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
7/17/2019 Supplement 6 Heizer Operations management
2/74
2008 Prentice Hall, Inc. S6 2
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
7/17/2019 Supplement 6 Heizer Operations management
3/74
2008 Prentice Hall, Inc. S6 3
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
7/17/2019 Supplement 6 Heizer Operations management
4/74
2008 Prentice Hall, Inc. S6 4
(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
7/17/2019 Supplement 6 Heizer Operations management
5/74
2008 Prentice Hall, Inc. S6 5
(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
7/17/2019 Supplement 6 Heizer Operations management
6/74
2008 Prentice Hall, Inc. S6 6
%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#
7/17/2019 Supplement 6 Heizer Operations management
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
7/17/2019 Supplement 6 Heizer Operations management
8/74 2008 Prentice Hall, Inc. S6 8
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
7/17/2019 Supplement 6 Heizer Operations management
9/74 2008 Prentice Hall, Inc. S6 9
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$ese
represents onerepresents onesample of fiesample of fie
&o)es of cereal&o)es of cereal
Figure S6.1Figure S6.1
7/17/2019 Supplement 6 Heizer Operations management
10/74 2008 Prentice Hall, Inc. S6 10
SamplesSamples
'o measure t$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$ese steps
""fter enoug$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$tFigure S6.1Figure S6.1
7/17/2019 Supplement 6 Heizer Operations management
11/74 2008 Prentice Hall, Inc. S6 11
SamplesSamples
'o measure t$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$ese steps
"c#"c# '$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$ape
?reCuency
?reCuency
Figure S6.1Figure S6.1
7/17/2019 Supplement 6 Heizer Operations management
12/74 2008 Prentice Hall, Inc. S6 12
SamplesSamples
'o measure t$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$ese steps
"d#"d# -f only natural-f only naturalcauses ofcauses ofariation areariation arepresent, t$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$t'im
e'im
e?reCuency
?reCuency PredictionPrediction
Figure S6.1Figure S6.1
7/17/2019 Supplement 6 Heizer Operations management
13/74 2008 Prentice Hall, Inc. S6 13
SamplesSamples
'o measure t$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$ese steps
"e#"e# -f assigna&le-f assigna&lecauses arecauses arepresent, t$epresent, t$eprocess output isprocess output is
not sta&le oernot sta&le oertime and is nottime and is notpredica&lepredica&le
2eig$t2eig$t'im
e'im
e?reCuency
?reCuency PredictionPrediction
????????
????
????????
??????????????????
Figure S6.1Figure S6.1
7/17/2019 Supplement 6 Heizer Operations management
14/74 2008 Prentice Hall, Inc. S6 14
Control C$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
7/17/2019 Supplement 6 Heizer Operations management
15/74 2008 Prentice Hall, Inc. S6 15
Process ControlProcess Control
Figure S6.2Figure S6.2
?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
7/17/2019 Supplement 6 Heizer Operations management
16/74 2008 Prentice Hall, Inc. S6 16
'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
7/17/2019 Supplement 6 Heizer Operations management
17/74 2008 Prentice Hall, Inc. S6 17
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
7/17/2019 Supplement 6 Heizer Operations management
18/74 2008 Prentice Hall, Inc. S6 18
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))
Figure S6.3Figure S6.3
7/17/2019 Supplement 6 Heizer Operations management
19/74
2008 Prentice Hall, Inc. S6 19
Sampling >istri&utionSampling >istri&ution
) E) E
"mean#"mean#
SamplingSamplingdistri&utiondistri&utionof meansof means
ProcessProcessdistri&utiondistri&utionof meansof means
Figure S6.4Figure S6.4
7/17/2019 Supplement 6 Heizer Operations management
20/74
2008 Prentice Hall, Inc. S6 20
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$er
7/17/2019 Supplement 6 Heizer Operations management
21/74
2008 Prentice Hall, Inc. S6 21
Setting C$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$e
sample meanssample meansEE
/ n/ n
EE population standardpopulation standard
7/17/2019 Supplement 6 Heizer Operations management
22/74
2008 Prentice Hall, Inc. S6 22
Setting Control (imitsSetting Control (imits
Hour 4Hour 4
SampleSample 2eig$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 !"
