06 Process Capability V16

8/9/2019 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.



ControlImprove 2006 American Society for Quality. All Rights Reserved.

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'




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




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




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




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$





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&







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' .





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




AnalyzeMeasure Page 1( Process Capability, Version 2.1

DefineDefine

Capability Analysis 'sing the Assistant

Assistant) Capability Analysis




AnalyzeMeasure Page 1) Process Capability, Version 2.1

DefineDefine

Complete the !ialog




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.




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.





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.




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


!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.





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.





DefineDefine

Setting 'p the Traditional Analysis





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





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




AnalyzeMeasure Page 2( Process Capability, Version 2.1

DefineDefine

'sing the Assistant

Assistant) Capability Analysis




AnalyzeMeasure Page 2) Process Capability, Version 2.1

DefineDefine

Completing the Assistant !ialog

#his may varydepending the process

speci+cations andGorcustomer reHuirements.




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


Binomial Capability Analysis #or 'nits <ailed*eport Card







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


< 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.




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





DefineDefine

StatGuide .s ery .n#ormati/e

Right clic' on the graph> select Stat$uide.





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




AnalyzeMeasure Page (1 Process Capability, Version 2.1

DefineDefine

Capability Analysis 'sing the Assistant





DefineDefine

Completing the !ialog

#his may varydepending the process

speci+cations andGorcustomer reHuirements.




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


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.




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.




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


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.




AnalyzeMeasure Page (+ Process Capability, Version 2.1

DefineDefine

Poisson Process Capability Analysis

StatFQuality !oolsFCapability AnalysisFPoisson





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'




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





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




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




AnalyzeMeasure Page )1 Process Capability, Version 2.1

DefineDefine

Solutions to Student

(xercises




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 ++



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.

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06 Process Capability V16