Supplement 6 Heizer Operations management

7/17/2019 Supplement 6 Heizer Operations management

1/74

2008 Prentice Hall, Inc. S6 1

OperationsManagementSupplement 6 Supplement 6 Statistical ProcessStatistical Process

ControlControlPowerPoint presentation to accompanyPowerPoint presentation to accompany

Heizer/RenderHeizer/Render

Principles of Operations Management, ePrinciples of Operations Management, e

Operations Management, !eOperations Management, !e


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OutlineOutline

Statistical Process Control "SPC#Statistical Process Control "SPC#

Control C$arts for %aria&lesControl C$arts for %aria&les

'$e Central (imit '$eorem'$e Central (imit '$eoremSetting Mean C$art (imits ")*C$arts#Setting Mean C$art (imits ")*C$arts#

Setting Range C$art (imits "R*C$arts#Setting Range C$art (imits "R*C$arts#

+sing Mean and Range C$arts+sing Mean and Range C$arts

Control C$arts for ttri&utesControl C$arts for ttri&utes

Managerial -ssues and Control C$artsManagerial -ssues and Control C$arts


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Outline ContinuedOutline Continued

Process Capa&ilityProcess Capa&ility

Process Capa&ility RatioProcess Capa&ility Ratio (C(Cpp))

Process Capa&ility -nde)Process Capa&ility -nde) (C(Cp.p.))

cceptance Samplingcceptance Sampling

Operating C$aracteristic CureOperating C$aracteristic Cureerage Outgoing 0ualityerage Outgoing 0uality


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(earning O&1ecties(earning O&1ecties

2$en you complete t$is supplement2$en you complete t$is supplementyou s$ould &e a&le to3you s$ould &e a&le to3

4545 )plain t$e use of a control c$art)plain t$e use of a control c$art

7575 )plain t$e role of t$e central limit)plain t$e role of t$e central limitt$eorem in SPCt$eorem in SPC

8585 9uild )*c$arts and R*c$arts9uild )*c$arts and R*c$arts:5:5 (ist t$e fie steps inoled in(ist t$e fie steps inoled in

&uilding control c$arts&uilding control c$arts


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(earning O&1ecties(earning O&1ecties

2$en you complete t$is supplement you2$en you complete t$is supplement yous$ould &e a&le to3s$ould &e a&le to3

;5;5 9uild p*c$arts and c*c$arts9uild p*c$arts and c*c$arts

6565 )plain process capa&ility and)plain process capa&ility andcomputecompute CCppandand CCp.p.

55 )plain acceptance sampling)plain acceptance sampling


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%aria&ility is in$erent%aria&ility is in$erentin eery processin eery process

=atural or common=atural or commoncausescauses

Special or assigna&le causesSpecial or assigna&le causes

Proides a statistical signal w$enProides a statistical signal w$enassigna&le causes are presentassigna&le causes are present

>etect and eliminate assigna&le>etect and eliminate assigna&le

causes of ariationcauses of ariation

Statistical Process ControlStatistical Process Control

"SPC#"SPC#


7/74 2008 Prentice Hall, Inc. S6 7

=atural %ariations=atural %ariations

lso called common causeslso called common causes

ffect irtually all production processesffect irtually all production processes

)pected amount of ariation)pected amount of ariation Output measures follow a pro&a&ilityOutput measures follow a pro&a&ility

distri&utiondistri&ution

?or any distri&ution t$ere is a measure?or any distri&ution t$ere is a measureof central tendency and dispersionof central tendency and dispersion

-f t$e distri&ution of outputs falls wit$in-f t$e distri&ution of outputs falls wit$inaccepta&le limits, t$e process is said toaccepta&le limits, t$e process is said to

&e @in controlA&e @in controlA



ssigna&le %ariationsssigna&le %ariations

lso called special causes of ariationlso called special causes of ariation

Benerally t$is is some c$ange in t$e processBenerally t$is is some c$ange in t$e process

%ariations t$at can &e traced to a specific%ariations t$at can &e traced to a specificreasonreason

'$e o&1ectie is to discoer w$en'$e o&1ectie is to discoer w$en

assigna&le causes are presentassigna&le causes are present liminate t$e &ad causesliminate t$e &ad causes