7/17/2019 Supplement 6 Heizer Operations management
23/74
2008 Prentice Hall, Inc. S6 23
17 = UCL17 = UCL
15 = LCL15 = LCL
16 = $e&16 = $e&
Setting Control (imitsSetting Control (imits
Control C$artControl C$artfor sample offor sample of! &o)es! &o)es
Sample num&erSample num&er
FF FF FF FF FF FF FF FF FF FF FF FF
44 77 88 :: ;; 66
7/17/2019 Supplement 6 Heizer Operations management
24/74
2008 Prentice Hall, Inc. S6 24
Setting C$art (imitsSetting C$art (imits
?or )*C$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$e sample means
7/17/2019 Supplement 6 Heizer Operations management
25/74
2008 Prentice Hall, Inc. S6 25
Control C$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
7/17/2019 Supplement 6 Heizer Operations management
26/74
2008 Prentice Hall, Inc. S6 26
Setting Control (imitsSetting Control (imits
Process aerage )Process aerage ) = 12= 12ouncesounces
erage range Rerage range R = .25= .25
Sample size nSample size n = 5= 5
7/17/2019 Supplement 6 Heizer Operations management
27/74
2008 Prentice Hall, Inc. S6 27
Setting Control (imitsSetting Control (imits
UCLUCL)) E ) G E ) G 22RR
= 12 # (.577)(.25)= 12 # (.577)(.25)
= 12 # .144= 12 # .144
= 12.144= 12.144 ouncesounces
Process aerage )Process aerage ) = 12= 12ouncesounces
erage range Rerage range R = .25= .25
Sample size nSample size n = 5= 5
?rom?rom'e S6.1'e S6.1
7/17/2019 Supplement 6 Heizer Operations management
28/74
2008 Prentice Hall, Inc. S6 28
Setting Control (imitsSetting Control (imits
UCLUCL)) E ) G E ) G 22RR
= 12 # (.577)(.25)= 12 # (.577)(.25)
= 12 # .144= 12 # .144
= 12.144= 12.144 ouncesounces
LCLLCL)) E ) * E ) * 22RR
= 12 - .144= 12 - .144
= 11.857= 11.857 ouncesounces
Process aerage )Process aerage ) = 12= 12ouncesounces
erage range Rerage range R = .25= .25
Sample size nSample size n = 5= 5
UCL = 12.144UCL = 12.144
$e& = 12$e& = 12
LCL = 11.857LCL = 11.857
7/17/2019 Supplement 6 Heizer Operations management
29/74
2008 Prentice Hall, Inc. S6 29
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
7/17/2019 Supplement 6 Heizer Operations management
30/74
2008 Prentice Hall, Inc. S6 30
Setting C$art (imitsSetting C$art (imits
?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
7/17/2019 Supplement 6 Heizer Operations management
31/74
2008 Prentice Hall, Inc. S6 31
Setting Control (imitsSetting Control (imits
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
Sample size nSample size n = 5= 5
?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
7/17/2019 Supplement 6 Heizer Operations management
32/74
2008 Prentice Hall, Inc. S6 32
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
Figure S6.5Figure S6.5
)*c$art)*c$art")*c$art detects")*c$art detectss$ift in centrals$ift in centraltendency#tendency#
UCLUCL
LCLLCL
7/17/2019 Supplement 6 Heizer Operations management
33/74
2008 Prentice Hall, Inc. S6 33
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
Figure S6.5Figure S6.5
""
'$ese'$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
7/17/2019 Supplement 6 Heizer Operations management
34/74
2008 Prentice Hall, Inc. S6 34
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
7/17/2019 Supplement 6 Heizer Operations management
35/74
2008 Prentice Hall, Inc. S6 35
Manual and utomatedManual and utomatedControl C$artsControl C$arts
7/17/2019 Supplement 6 Heizer Operations management
36/74
2008 Prentice Hall, Inc. S6 36
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#
7/17/2019 Supplement 6 Heizer Operations management
37/74
2008 Prentice Hall, Inc. S6 37
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
7/17/2019 Supplement 6 Heizer Operations management
38/74
2008 Prentice Hall, Inc. S6 38
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)
7/17/2019 Supplement 6 Heizer Operations management
39/74
2008 Prentice Hall, Inc. S6 39
544544 5454
5!5!
