * +efinitions * Principles * Precision and Accuracy * Shift
* Capability and ,nspection2. Calculating Capability
* !he Standard -ormal !ransform * sing / to Calculate Capability * #ercises
1. sing initab to calculate Capability Analysis3. Capability #amples
* Continuous +ata * Attribute +ata
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AnalyzeMeasure Page ) Process Capability, Version 2.1
Define
Define
!e"nitions
The Basics
C p 4
P p 4
C p' 4
P p' 4
Specification 5idth s7S! Process 5idth
4 S& 8 &S&6σS!
Specification 5idth s7&! Process 5idth
4 S& 8 &S&6σ&!
&esser of9 or S& 8 :1σS!
: 8 &S&1σS!
&esser of9 or S& 8 :1σ&!
: 8 &S&1σ&!
S! 4 Short !erm 5ithin7
&! 4 &ong !erm ;verall7
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AnalyzeMeasure Page * Process Capability, Version 2.1
Define
Define
Principle
The Basics
Process "idth
Specification"idth
Specification 5idth s7Short8term Process 5idth
4 S& 8 &S&6σST
C p 4
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AnalyzeMeasure Page + Process Capability, Version 2.1
Define
Define
,ncrease in nonconformance due
to shift in process centering.
1.235 1.239 1.241 1.245
T
!he process "idthis independent ofthe design "idth.
!he inherentprecision of aprocess is notdetermined by thedesignspecifications.
T
1.233 1.235 1.239 1.241 1.245
!he process centeris independent ofthe design center.
!he ability of aprocess to repeatany given centeringcondition isindependent of thedesignspecifications.
USL USLLSL LSL
Process Precision and Process Accuracy
The Basics
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All Rights Reserved.AnalyzeMeasure
Page Process Capability, Version 2.1DefineDefine
Shi#t $appens
TheBasics Long TermLong Term
Process CapabilityProcess Capability
6σ3σ2σ082σ83σ86σ
S&&S&
S ort TermS ort Term
Process CapabilityProcess Capability
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All Rights Reserved.AnalyzeMeasure
Page - Process Capability, Version 2.1DefineDefine
The Standard %ormal Trans#orm
Calculating
Capability
( ) . /
µ
σ
−=
Converts any normal data to the standard normal so the / table canbe used.
If !e "no! # t en !e can calculate or vice versa$
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AnalyzeMeasure Page 0 Process Capability, Version 2.1
DefineDefine
Process &
Process "idth
Specification"idth
S&8&S&Process / 4
2 σ
&S& S&
µ
Process / 4 half of thenumber of standarddeviations bet"een S&and &S&
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AnalyzeMeasure Page 11 Process Capability, Version 2.1
DefineDefine
Class (xercise
Calculating
Capability=or the data sho"n belo"> use the formulas given in ?definitions@to calculate estimates of9
C p
C p'
Part ) Short !erm data9: 4 < σ st4 2
&S& 4 0S& 4 )0
Part 29 Presume the &S& is changed to 4 ). Recalculate processcapabilities9
C p>
C p' .
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AnalyzeMeasure Page 12 Process Capability, Version 2.1
DefineDefine
athe Process Capability Study
Capability
(xample"#ata$ile"Cams&aft.mt' initab "or'sheet7
Camshafts are cut by a lathe
!he data is in column 1 Supp27
Specification is 600 <
Camshafts are produced in subgroups of one one at a time7
5hat can "e learn from this dataB
5hat is the process capabilityB
5e "ill use both of initab s methods to assess capability
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AnalyzeMeasure Page 1( Process Capability, Version 2.1
DefineDefine
Capability Analysis 'sing the Assistant
Assistant) Capability Analysis
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AnalyzeMeasure Page 1) Process Capability, Version 2.1
DefineDefine
Complete the !ialog
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AnalyzeMeasure Page 1* Process Capability, Version 2.1
DefineDefine
Capability *eports +
Minitab produces 4 reports. We will look at each one starting
with the report card.
i
%Stability
eliminate any special cause variation in your process before continuing with this analysis.stable, examine the control charts on the Diagnostic eport. !nvestigate out"of"control points andStability is an important assumption of capability analysis. #o determine whether your process is
Subgroups$umber of
sources of process variation when collected over a long enough period of time. %ou have &'' subgroups. (or a capability analysis, this is usually enough to capture the di)erent
$ormalityshould be reasonably accurate.