-ncorporate t$e good causes-ncorporate t$e good causes



SamplesSamples

'o measure t$e process, we ta.e samples'o measure t$e process, we ta.e samplesand analyze t$e sample statistics followingand analyze t$e sample statistics followingt$ese stepst$ese steps

"a#"a# Samples of t$eSamples of t$eproduct, say fieproduct, say fie&o)es of cereal&o)es of cerealta.en off t$e fillingta.en off t$e filling

mac$ine line, arymac$ine line, aryfrom eac$ ot$er infrom eac$ ot$er inweig$tweig$t

?reCuency

?reCue

ncy

2eig$t2eig$t

DD

DDDD DD

DDDD

DDDD

DD

DD DD DDDD DD DDDD

DD DD DDDD DD DDDD DD DDDD

ac$ of t$eseac$ of t$ese

represents onerepresents onesample of fiesample of fie

&o)es of cereal&o)es of cereal

Figure S6.1Figure S6.1



SamplesSamples


""fter enoug$fter enoug$samples aresamples areta.en from ata.en from asta&le process,sta&le process,

t$ey form at$ey form apattern called apattern called adistri&utiondistri&ution

'$e solid line'$e solid linerepresents t$erepresents t$e

distri&utiondistri&ution

?reCue

ncy

?reCue

ncy

2eig$t2eig$tFigure S6.1Figure S6.1



SamplesSamples


"c#"c# '$ere are many types of distri&utions, including'$ere are many types of distri&utions, includingt$e normal "&ell*s$aped# distri&ution, &utt$e normal "&ell*s$aped# distri&ution, &utdistri&utions do differ in terms of centraldistri&utions do differ in terms of centraltendency "mean#, standard deiation ortendency "mean#, standard deiation or

ariance, and s$apeariance, and s$ape

2eig$t2eig$t

Central tendencyCentral tendency

2eig$t2eig$t

%ariation%ariation

2eig$t2eig$t

S$apeS$ape

?reCuency

?reCuency




SamplesSamples


"d#"d# -f only natural-f only naturalcauses ofcauses ofariation areariation arepresent, t$epresent, t$e

output of aoutput of aprocess forms aprocess forms adistri&ution t$atdistri&ution t$atis sta&le oeris sta&le oertime and istime and is

predicta&lepredicta&le

2eig$t2eig$t'im

e'im

e?reCuency

?reCuency PredictionPrediction




SamplesSamples


"e#"e# -f assigna&le-f assigna&lecauses arecauses arepresent, t$epresent, t$eprocess output isprocess output is

not sta&le oernot sta&le oertime and is nottime and is notpredica&lepredica&le

2eig$t2eig$t'im

e'im

e?reCuency

?reCuency PredictionPrediction

????????

????

????????

??????????????????




Control C$artsControl C$arts

Constructed from $istorical data, t$eConstructed from $istorical data, t$epurpose of control c$arts is to $elppurpose of control c$arts is to $elp

distinguis$ &etween natural ariationsdistinguis$ &etween natural ariationsand ariations due to assigna&leand ariations due to assigna&lecausescauses



Process ControlProcess Control


?reuency?reuency

"weig$t, lengt$, speed, etc5#"weig$t, lengt$, speed, etc5#

SizeSize

(ower control limit(ower control limit +pper control limit+pper control limit

"a# -n statistical"a# -n statisticalcontrol and capa&lecontrol and capa&leof producing wit$inof producing wit$incontrol limitscontrol limits

" -n statistical" -n statisticalcontrol &ut notcontrol &ut notcapa&le of producingcapa&le of producingwit$in control limitswit$in control limits

"c# Out of control"c# Out of control



'ypes of >ata'ypes of >ata

C$aracteristics t$atC$aracteristics t$atcan ta.e any realcan ta.e any realaluealue

May &e in w$ole orMay &e in w$ole orin fractionalin fractional

num&ersnum&ers Continuous randomContinuous random

aria&lesaria&les

%aria&les%aria&les ttri&utesttri&utes

>efect*related>efect*relatedc$aracteristicsc$aracteristics

Classify productsClassify productsas eit$er good oras eit$er good or&ad or count&ad or count

defectsdefects Categorical orCategorical or

discrete randomdiscrete randomaria&lesaria&les



Central (imit '$eoremCentral (imit '$eorem

Regardless of t$e distri&ution of t$eRegardless of t$e distri&ution of t$epopulation, t$e distri&ution of sample meanspopulation, t$e distri&ution of sample meansdrawn from t$e population will tend to followdrawn from t$e population will tend to follow

a normal curea normal cure

4545 '$e mean of t$e sampling'$e mean of t$e samplingdistri&utiondistri&ution (())))will &e t$e samewill &e t$e sameas t$e population meanas t$e population mean