5
7/17/2019 Supplement 6 Heizer Operations management
40/74
2008 Prentice Hall, Inc. S6 40
544544 5454
5!5!
5
7/17/2019 Supplement 6 Heizer Operations management
41/74
2008 Prentice Hall, Inc. S6 41
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
7/17/2019 Supplement 6 Heizer Operations management
42/74
2008 Prentice Hall, Inc. S6 42
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
7/17/2019 Supplement 6 Heizer Operations management
43/74
2008 Prentice Hall, Inc. S6 43
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
7/17/2019 Supplement 6 Heizer Operations management
44/74
2008 Prentice Hall, Inc. S6 44
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
7/17/2019 Supplement 6 Heizer Operations management
45/74
2008 Prentice Hall, Inc. S6 45
2$ic$ Control C$art to +se2$ic$ Control C$art to +se
+sing t$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$many o&serationsmany o&serations
ttri&ute >atattri&ute >ata
7/17/2019 Supplement 6 Heizer Operations management
46/74
2008 Prentice Hall, Inc. S6 46
2$ic$ Control C$art to +se2$ic$ Control C$art to +se
+sing a c*C$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
7/17/2019 Supplement 6 Heizer Operations management
47/74
2008 Prentice Hall, Inc. S6 47
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
Figure S6.7Figure S6.7
7/17/2019 Supplement 6 Heizer Operations management
48/74
2008 Prentice Hall, Inc. S6 48
+pper control limit+pper control limit
'arget'arget
(ower control limit(ower control limit
Patterns in Control C$artsPatterns in Control C$arts
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
Figure S6.7Figure S6.7
7/17/2019 Supplement 6 Heizer Operations management
49/74
2008 Prentice Hall, Inc. S6 49
+pper control limit+pper control limit
'arget'arget
(ower control limit(ower control limit
Patterns in Control C$artsPatterns in Control C$arts
'rends in eit$er'rends in eit$erdirection, ; plots5direction, ; plots5-nestigate for cause of-nestigate for cause of
progressie c$ange5progressie c$ange5
Figure S6.7Figure S6.7
7/17/2019 Supplement 6 Heizer Operations management
50/74
2008 Prentice Hall, Inc. S6 50
+pper control limit+pper control limit
'arget'arget
(ower control limit(ower control limit
Patterns in Control C$artsPatterns in Control C$arts
'wo plots ery near'wo plots ery nearlower "or upper#lower "or upper#control5 -nestigate forcontrol5 -nestigate for
cause5cause5
Figure S6.7Figure S6.7
7/17/2019 Supplement 6 Heizer Operations management
51/74
2008 Prentice Hall, Inc. S6 51
+pper control limit+pper control limit
'arget'arget
(ower control limit(ower control limit
Patterns in Control C$artsPatterns in Control C$arts
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
7/17/2019 Supplement 6 Heizer Operations management
52/74
2008 Prentice Hall, Inc. S6 52
+pper control limit+pper control limit
'arget'arget
(ower control limit(ower control limit
Patterns in Control C$artsPatterns in Control C$arts
rratic &e$aior5rratic &e$aior5-nestigate5-nestigate5
Figure S6.7Figure S6.7
7/17/2019 Supplement 6 Heizer Operations management
53/74
2008 Prentice Hall, Inc. S6 53
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
7/17/2019 Supplement 6 Heizer Operations management
54/74
2008 Prentice Hall, Inc. S6 54
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
7/17/2019 Supplement 6 Heizer Operations management
55/74
2008 Prentice Hall, Inc. S6 55
Process Capa&ility RatioProcess Capa&ility Ratio
CC++EE+pper Specification * (ower Specification+pper Specification * (ower Specification
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
7/17/2019 Supplement 6 Heizer Operations management
56/74
2008 Prentice Hall, Inc. S6 56
Process Capa&ility RatioProcess Capa&ility Ratio
CC++EE+pper Specification * (ower Specification+pper Specification * (ower Specification
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
= = 1.938= = 1.938213 - 207213 - 207
6(.516)6(.516)
7/17/2019 Supplement 6 Heizer Operations management
57/74