%our data passed the normality test. *s long as you have enough data, the capability estimates
of Data*mount
precise. #he total number of observations is &'' or more. #he capability estimates should be reasonably
Chec, Status !escription
Capability Analysis #or Supp-*eport Card
#he report card indicates we should assess process stabilityshown on the next page otherwise we can have con+dence inthe validity of the report.
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AnalyzeMeasure Page 1+ Process Capability, Version 2.1
DefineDefine
Capability *eports -
'-
''
d i / i d u a l 0 a l u e
-.'
2.-
M o / i n g
* a n g e
*nderson"Darling5
. 1M* Chart6on+rm that the process is stable.
%ormality Plot #he points should be close to the line.
Capability Analysis #or Supp-!iagnostic *eport
#he diagnosticreport showthe data can
be representedby the normal
distributionand that the
process isrelatively
stable. *gainthis indicateswe can havecon+dence inthe analysis.
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AnalyzeMeasure Page 1 Process Capability, Version 2.1
DefineDefine
Capability *eports 2
7S7 #arget #otal $Subgroup si9eMeanStDev overall5
Process Characteri3ation
6p6pk:.;ench
*ctual overall5 3p
3pk:.;ench< =ut of spec observed5< =ut of spec expected533M D3M=5 observed533M D3M=5 expected5
3otential within5
Capability Statistics
Capability $istogram*re the data inside the limits and close to the target>
*ctual overall5 capability is what the customer experiences.
3otential within5 capability is what could be achieved if process
Capability Analysis #or Supp-Process Per#ormance *eport #he di)erence
between actual andpotential re?ect theprocess shift anddrift between the
long and short term.
#his is thereport you
would sharewith yourteam andinclude as
the baselinein yourpro@ectreport.
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AnalyzeMeasure Page 1- Process Capability, Version 2.1
DefineDefine
Capability *eports 4
'
o5
:.;ench A 2.4&
B'.&'.'-'
es
3 A '.221
7S7 #arget
*ctual overall5 capability is what the customer expe spec limits.percentage of parts from the process that are outsid"" #he defect rate is './&<, which estimates thetarget p B '.'-5."" #he process mean does not di)er signi+cantly fro6onclusions
8pper Spec #arget
Customer *e7uirements
MeanStandard deviation
*ctual overall5 capability
3p3pk:.;ench< =ut of s ec
Process Characteri3ation
!oes the process mean di8er #rom 6009
Actual :o/erall; Capability*re the data inside the limits and close to the target>
Comments
Capability Analysis #or Supp-Summary *eport
$o5 capable is the process9 * succinctsummary ofthe
capabilityanalysis.
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AnalyzeMeasure Page 10 Process Capability, Version 2.1
DefineDefine
Alternate Capability Analysis
#he assistant was introduced in Minitab version & . We will also
learn to use the traditional methods. ;oth methods provide thesame analysis although presented somewhat di)erently. Whichto use is your choice although some recommendations will bemade.
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AnalyzeMeasure Page 2 Process Capability, Version 2.1
DefineDefine
Setting 'p the Traditional Analysis
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AnalyzeMeasure Page 21 Process Capability, Version 2.1
DefineDefine
Minitab Calculates Process Capability
Capability(xamples
"#ata$ile"Cams&aft.mt'
se the Supp2 column &S& 4 <D< S& 4 60< Subgroups of )
'4.-'1.''&.-''.'- /.-- 0.'- -.-
7S7 #arget 8S7
Sample $ &''StDev Within5 &.0'4StDev =verall5 &./0/ &
7S7 - -.''''' #arget ''.'''''8S7 '-.'''''Sample Mean ''.21'''
/
y
'/4-/
0'1
Process Capability o# Supp-
WorksheetF 6amshaft.M#W
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AnalyzeMeasure Page 22 Process Capability, Version 2.1
DefineDefine
Attribute Capability Analysis
Capability (xamples
Company :E/ has attribute data for its primary defect> crac's inthe finish.
!he data for an entire year is in9
"#ata$ile"Procap.mt'
* nits Submitted
* nits =ailed
sing this data> construct an attribute process capability studyusing both of initab s methods
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AnalyzeMeasure Page 2( Process Capability, Version 2.1
DefineDefine
'sing the Assistant
Assistant) Capability Analysis
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AnalyzeMeasure Page 2) Process Capability, Version 2.1
DefineDefine
Completing the Assistant !ialog
#his may varydepending the process
speci+cations andGorcustomer reHuirements.