) E) E

nn))EE

7575 '$e standard deiation of t$e'$e standard deiation of t$esampling distri&utionsampling distri&ution (())))willwill

eual t$e population standardeual t$e population standarddeiationdeiation ((

))diided &y t$ediided &y t$e

suare root of t$e sample size, nsuare root of t$e sample size, n



Population and SamplingPopulation and Sampling>istri&utions>istri&utions

'$ree population'$ree populationdistri&utionsdistri&utions

9eta

=ormal

+niform

>istri&ution of>istri&ution ofsample meanssample means

StandardStandarddeiation ofdeiation oft$e samplet$e samplemeansmeans

EE))EE

nn

Mean of sample means E )Mean of sample means E )

F F F F F F F

**33)) **22)) **11)) )) GG11)) GG22)) GG33))

99.73%99.73%of all )of all )fall wit$infall wit$in 3 3

))

95.45%95.45%fall wit$infall wit$in 2 2))



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Sampling >istri&utionSampling >istri&ution

) E) E

"mean#"mean#

SamplingSamplingdistri&utiondistri&utionof meansof means

ProcessProcessdistri&utiondistri&utionof meansof means



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Control C$arts for %aria&lesControl C$arts for %aria&les

?or aria&les t$at $ae?or aria&les t$at $aecontinuous dimensionscontinuous dimensions

2eig$t, speed, lengt$,2eig$t, speed, lengt$,strengt$, etc5strengt$, etc5

)*c$arts are to control)*c$arts are to controlt$e central tendency of t$e processt$e central tendency of t$e process

R*c$arts are to control t$e dispersion ofR*c$arts are to control t$e dispersion oft$e processt$e process

'$ese two c$arts must &e used toget$er'$ese two c$arts must &e used toget$er


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Setting C$art (imitsSetting C$art (imits

?or )*C$arts w$en we .now?or )*C$arts w$en we .now

+pper control limit+pper control limit (UCL)(UCL)E ) G zE ) G z))

(ower control limit(ower control limit (LCL)(LCL)E ) * zE ) * z

))

w$erew$ere )) EE mean of t$e sample meansmean of t$e sample meansor a target alue set for t$e processor a target alue set for t$e process

zz EE num&er of normal standardnum&er of normal standarddeiationsdeiations

)) EE standard deiation of t$estandard deiation of t$e

sample meanssample meansEE

/ n/ n

EE population standardpopulation standard


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Setting Control (imitsSetting Control (imits

Hour 4Hour 4

SampleSample 2eig$t of2eig$t of=um&er=um&er Oat ?la.esOat ?la.es

11 1717

22 131333 1616

44 1818

55 1717

66 1616

77 1515

88 1717

99 1616

MeanMean 16.116.1

==11

HourHour MeanMean HourHour MeanMean

11 16.116.1 77 15.215.2

22 16.816.8 88 16.416.4

33 15.515.5 99 16.316.3

44 16.516.5 1010 14.814.8

55 16.516.5 1111 14.214.2

66 16.416.4 1212 17.317.3n E !n E !

LCLLCL))E ) * zE ) * z))EE 16 - 3(1/3) = 15 !"16 - 3(1/3) = 15 !"

?or?or 99.73%99.73%control limits, zcontrol limits, z = 3= 3

UCLUCL))E ) G zE ) G z))= 16 # 3(1/3) = 17 !"= 16 # 3(1/3) = 17 !"