2008 Prentice Hall, Inc. S6 57
Process Capa&ility RatioProcess Capa&ility Ratio
CC++EE+pper Specification * (ower Specification+pper Specification * (ower Specification
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
= = 1.938= = 1.938213 - 207213 - 207
6(.516)6(.516)Process is
capa&le
7/17/2019 Supplement 6 Heizer Operations management
58/74
2008 Prentice Hall, Inc. S6 58
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
7/17/2019 Supplement 6 Heizer Operations management
59/74
2008 Prentice Hall, Inc. S6 59
Process Capa&ility -nde)Process Capa&ility -nde)
=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"
7/17/2019 Supplement 6 Heizer Operations management
60/74
2008 Prentice Hall, Inc. S6 60
Process Capa&ility -nde)Process Capa&ility -nde)
=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"
CC+,+,E minimum of ,E minimum of ,(.251) - .250(.251) - .250
(3).0005(3).0005
7/17/2019 Supplement 6 Heizer Operations management
61/74
2008 Prentice Hall, Inc. S6 61
Process Capa&ility -nde)Process Capa&ility -nde)
=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"
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
7/17/2019 Supplement 6 Heizer Operations management
62/74
2008 Prentice Hall, Inc. S6 62
-nterpreting-nterpreting CC+,+,
C+,= negatie num&er
C+,= zero
C+,= &etween0 and1
C+,= 1
C+, 1
Figure S6.8Figure S6.8
7/17/2019 Supplement 6 Heizer Operations management
63/74
2008 Prentice Hall, Inc. S6 63
cceptance Samplingcceptance Sampling
?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
7/17/2019 Supplement 6 Heizer Operations management
64/74
2008 Prentice Hall, Inc. S6 64
cceptance Samplingcceptance Sampling
?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$e
supplier
Culled fordefecties"4L inspection#
7/17/2019 Supplement 6 Heizer Operations management
65/74
2008 Prentice Hall, Inc. S6 65
Operating C$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$e pro&a&ility of accepting a lot
and its uality leeland its uality leel
7/17/2019 Supplement 6 Heizer Operations management
66/74
2008 Prentice Hall, Inc. S6 66
Return w$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
7/17/2019 Supplement 6 Heizer Operations management
67/74
2008 Prentice Hall, Inc. S6 67
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
Figure S6.9Figure S6.9
7/17/2019 Supplement 6 Heizer Operations management
68/74
2008 Prentice Hall, Inc. S6 68
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$an('P>('P>
7/17/2019 Supplement 6 Heizer Operations management
69/74
2008 Prentice Hall, Inc. S6 69
ProducerIs and ConsumerIsProducerIs and ConsumerIs
Ris.sRis.s ProducerNs ris.ProducerNs ris. (())
Pro&a&ility of re1ecting a good lotPro&a&ility of re1ecting a good lot
Pro&a&ility of re1ecting a lot w$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$e ('P>
7/17/2019 Supplement 6 Heizer Operations management
70/74
2008 Prentice Hall, Inc. S6 70
OC Cures for >ifferentOC Cures for >ifferent
Sampling PlansSampling Plans
nn= 50*= 50* cc= 1= 1
nn= 100*= 100* cc= 2= 2
7/17/2019 Supplement 6 Heizer Operations management
71/74
2008 Prentice Hall, Inc. S6 71
erage Outgoing 0ualityerage Outgoing 0uality
w$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$e sample
= =((PPdd)()(PPaa)()(= * n= * n))
==
7/17/2019 Supplement 6 Heizer Operations management
72/74
2008 Prentice Hall, Inc. S6 72
erage Outgoing 0ualityerage Outgoing 0uality
4545 -f a sampling plan replaces all defecties-f a sampling plan replaces all defecties
7575 -f we .now t$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(#
7/17/2019 Supplement 6 Heizer Operations management
73/74
2008 Prentice Hall, Inc. S6 73
utomated -nspectionutomated -nspection
ModernModerntec$nologiestec$nologiesallow irtuallyallow irtually4L4Linspection atinspection atminimal costsminimal costs
=ot suita&le=ot suita&lefor allfor allsituationssituations
7/17/2019 Supplement 6 Heizer Operations management
74/74
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