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AnalyzeMeasure Page 2* Process Capability, Version 2.1
DefineDefine
Capability *eport +
i
i
%Stability
eliminate any special cause variation in your process before continuing with this analysis.stable, examine the control charts on the Diagnostic eport. !nvestigate out"of"control points andStability is an important assumption of capability analysis. #o determine whether your process is
Subgroups$umber of
variation.least 2- subgroups over a long enough period of time to capture the di)erent sources of process
%ou only have &2 subgroups. (or a capability analysis, it is generally recommended that you collec
of Data*mount
for your application, you can gather more data to increase the precision. #he -< con+dence interval for the < of defective items is .01, &'.&&5. !f this interval is too wid
Chec, Status !escription
Binomial Capability Analysis #or 'nits <ailed*eport Card
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AnalyzeMeasure Page 2 Process Capability, Version 2.1
DefineDefine
Capability *eport 2
< defective to '.$o test is performed when you set the maximum acceptabl
B'.&'.'-'
es
'<
acceptable level of '. #he process < defective is greater than the m *cceptable < defectiveF '
$umber of subgroups*verage subgroup si9e
#otal items tested$umber of defectives
Process Characteri3ation
< Defective -< 6!33M D3M=5
Process Capability
. s the = de#ecti/e at or belo5 09
>bser/ed = !e#ecti/e per Subgroup!s the < defective at or below the acceptable level>
Comments
Binomial Capability Analysis #or 'nits <ailedSummary *eport #his shows
the processsigma is&.2 and
the processis not
capable ofmeeting itsreHuirement
s. $oteFMinitab
does notadd &.- to
anycalculated
processsigma
values.
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AnalyzeMeasure Page 2- Process Capability, Version 2.1
DefineDefine
Attribute Capability Analysis? Minitab
StatFQuality !oolsFCapability Analysis %inomial7Capability (xamples
Sample
P r o p o r t i o n
&2&&&'/0-412&
'.&2
'.&'
'.'/
J 3A'.' &
867A'.&'//-
767A'.'/ 4/
Sample
= ! e
# e c t i / e
&2&'/42
.
&'.'
.-
.'
/.-
'.'' & 4
F 02 & F &'&' &
:F &.2/ 1 F
&.20-- F &.2 0&
F .01
F &'.&&
Sample Si3e&''''/'''
&2&'/4
&&
&
&&
&
Binomial Process Capability Analysis o# 'nits <ailed
WorksheetF 3 =66*3.M#W
P Chart
#ests performed with uneHual sample si9es
Cumulati/e =!e#ecti/e
*ate o# !e#ecti/es
!ist o# = !e#ecti/e
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AnalyzeMeasure Page 20 Process Capability, Version 2.1
DefineDefine
StatGuide .s ery .n#ormati/e
Right clic' on the graph> select Stat$uide.
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AnalyzeMeasure Page ( Process Capability, Version 2.1
DefineDefine
Poisson Capability Analysis
Capability(xamples
* Service organi9ation has attribute data for purchaseorder errors. =ne hundred 3=s are examined each day.
#he number of defects in each sample is in 3= defects.
Defects per unit are typically 3oisson distributed.6onstruct a process capability using StatBKuality
#oolsB3rocess 6apability *nalysis 3oisson
#ata5Poisson Process Capability.M 6
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AnalyzeMeasure Page (1 Process Capability, Version 2.1
DefineDefine
Capability Analysis 'sing the Assistant
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AnalyzeMeasure Page (2 Process Capability, Version 2.1
DefineDefine
Completing the !ialog
#his may varydepending the process
speci+cations andGorcustomer reHuirements.
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AnalyzeMeasure Page (( Process Capability, Version 2.1
DefineDefine
Capability *eport +
i
i
%Stability
eliminate any special cause variation in your process before continuing with this analysis.stable, examine the control charts on the Diagnostic eport. ! nvestigate out"of"control points andStability is an important assumption of capability analysis. #o determine whether your process is
Subgroups$umber of
sources of process variation when collected over a long enough period of time. %ou have &''' subgroups. (or a capability analysis, this is usually enough to capture the di)erent
of Data*mount
wide for your application, you can gather more data to increase the precision. #he -< con+dence interval for the number of defects per unit is '.'&, '.'&5. !f this interval is to
Chec, Status !escription
Poisson Capability Analysis #or P> !e#ects*eport Card
*gain the report warns about potential stability issues. #hisis typical at the beginning phases of a pro@ect. 3erformance
predictions must be tempered by the lack of stability. =n theother hand we have to start somewhere.
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AnalyzeMeasure Page () Process Capability, Version 2.1
DefineDefine
Capability *eport -
'.'4-
'.'1'
'.'&-
'.'''