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17 = UCL17 = UCL

15 = LCL15 = LCL

16 = $e&16 = $e&


Control C$artControl C$artfor sample offor sample of! &o)es! &o)es

Sample num&erSample num&er

FF FF FF FF FF FF FF FF FF FF FF FF

44 77 88 :: ;; 66


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?or )*C$arts w$en we donIt .now?or )*C$arts w$en we donIt .now

(ower control limit(ower control limit (LCL)(LCL)E ) * E ) * 22RR

+pper control limit+pper control limit (UCL)(UCL)E ) G E ) G 22RR

w$erew$ere RR EE aerage range of t$eaerage range of t$e

samplessamples22 EE control c$art factor found incontrol c$art factor found in

'a&le S654'a&le S654

)) EE mean of t$e sample meansmean of t$e sample means


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Control C$art ?actorsControl C$art ?actors

'e S6.1'e S6.1

Sample SizeSample Size Mean ?actorMean ?actor +pper Range+pper Range (ower(ower

RangeRangenn 22 >>44 >>3322 1.8801.880 3.2683.268 00

33 1.0231.023 2.5742.574 00

44 .729.729 2.2822.282 00

55 .577.577 2.1152.115 00

66 .483.483 2.0042.004 00

77 .419.419 1.9241.924 0.0760.076

88 .373.373 1.8641.864 0.1360.13699 .337.337 1.8161.816 0.1840.184

1010 .308.308 1.7771.777 0.2230.223

1212 .266.266 1.7161.716 0.2840.284


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Process aerage )Process aerage ) = 12= 12ouncesounces

erage range Rerage range R = .25= .25

Sample size nSample size n = 5= 5


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UCLUCL)) E ) G E ) G 22RR

= 12 # (.577)(.25)= 12 # (.577)(.25)

= 12 # .144= 12 # .144

= 12.144= 12.144 ouncesounces




?rom?rom'e S6.1'e S6.1


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UCLUCL)) E ) G E ) G 22RR

= 12 # (.577)(.25)= 12 # (.577)(.25)

= 12 # .144= 12 # .144


LCLLCL)) E ) * E ) * 22RR

= 12 - .144= 12 - .144





UCL = 12.144UCL = 12.144

$e& = 12$e& = 12

LCL = 11.857LCL = 11.857


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R C$artR C$art

'ype of aria&les control c$art'ype of aria&les control c$art

S$ows sample ranges oer timeS$ows sample ranges oer time

>ifference &etween smallest and>ifference &etween smallest andlargest alues in samplelargest alues in sample

Monitors process aria&ilityMonitors process aria&ility

-ndependent from process mean-ndependent from process mean


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?or R*C$arts?or R*C$arts

(ower control limit(ower control limit (LCL(LCLRR))E >E >33RR

+pper control limit+pper control limit (UCL(UCLRR))E >E >44RR

w$erew$ere

RR EE aerage range of t$eaerage range of t$esamplessamples

>>33and >and >44 EE control c$art factorscontrol c$art factors

from 'a&le S654from 'a&le S654


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UCLUCLRR E >E >44RR

= (2.115)(5.3)= (2.115)(5.3)

= 11.2= 11.2poundspounds

LCLLCLRR E >E >33RR

= (0)(5.3)= (0)(5.3)

= 0= 0poundspounds

erage range Rerage range R = 5.3= 5.3poundspounds


?rom?rom 'e S6.1'e S6.1>>44= 2.115*= 2.115* >>33= 0= 0

UCL = 11.2UCL = 11.2

$e& = 5.3$e& = 5.3

LCL = 0LCL = 0


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Mean and Range C$artsMean and Range C$arts

"a#"a#

'$ese'$esesamplingsamplingdistri&utionsdistri&utionsresult in t$eresult in t$e

c$arts &elowc$arts &elow

"Sampling mean is"Sampling mean iss$ifting upward &uts$ifting upward &utrange is consistent#range is consistent#

R*c$artR*c$art"R*c$art does not"R*c$art does notdetect c$ange indetect c$ange inmean#mean#

UCLUCL

LCLLCL


)*c$art)*c$art")*c$art detects")*c$art detectss$ift in centrals$ift in centraltendency#tendency#

UCLUCL

LCLLCL


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Mean and Range C$artsMean and Range C$arts

R*c$artR*c$art"R*c$art detects"R*c$art detectsincrease inincrease indispersion#dispersion#

UCLUCL

LCLLCL


""

'$ese'$esesamplingsamplingdistri&utionsdistri&utionsresult in t$eresult in t$e

c$arts &elowc$arts &elow

"Sampling mean"Sampling meanis constant &utis constant &utdispersion isdispersion isincreasing#increasing#

