Process Capability and Cpk

8/19/2019 Process Capability and Cpk

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Training materials, referencedocuments, and functional SPCtemplates are available free on

the Rockford Powertrain website. o to!

www.rockfordpowertrain.com"supplier


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Process Capability

• Enables successful manufacturing andsales

• Prevents scrap, sorting, rework• Allows jobs to run well• Has major impact on cost and schedule


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“Process Capability”

is the ability of a processto make a feature

within its tolerance .


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Everything aries(and the variation can be seen if we measure precisely enough)

• Heights• !eights

• "engths• !idths• #iameters• !attage

• Horsepower • $iles per %allon

• Pressure• &oughness

• 'trength• Conductivity• "oudness• 'peed

• (or)ue• Etc. etc. etc.


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Eli !hitney in *+ -• !on a ./'/ $ilitary contract to supply *0,000 guns• &educed variation and created interchangeable parts for

assembly and service by1 2 3nstalling powered factory machinery 2 .sing speciali4ed fi5tures, tools, jigs, templates, and end6stops 2 Creating drawings, routings, operations 7 training


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$anufacturing in the 8* st Century• 3nternational competition to provide defect6free products

at competitive cost• &educing variation and providing interchangeable parts

for assembly and service by1 2 .sing machine tools 2 .sing speciali4ed fi5tures, tools, jigs, templates, and end6stops 2 .sing drawings, routings, operations 7 training


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%raphing the tolerance and a measurement

It’s useful to see the tolerance and the part measurement on a graphSuppose that:

.51 .51! .51" .515 . 51# .51$ .51% .51& .5 ' .5 1 .5 .5 ! .5 " .5 5 .5 #.5 $ .5 %


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((the tolerance is .515”

Speci)cation*imit +I,

.51 .51! .51" .515 . 51# .51$ .51% .51& .5 ' .5 1 .5 .5 ! .5 " .5 5 .5 #.5 $ .5 %


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((the tolerance is .515” to .5 5”

Speci)cation*imit +-


.51 .51! .51" .515 . 51# .51$ .51% .51& .5 ' .5 1 .5 .5 ! .5 " .5 5 .5 #.5 $ .5 %


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((the tolerance is .515” to .5 5”((and an indi/idual part is measured at .5 '”.



.51 .51! .51" .515 . 51# .51$ .51% .51& .5 ' .5 1 .5 .5 ! .5 " .5 5 .5 #.5 $ .5 %

X


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%raphing the tolerance and measurements

Suppose 0e made and measured se/eralmore units and they 0ere all 2 -C3*4 thesame

6e 0ouldn’t ha/e /ery many part problems



.51 .51! .51" .515 . 51# .51$ .51% .51& .5 ' .5 1 .5 .5 ! .5 " .5 5 .5 #.5 $ .5 %

X

X

X

X


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%raphing the tolerance and measurements

In the real 0orld units are ,73 2 -C3*4 thesame. 2/erything 8-9I2S.

3he uestion isn’t I; units /ary.It’s ho0 much 0hen and 0hy.



.51 .51! .51" .515 . 51# .51$ .51% .51& .5 ' .5 1 .5 .5 ! .5 " .5 5 .5 #.5 $ .5 %

XX

XXX

XXXXX

XXXXXXX


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3he “normal bell cur/e”

6idths heights depths thic


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6hat is a “standard de/iation”>

If 0e measure the ?IS3-,C2 from the C2,329 of the bellto each indi/idual measurement that ma


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Fo0 much of the cur/e is included in ho0 many standardde/iations>

;rom D1 to 1 is about #%E of the bell cur/e.;rom D to is about &5E;rom D! to ! is about &&.$!E;rom D" to " is about &&.&&E

(NOT#$ %e usually show the bell from &' to ' to make it easier to draw,but in concept, the )tails of the bell get ery thin and go on fore er!"

#$ #% #& #' #( #) *) *( *' *& *% *$+


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-

B

6hat is Cp +t is a measure of howwella process is within a speci cation!