! e # e c t s p e r
' n
i t
'.'&2
'.''/
'.''4
! e # e c t s p e r
' n
i t
' Chart6on+rm that the process is stable.
Cumulati/e !P'*s the points level out, the estimate of D38 becomes more reliable.
Poisson Capability Analysis #or P> !e#ects!iagnostic *eport
#he 8 chart showsrelatively freHuentout of control
points. Laving thedates or other
relevant datarecorded wouldhave made
analysis moreviable.
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AnalyzeMeasure Page (* Process Capability, Version 2.1
DefineDefine
Capability Analysis 2
acceptable D38 to '.$o test is performed when you set the maximum
B'.&'.'-'
es
'
"" #he chance of producing a unit with no defects is level of '."" #he process D38 is greater than the maximum acce6onclusions *cceptable D38F '
$umber of subgroupsSubgroup si9e
#otal units tested #otal defects
Process Characteri3ation
Defects per unit D385 -< 6! '.
Process Capability
. s the !P' at or belo5 09
>bser/ed !P' per Subgroup!s the D38 at or below the acceptable level>
#he chance of producing a unit with no defects.
Comments
Poisson Capability Analysis #or P> !e#ectsSummary *eport #his shows
the processyield is -<
and theprocess is
not capable
of meetingitsreHuirement
s.
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AnalyzeMeasure Page (+ Process Capability, Version 2.1
DefineDefine
Poisson Process Capability Analysis
StatFQuality !oolsFCapability AnalysisFPoisson
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AnalyzeMeasure Page ( Process Capability, Version 2.1
DefineDefine
Poisson Process Capability Analysis
Sample
S a m p l e
C o u n
t P e r
' n i t'.'4-
'.'1'
'.'&-
'.'''
J 8A'.'' --
867A'.'1//0
767A'
Sample
! P '
&'''/''''4''2'''
'.'&''
'.''0-
'.''-'
'.''2-
'.''''
'.''
!F '.'' ' F '.'&'2
F '.'''' F '.'-'' F
'.''''
!F './ -4
F &.'&0- 8F
er/ed !e#ects
42
'.'-'.'4'.'1'.'2&
&&&
2
2
2
&&
2
&&
22
22
&
2
&
&
&
22222
&
&
2
2
&
&
&
&
Poisson Capability Analysis o# P> !e#ects
WorksheetF 3oisson 3rocess 6apability.M#W
' Chart
Cumulati/e !P'
Poisson Plot
!ist o# !P'
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AnalyzeMeasure Page (- Process Capability, Version 2.1
DefineDefine
Calculating Process Sigma
Remember R!E4 e 8+P
=rom the previous analysis +P 4 .00D6
R!E 4 .DD03
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AnalyzeMeasure Page (0 Process Capability, Version 2.1
DefineDefine
Con/ert *T to Process Sigma
CalcFProbability +istributionsF-ormal+istribution
&ong !erm Process sigma 4 2.131
!o convert to Short !erm add ).< 4 1.G31
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AnalyzeMeasure Page ) Process Capability, Version 2.1
DefineDefine
What We $a/e earned
Process Capability
). !he %asics * +efinitions * Principles * Precision and Accuracy * Shift
* Capability and ,nspection2. Calculating Capability
* !he Standard -ormal !ransform * sing / to Calculate Capability * #ercises
1. sing initab to calculate Capability Analysis3. Capability #amples
* Continuous +ata * Attribute +ata
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AnalyzeMeasure Page )1 Process Capability, Version 2.1
DefineDefine
Solutions to Student
(xercises
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AnalyzeMeasure Page )2 Process Capability, Version 2.1
DefineDefine
Cp@Cp, (xercise Solutions :Part +;
8333.1210
2*6010
6==−=−=
S2
3S34S3Cpσ
−−=S2 S2
3S3 . or
. 4S3 MinCp!
σ σ 33
8333.65
2*305
2*3510 == −−= or MinCp!
$oteF
N 6pk A 6p when
the process iscentered.
N 6pk canOt belarger than 6p.
N 6pk can bepositive or negative.
Slide ++
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Cp@Cp, (xercise Solution :Part -;
75.12
9
2*6
110
6 ==−=−=S
3S34S3Cpσ
−−=S2 S2
3S3 . or
. 4S3 MinCp!
σ σ 33
6667.6
4
2*3
15
2*3
510== −−= or MinCp!
$oteF
N 6pk 6p when
the process is notcentered.