)*c$art)*c$art")*c$art does not")*c$art does notdetect t$e increasedetect t$e increasein dispersion#in dispersion#

UCLUCL

LCLLCL


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Steps -n Creating ControlSteps -n Creating Control

C$artsC$arts4545 'a.e samples from t$e population and'a.e samples from t$e population and

compute t$e appropriate sample statisticcompute t$e appropriate sample statistic

7575 +se t$e sample statistic to calculate control+se t$e sample statistic to calculate controllimits and draw t$e control c$artlimits and draw t$e control c$art

8585 Plot sample results on t$e control c$art andPlot sample results on t$e control c$art anddetermine t$e state of t$e process "in or out ofdetermine t$e state of t$e process "in or out ofcontrol#control#

:5:5 -nestigate possi&le assigna&le causes and-nestigate possi&le assigna&le causes andta.e any indicated actionsta.e any indicated actions

;5;5 Continue sampling from t$e process and resetContinue sampling from t$e process and resett$e control limits w$en necessaryt$e control limits w$en necessary


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Manual and utomatedManual and utomatedControl C$artsControl C$arts


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Control C$arts for ttri&utesControl C$arts for ttri&utes

?or aria&les t$at are categorical?or aria&les t$at are categorical

Bood/&ad, yes/no,Bood/&ad, yes/no,

accepta&le/unaccepta&leaccepta&le/unaccepta&le Measurement is typically countingMeasurement is typically counting

defectiesdefecties

C$arts may measureC$arts may measurePercent defectie "p*c$art#Percent defectie "p*c$art#

=um&er of defects "c*c$art#=um&er of defects "c*c$art#


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Control (imits for p*C$artsControl (imits for p*C$arts

Population will &e a &inomial distri&ution,Population will &e a &inomial distri&ution,&ut applying t$e Central (imit '$eorem&ut applying t$e Central (imit '$eorem

allows us to assume a normal distri&utionallows us to assume a normal distri&ution

for t$e sample statisticsfor t$e sample statistics

UCLUCLppE p G zE p G zppJJ

LCLLCL

ppE p * zE p * z

pp

JJ

w$erew$ere pp EE mean fraction defectie in t$e samplemean fraction defectie in t$e sample

zz EE num&er of standard deiationsnum&er of standard deiations

pp EE standard deiation of t$e sampling distandard deiation of t$e sampling di

nn EE sample sizesample size

JJ

pp(1 -(1 -pp))

nnppEEJJ


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p*C$art for >ata ntryp*C$art for >ata ntrySampleSample =um&er=um&er ?raction?raction SampleSample =um&er=um&er ?raction?raction=um&er=um&er of rrorsof rrors >efectie>efectie =um&er=um&er of rrorsof rrors >efectie>efectie

11 66 .06.06 1111 66 .06.06

22 55 .05.05 1212 11 .01.01

33 00 .00.00 1313 88 .08.08

44 11 .01.01 1414 77 .07.0755 44 .04.04 1515 55 .05.05

66 22 .02.02 1616 44 .04.04

77 55 .05.05 1717 1111 .11.11

88 33 .03.03 1818 33 .03.03

99 33 .03.03 1919 00 .00.001010 22 .02.02 2020 44 .04.04

'otal'otal = 80= 80

(.04)(1 - .04)(.04)(1 - .04)

100100ppEE = .02= .02JJ

pp = = .04= = .048080

(100)(20)(100)(20)


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544544 5454

5!5!

5


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544544 5454

5!5!

5


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Control (imits for c*C$artsControl (imits for c*C$arts

Population will &e a Poisson distri&ution,Population will &e a Poisson distri&ution,&ut applying t$e Central (imit '$eorem&ut applying t$e Central (imit '$eorem

allows us to assume a normal distri&utionallows us to assume a normal distri&ution

for t$e sample statisticsfor t$e sample statistics

w$erew$ere cc EE mean num&er defectie in t$e samean num&er defectie in t$e sa

UCLUCLccE c GE c G 33 cc LCLLCLccE cE c --33 cc


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c*C$art for Ca& Companyc*C$art for Ca& Company

cc = 54= 54complaintscomplaints/9/9daysdays = 6= 6 complaintscomplaints//dayday

F

4

F

7

F

8

F

:

F

;

F

6

F

F

ay>ay

=u

m&erdefecti/e

=um&erdefecti/e4:4:

4747

44


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Managerial -ssues andManagerial -ssues and

Control C$artsControl C$arts

Select points in t$e processes t$atSelect points in t$e processes t$atneed SPCneed SPC

>etermine t$e appropriate c$arting>etermine t$e appropriate c$arting

tec$niuetec$niue

Set clear policies and proceduresSet clear policies and procedures

'$ree ma1or management decisions3'$ree ma1or management decisions3


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2$ic$ Control C$art to +se2$ic$ Control C$art to +se

+sing an )*c$art and R*c$art3+sing an )*c$art and R*c$art3

O&serations are aria&lesO&serations are aria&les

CollectCollect 20 - 2520 - 25samples of nsamples of n = 4= 4, or n, or n ==55, or more, eac$ from a sta&le process, or more, eac$ from a sta&le processand compute t$e mean for t$e )*c$artand compute t$e mean for t$e )*c$art

and range for t$e R*c$artand range for t$e R*c$art 'rac. samples of n o&serations eac$'rac. samples of n o&serations eac$

%aria&les >ata%aria&les >ata


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+sing t$e p*c$art3+sing t$e p*c$art3

O&serations are attri&utes t$at canO&serations are attri&utes t$at can&e categorized in two states&e categorized in two states

2e deal wit$ fraction, proportion, or2e deal wit$ fraction, proportion, orpercent defectiespercent defecties

Hae seeral samples, eac$ wit$Hae seeral samples, eac$ wit$many o&serationsmany o&serations

ttri&ute >atattri&ute >ata


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+sing a c*C$art3+sing a c*C$art3

O&serations are attri&utes w$oseO&serations are attri&utes w$osedefects per unit of output can &edefects per unit of output can &ecountedcounted

'$e num&er counted is a small part of'$e num&er counted is a small part oft$e possi&le occurrencest$e possi&le occurrences

>efects suc$ as num&er of &lemis$es>efects suc$ as num&er of &lemis$eson a des., num&er of typos in a pageon a des., num&er of typos in a pageof te)t, flaws in a &olt of clot$of te)t, flaws in a &olt of clot$

ttri&ute >atattri&ute >ata


47/74


Patterns in Control C$artsPatterns in Control C$arts

=ormal &e$aior5=ormal &e$aior5

Process is @in control5AProcess is @in control5A

+pper control limit+pper control limit

'arget'arget

(ower control limit(ower control limit



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'arget'arget



One plot out a&oe "orOne plot out a&oe "or&elow#5 -nestigate for&elow#5 -nestigate forcause5 Process is @outcause5 Process is @out

of control5Aof control5A



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'arget'arget



'rends in eit$er'rends in eit$erdirection, ; plots5direction, ; plots5-nestigate for cause of-nestigate for cause of

progressie c$ange5progressie c$ange5



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'arget'arget



'wo plots ery near'wo plots ery nearlower "or upper#lower "or upper#control5 -nestigate forcontrol5 -nestigate for

cause5cause5



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'arget'arget



Run of ; a&oe "orRun of ; a&oe "or&elow# central line5&elow# central line5-nestigate for cause5-nestigate for cause5Figure S6.7Figure S6.7


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'arget'arget



rratic &e$aior5rratic &e$aior5-nestigate5-nestigate5



53/74


Process Capa&ilityProcess Capa&ility

'$e natural ariation of a process'$e natural ariation of a processs$ould &e small enoug$ to produces$ould &e small enoug$ to produce

products t$at meet t$e standardsproducts t$at meet t$e standardsreuiredreuired

process in statistical control does not process in statistical control does notnecessarily meet t$e designnecessarily meet t$e designspecificationsspecifications

Process capa&ility is a measure of t$eProcess capa&ility is a measure of t$erelations$ip &etween t$e naturalrelations$ip &etween t$e naturalariation of t$e process and t$e designariation of t$e process and t$e designspecificationsspecifications


54/74


Process Capa&ility RatioProcess Capa&ility Ratio

CC++EE+pper Specification * (ower Specification+pper Specification * (ower Specification