Cp< G - di/ided by B- G ?istance from process mean to closest spec limitB G ! Standard ?e/iations @also called “! Sigma”A

- bigger Cp< is better because fe0er units 0ill be beyond spec.@- bigger “-” and a smaller “B” are better.A

Speci)cation*imit

Speci)cation*imit

HS**S*

HC*


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-

B

“Process Capability” is the ability of aprocess to )t its output 0ithin thetolerances.

a *-9J29 “-”and a S+-**29 “B”means B23329 “Process Capability”

Speci)cation*imit

Speci)cation*imit

Cp< G- di/ided byB


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-

B

-n -nalogy

nalogy! 3he bell cur/e is your automobile. 3he spec limits are the edges of your garage door.If - G B you are hitting the frame of your garage door 0ith your car.

Speci)cation*imit

Speci)cation*imit

Cp< G- di/ided byB


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-

B

Fo0 can 0e ma

1. ?esign the product so a 0ider tolerance is functional @“robust design”A. Choose e uipment and methods for a good safety margin @“process capabilit!. Correctly adKust but only 0hen needed @“control”A". ?isco/er 0ays to narro0 the natural /ariation @“impro/ement”A

Speci)cation*imit

Speci)cation*imit

Cp< G- di/ided byB


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-

B

6hat does a ery good Cp< do for us>

3his process is producing good units with a good safetymargin .

,ote that 0hen Cp< G our process mean is # standardde/iations from the nearest spec so 0e say it has -$ SigmaCapability.

Speci)cation*imit

Speci)cation*imit

3his Cp< isabout .8ery good

+ean


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-

B

6hat does a problem Cp< loo< li

3his process is in danger of producing some defects.It is too close to the speci)cation limits.

(-emember$ the bell cur e tail goes further than .//we only show the bell to '0sigma to make it easier to draw!"

Speci)cation*imit

Speci)cation*imit

3his Cp< is Kustslightly greaterthan 1. ,otgood


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-

B

6hat does a ery bad Cp< loo< li

- signi)cant part of the “tail” is hanging out beyond the spec limits. 3his process is producing scrap re0or< and customer reKects.

,otice that if distance “-” approaches Lerothe Cp< 0ould approach Lero andthe process 0ould become 5'E defecti/e

Speci)cation*imit

Speci)cation*imit

3his Cp< is lessthan 1. 6edesire aminimum of1.!! and

ultimately 0e0ant or more.


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9ree software is available to draw a histogramand calculate average, standard deviation, and Cpk/

"ocated at1 www/rockfordpowertrain/com:supplier


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6hat “SiM Sigma Philosophy” did +otorolateach its suppliers in the 1&%'’s>

In the 1&%'’s +otorola achie/ed dramatic uality impro/ementsand 0on the HS-’s +alcolm Baldrige ,ational Nuality -0ard.

+otorola began seminars teaching its “SiM Sigma Philosophy” toits suppliers and to other companies.

3he follo0ing fe0 slides depict some original messages from thattime.

Speci)cation*imit

Speci)cation*imit


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9obust ?esign D part of the original SiM Sigma

3he ne0 design abo/e has tolerances set “tight” to a


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9obust ?esign D part of the original SiM Sigma

C-H3I7,:

Suppliers must negotiate the 0idening of tolerances B2;792 competiti/ebids uotations and acceptance of orders. Competiti/e bids arecommitments to meet all eMisting tolerances. ;ailure to meet customertolerances means failure to meet contract re uirements. Pre/entbreaches of contract.

,e0 ProductSpeci)cation*imit


Ono0n2Misting

Process



Ono0n

2MistingProcess


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9obust Processes D part of the original SiM Sigma

3he process abo/e /aries so much that it “)lls” the design tolerance. 3hedi erent process belo0 has good repeatability for “siM sigma capability”.