66

capa&le process must $ae a capa&le process must $ae a CC++of atof at

leastleast 1.01.0

>oes not loo. at $ow well t$e process>oes not loo. at $ow well t$e process

is centered in t$e specification rangeis centered in t$e specification range Often a target alue ofOften a target alue of CC++= 1.33= 1.33 is usedis used

to allow for off*center processesto allow for off*center processes

Si) Sigma uality reuires aSi) Sigma uality reuires aCC++= 2.0= 2.0


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66

-nsurance claims process-nsurance claims process

Process mean )Process mean ) = 210.0= 210.0minutesminutes

Process standard deiationProcess standard deiation

= .516= .516minutesminutes>esign specification>esign specification = 210 3= 210 3minutesminutes


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66





= = 1.938= = 1.938213 - 207213 - 207

6(.516)6(.516)


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66





= = 1.938= = 1.938213 - 207213 - 207

6(.516)6(.516)Process is

capa&le


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Process Capa&ility -nde)Process Capa&ility -nde)

capa&le process must $ae a capa&le process must $ae a CC+,+,of atof at

leastleast 1.01.0 capa&le process is not necessarily in t$e capa&le process is not necessarily in t$e

center of t$e specification, &ut it falls wit$incenter of t$e specification, &ut it falls wit$int$e specification limit at &ot$ e)tremest$e specification limit at &ot$ e)tremes

CC+,+,E minimum of ,E minimum of ,

+pper+pperSpecification * )Specification * )

(imit(imit

(ower(ower) *) * SpecificationSpecification

(imit(imit


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=ew Cutting Mac$ine=ew Cutting Mac$ine

=ew process mean )=ew process mean ) = .250 i&e"= .250 i&e"

Process standard deiationProcess standard deiation = .0005 i&e"= .0005 i&e"

+pper Specification (imit+pper Specification (imit = .251 i&e"= .251 i&e"(ower Specification (imit(ower Specification (imit= .249 i&e"= .249 i&e"


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CC+,+,E minimum of ,E minimum of ,(.251) - .250(.251) - .250

(3).0005(3).0005


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CC+,+,= = 0.67= = 0.67.001.001

.0015.0015

=ew mac$ine is=O' capa&le

CC+,+,E minimum of ,E minimum of ,(.251) - .250(.251) - .250

(3).0005(3).0005

.250 - (.249).250 - (.249)

(3).0005(3).0005

9ot$ calculations result in9ot$ calculations result in


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-nterpreting-nterpreting CC+,+,

C+,= negatie num&er

C+,= zero

C+,= &etween0 and1

C+,= 1

C+, 1



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?orm of uality testing used for?orm of uality testing used forincoming materials or finis$ed goodsincoming materials or finis$ed goods

'a.e samples at random from a lot'a.e samples at random from a lot"s$ipment# of items"s$ipment# of items

-nspect eac$ of t$e items in t$e sample-nspect eac$ of t$e items in t$e sample

>ecide w$et$er to re1ect t$e w$ole lot>ecide w$et$er to re1ect t$e w$ole lot

&ased on t$e inspection results&ased on t$e inspection results

Only screens lotsK does not drieOnly screens lotsK does not drieuality improement effortsuality improement efforts


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?orm of uality testing used for?orm of uality testing used forincoming materials or finis$ed goodsincoming materials or finis$ed goods

'a.e samples at random from a lot'a.e samples at random from a lot"s$ipment# of items"s$ipment# of items

-nspect eac$ of t$e items in t$e sample-nspect eac$ of t$e items in t$e sample

>ecide w$et$er to re1ect t$e w$ole lot>ecide w$et$er to re1ect t$e w$ole lot

&ased on t$e inspection results&ased on t$e inspection results

Only screens lotsK does not drieOnly screens lotsK does not drieuality improement effortsuality improement efforts

Re1ected lots can &e3 Returned to t$e

supplier

Culled fordefecties"4L inspection#


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Operating C$aracteristicOperating C$aracteristic

CureCure S$ows $ow well a sampling planS$ows $ow well a sampling plan

discriminates &etween good anddiscriminates &etween good and&ad lots "s$ipments#&ad lots "s$ipments#