It’s a false(economy to choose an allegedly lo0er(cost process that “usesup” all tolerance. 3he resulting scrap re0or< reKections recalls damageto reputation crisis communications and )re()ghting cancel out thealleged economy. “9obust Process” re uires s


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# Sigma Philosophy D ,ot Qust 3he Shop ;loor1etting e ery person )capable and in )self control

Achieving delivery and project deadlines

$eeting budgets 7 financial goals Administrative tasks#esign workPurchasing:sourcing'pecial projects'ecurity and 'afety

Health and Environmental"egal compliance

Anything that can bedefined and measured


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etting every person -capable and in -self control

Defined & Understood

Requirements

bility to!easure Results

"rocess#apability andbility to #ontrol

$he %Requisites

f 'elf #ontrol


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Summary!R 3o call a process “capable” typically re uires atleast a Cp< of 1.!! @ and ( " standardde/iations 0ithin toleranceA

R +any customers desire a Cp< of .' @ and ( #

standard de/iations 0ithin toleranceAR 7rganiLations need:

1. ;easible designs. Capable processes

!. Process self(control


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Conclusion!Process Capability:

es* +o*

+o*

+o*

es*

es*

potentially capableif re centered

potentially capableif re centered

too wide


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&eview ;uestion *

!hat is


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&eview ;uestion 8

How is the calculatedor estimated=


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&eview ;uestion ?

!hat is a


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&eview ;uestion B

!hat is Cpk used for=


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&eview ;uestion

'uppose that a feature tolerance is /+ 0>:/+D0>,and the process average is /+ >,and the process standard deviation is /008>

is the process satisfactory and capable=


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&eview ;uestion D

'uppose that a tor)ue tolerance is 8 footpounds minimum,

and the process average is 8D foot pounds,and the process standard deviation is ? foot

poundsis the process capable=


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&eview ;uestion +

'uppose that a diameter tolerance is -/0*0> to-/0D0>,

and the process average is -/0B*>,and the process standard deviation is /008>

is the process capable=


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&eview ;uestion Foe is boring an inside diameter on a lathe/(he diameter tolerance is */ -0> to 8/080>/Foe has measured three random samples at8/00 >, 8/00B>, and 8/00D>/• Estimate the process average/• Estimate the standard deviation @best guess /• Estimate whether the process can be capable/


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&eview ;uestion *0(echCorp is demonstrating a new

grease dispenser machine/(echCorp claims that they can #uring the demo, ten samples of grease in a row were

dispensed @in ounces as follows18/?, 8/0, 8/D, ?/0, 8/*, 8/+, 8/ , 8/ , 8/0, 8/B

• Gased on the sample data, evaluate (echCorp sclaim that they can


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;ui4 ;uestion 8

(rue of 9alse=

!e can estimate the process averageby taking a set of sample measurements,

adding them up, and dividing by thenumber of measurements/


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;ui4 ;uestion ?(rue or 9alse=

A


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;ui4 ;uestion B

(rue or 9alse=

!hen using Cpk, the goal is to keep theCpk value as low as possible/


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;ui4 ;uestion (rue or 9alse=

3f the feature tolerance is /? 0>:/?D0>,and the process average is /? *>,and the process standard deviation is /00B>

then the process should be called


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;ui4 ;uestion D(rue or 9alse=

3f a pressure tolerance is 8 0 P'3 minimum,and the process average is 8D0 P'3,and the process standard deviation is B P'3,

then the process is


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;ui4 ;uestion +

(rue or 9alse=

3f a height tolerance is +/0*0> to +/0D0>,and the process average is +/0B8>,and the process standard deviation is /008>

then the process is


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;ui4 ;uestion -(rue or 9alse=

3f "arry is cutting an L/#/ and the diameter iseasily adjustable, the tolerance is B/0 > toB/0 >, the process average is B/0 >, andthe standard deviation is /00*>

then "arry should be able to make theprocess fully by adjusting theprocess/


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;ui4 ;uestion (rue or 9alse=

3f Fill is boring an 3/#/ with a tolerance of */B+ >to */ 8 >, and has measured three samplesat */ 0*>, */ 00>, and */B >

then the average of the samples is */ 0*>,

the standard deviation is probably largerthan /0*0>, and the Cpk is probably 4ero/