S$ows t$e relations$ip &etweenS$ows t$e relations$ip &etweent$e pro&a&ility of accepting a lott$e pro&a&ility of accepting a lot

and its uality leeland its uality leel


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Return w$oles$ipment

'$e @PerfectA OC Cure'$e @PerfectA OC Cure

L >efectie in (otL >efectie in (ot

P",cc

ept2$oleS$

ipment#

P",cc

ept2$oleS$

ipment#

44

;;

;;

7;7;

F F F F F F F F F F F

44 77 88 :: ;; 66


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n OC Curen OC Cure

Pro&a&ilityPro&a&ilityofof

cceptancecceptance

PercentPercentdefectiedefectie

F F F F F F F F F

44 77 88 :: ;; 66

('P>('P>0(0(

9ad lots9ad lots-ndifference-ndifference

zonezoneBoodBoodlotslots



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0( and ('P>0( and ('P>

ccepta&le 0uality (eel "0(#ccepta&le 0uality (eel "0(#

Poorest leel of uality we arePoorest leel of uality we arewilling to acceptwilling to accept

(ot 'olerance Percent >efectie(ot 'olerance Percent >efectie"('P>#"('P>#

0uality leel we consider &ad0uality leel we consider &ad

Consumer "&uyer# does not want toConsumer "&uyer# does not want toaccept lots wit$ more defects t$anaccept lots wit$ more defects t$an('P>('P>


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ProducerIs and ConsumerIsProducerIs and ConsumerIs

Ris.sRis.s ProducerNs ris.ProducerNs ris. (())

Pro&a&ility of re1ecting a good lotPro&a&ility of re1ecting a good lot

Pro&a&ility of re1ecting a lot w$en t$ePro&a&ility of re1ecting a lot w$en t$efraction defectie is at or a&oe t$efraction defectie is at or a&oe t$e

0(0(

ConsumerNs ris.ConsumerNs ris. ((

))Pro&a&ility of accepting a &ad lotPro&a&ility of accepting a &ad lot

Pro&a&ility of accepting a lot w$enPro&a&ility of accepting a lot w$enfraction defectie is &elow t$e ('P>fraction defectie is &elow t$e ('P>


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OC Cures for >ifferentOC Cures for >ifferent

Sampling PlansSampling Plans

nn= 50*= 50* cc= 1= 1

nn= 100*= 100* cc= 2= 2


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erage Outgoing 0ualityerage Outgoing 0uality

w$erew$ere

PPdd E true percent defectie of t$e lotE true percent defectie of t$e lot

PPaa

E pro&a&ility of accepting t$e lotE pro&a&ility of accepting t$e lot

== E num&er of items in t$e lotE num&er of items in t$e lot

nn E num&er of items in t$e sampleE num&er of items in t$e sample

= =((PPdd)()(PPaa)()(= * n= * n))

==


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erage Outgoing 0ualityerage Outgoing 0uality

4545 -f a sampling plan replaces all defecties-f a sampling plan replaces all defecties

7575 -f we .now t$e incoming percent-f we .now t$e incoming percentdefectie for t$e lotdefectie for t$e lot

2e can compute t$e aerage outgoing2e can compute t$e aerage outgoinguality "O0# in percent defectieuality "O0# in percent defectie

'$e ma)imum O0 is t$e $ig$est percent'$e ma)imum O0 is t$e $ig$est percentdefectie or t$e lowest aerage ualitydefectie or t$e lowest aerage ualityand is called t$e aerage outgoing ualityand is called t$e aerage outgoing ualityleel "O0(#leel "O0(#


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utomated -nspectionutomated -nspection

ModernModerntec$nologiestec$nologiesallow irtuallyallow irtually4L4Linspection atinspection atminimal costsminimal costs

=ot suita&le=ot suita&lefor allfor allsituationssituations


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SPC and Process %aria&ilitySPC and Process %aria&ility

"a#"a#cceptancecceptancesampling "Somesampling "Some

&ad units accepted#&ad units accepted#

"" Statistical processStatistical processcontrol "eep t$econtrol "eep t$e

process in control#process in control#

"c#"c# CC+,+,11">esign">esign

a process t$ata process t$atis in control#is in control#

(ower(owerspecificationspecification

limitlimit

+pper+pperspecificationspecification

limitlimit

Process meanProcess mean

Documents

Supplement 6 Heizer Operations management