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;ui4 ;uestion *0(rue or 9alse=

3f Hi(echCo is demonstrating a new surface coating machine, and claims that theirmachine and during the demo the coatingthickness readings @in inches were as follows1

/08+, /08-, /08+, /08 , /08-, /08 , /08-, /08 , /08-, /08+then the sample readings suggest that Hi(echCo

might be telling the truth about being able to hold plusor minus /0*0 inches/


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Appendi5

Cpk and PP$

@Parts Per $illion #efective


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Cpk! void confusion and pitfalls R ?72S I3 8-94> Cp< varies when sampled

because it’s calculated from the a/erage and thestandard de/iation both of 0hich are estimatedfrom samples .

R C-9973S -,? S3ICOS> Ji/ing re0ards orreprimands based on minor short(term

uctuations of Cp< amounts to a lottery.Watch real trends.

R +-O2 - “P*-,3 -829-J2” CPO> It’s unhelpfulto report a plant average Cp< of multiplecharacteristics and products because:1. Cp< /alues depend on each chosen tolerance

. -n “o


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-

B

6hat is PP+ @defect Parts Per +illionA>

“PP+” is an estimate of the portion that is beyond the spec limit.If 0e


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6hat is the “#(Sigma Philosophy”“1.5(Sigma Shift”>

3he “# Sigma Philosophy” includes the premise that real(0orld processes

mo/e around to some eMtent and produce more defects than a staticprocess. -s an arbitrary con/ention this is represented as an “unfa/orableshift” of 1.5 sigma in Parts Per +illion tables for SiM Sigma programs. 3heintention is to plan conser/ati/ely.

/This means that the -PP0 vs. Sigma charts published for -$#Sigma Programs showhigher defect rates than the similar but traditional -1#tables in statistical te2tbooks. 3

Speci)cation*imit

Speci)cation*imit

Hnfa/orableprocess shiftof 1.5standardde/iations


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3he follo0ing page is a table sho0ing therelationships among the follo0ing:

R Cp


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#p,@#efined as

distance fromprocess mean tothe nearest spec,

divided by ?'tandard

#eviations

"How ManySigma

Capability?"#istance of

Process $ean to'pec "imit in

'tandard #eviations

-ithin 'pec

@Process PerfectlyCentered,Goth (ails

Considered%ood .nits Per

$illion

PP$ of the GellCurve

ut of 'pec @Process Perfectly

Centered,Goth (ails

Considered


ut of 'pec@Process Mot

Centered,Lnly Lne (ailConsidered

(he column A("E9( e)uates to *defective out of how

many total=


Lut of 'pec

with Six-SigmaPhilosophy

of 1.5 StandardDeviation Penalty

for AnticipatedUnfavorable

Process Mean Drift

0 0 0 *,000,000 00,000 8

0/*+ 0/ ?-8, 8 D*+,0+ ?0-, ?- ?

0/?? * D-8,D- ?*+,?** * -,D D

0/ */ -DD,?-D *??,D*B DD,-0+ * 00,000

0/D+ 8 B, 00 B , 00 88,+ 0 BB ?0-, ?-

0/-? 8/ -+, -* *8,B* D,8*0 *D* * -,D

* ? +,?00 8,+00 *,? 0 +B* DD,-0+

*/*+ ?/ , ? BD 8?? B,8 - 88,+ 0

*/??B , ?+ D? ?8 ?*, D0 D,8*0

*/ B/ , ?/8 D/- ?/B 8 B,0B- *,? 0

*/D+ , /B 0/D 0/? ?,B-?,0BD 8??

*/-? / , / D 0/0B 0/08 8, ?0, BB ?8

8 , / - 0/008 0/00* *,00 , +D,D ? %./

8/*+ D/ , / 8 0/0000- 0/0000B 8B,++-,8+D,8+? 0/?

#p,0 ""!0 and 1'i2 'igma1

Process Capability and Cpk

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