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Statistical Process Control Statistical Process Control
Operations Management - 5th Edition
Operations Management - 5th Edition
Chapter 4Chapter 4
Roberta Russell & Bernard W. Taylor, IIIRoberta Russell & Bernard W. Taylor, III
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Lecture OutlineLecture Outline
Basics of Statistical Process ControlBasics of Statistical Process Control
Control ChartsControl Charts
Control Charts for AttributesControl Charts for Attributes
Control Charts for VariablesControl Charts for Variables
Control Chart PatternsControl Chart Patterns SPC with ExcelSPC with Excel
Process CapabilityProcess Capability
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Basics of StatisticalBasics of Statistical
Process ControlProcess Control
Statistical Process Control (SPC)Statistical Process Control (SPC) monitoring production process tomonitoring production process to
detect and prevent poor qualitydetect and prevent poor quality SampleSample
subset of items produced to use for subset of items produced to use for inspectioninspection
Control ChartsControl Charts process is within statistical controlprocess is within statistical control
limitslimits
UCLUCL
LCLLCL
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VariabilityVariability
RandomRandom
common causescommon causes inherent in a processinherent in a process
can be eliminated onlycan be eliminated only
through improvements inthrough improvements in
the systemthe system
NonNon--RandomRandom
special causesspecial causes due to identifiable factorsdue to identifiable factors
can be modified throughcan be modified through
operator or managementoperator or management
actionaction
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SPC in TQMSPC in TQM
SPCSPC
tool for identifying problems and maketool for identifying problems and makeimprovementsimprovements
contributes to the TQM goal of continuouscontributes to the TQM goal of continuous
improvementsimprovements
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Quality MeasuresQuality Measures
AttributeAttribute
a product characteristic that can be evaluated with aa product characteristic that can be evaluated with adiscrete responsediscrete response
goodgood ± ± bad; yesbad; yes -- nono
VariableVariable
a product characteristic that is continuous and can bea product characteristic that is continuous and can bemeasuredmeasured
weightweight -- lengthlength
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Nature of defect is different in servicesNature of defect is different in services Service defect is a failure to meet customer Service defect is a failure to meet customer
requirementsrequirements
Monitor times, customer satisfactionMonitor times, customer satisfaction
Applying SPC toApplying SPC to
ServiceService
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Applying SPC toApplying SPC to
Service (cont.)Service (cont.)
HospitalsHospitals timeliness and quickness of care, staff responses to requests, accuracy of timeliness and quickness of care, staff responses to requests, accuracy of
lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittancelab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittanceand checkoutsand checkouts
Grocery StoresGrocery Stores waiting time to check out, frequency of outwaiting time to check out, frequency of out--of of--stock items, quality of foodstock items, quality of food
items, cleanliness, customer complaints, checkout register errorsitems, cleanliness, customer complaints, checkout register errors
Airlines Airlines flight delays, lost luggage and luggage handling, waiting time at ticketflight delays, lost luggage and luggage handling, waiting time at ticket
counters and checkcounters and check--in, agent and flight attendant courtesy, accurate flightin, agent and flight attendant courtesy, accurate flightinformation, passenger cabin cleanliness and maintenanceinformation, passenger cabin cleanliness and maintenance
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Applying SPC toApplying SPC to
Service (cont.)Service (cont.)
FastFast--Food RestaurantsFood Restaurants waiting time for service, customer complaints, cleanliness, foodwaiting time for service, customer complaints, cleanliness, food
quality, order accuracy, employee courtesyquality, order accuracy, employee courtesy
CatalogueCatalogue--Order CompaniesOrder Companies order accuracy, operator knowledge and courtesy, packaging,order accuracy, operator knowledge and courtesy, packaging,
delivery time, phone order waiting timedelivery time, phone order waiting time
Insurance CompaniesInsurance Companies billing accuracy, timeliness of claims processing, agentbilling accuracy, timeliness of claims processing, agent
availability and response timeavailability and response time
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Where to Use Control ChartsWhere to Use Control Charts
Process has a tendency to go out of controlProcess has a tendency to go out of control
Process is particularly harmful and costly if it goes out of Process is particularly harmful and costly if it goes out of
controlcontrol ExamplesExamples
at the beginning of a process because it is a waste of time andat the beginning of a process because it is a waste of time andmoney to begin production process with bad suppliesmoney to begin production process with bad supplies
before a costly or irreversible point, after which product is difficultbefore a costly or irreversible point, after which product is difficultto rework or correctto rework or correct
before and after assembly or painting operations that might cover before and after assembly or painting operations that might cover defectsdefects
before the outgoing final product or service is deliveredbefore the outgoing final product or service is delivered
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Control ChartsControl Charts
A graph that establishes A graph that establishescontrol limits of a processcontrol limits of a process
Control limitsControl limits upper and lower bands of aupper and lower bands of a
control chartcontrol chart
Types of chartsTypes of charts
Attributes Attributes pp--chartchart
cc--chartchart
VariablesVariables
range (Rrange (R--chart)chart)
mean (x bar mean (x bar ± ± chart)chart)
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Process ControlProcess Control
ChartChart
11 22 33 44 55 66 77 88 99 1010
Sample number Sample number
Upper Upper controlcontrol
limitlimit
ProcessProcessaverageaverage
Lower Lower
controlcontrollimitlimit
Out of controlOut of control
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Normal Distribution Normal Distribution
QQ=0=0 11WW 22WW 33WW--11WW--22WW--33WW
95%
99.74%
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A Process Is inA Process Is in
Control If «Control If «
1. « no sample points outside limits2. « most points near process average
3. « about equal number of points above
and below centerline
4. « points appear randomly distributed
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Control Charts for Control Charts for
AttributesAttributes
p-charts uses portion defective in a sample
c-charts
uses number of defects in an item
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p p--ChartChart
UCL = p + z W p
LCL = p - z W p
z = number of standard deviations from
process average
p = sample proportion defective; an estimate
of process averageW p = standard deviation of sample proportion
WW p p == p p(1(1 -- p p))
nn
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p p--Chart Exam pleChart Exam ple
20 samples of 100 pairs of jeans20 samples of 100 pairs of jeans
NUMBER OFNUMBER OF PROPORTIONPROPORTIONSAMPLESAMPLE DEFECTIVESDEFECTIVES DEFECTIVEDEFECTIVE
11 66 .06.06
22 00 .00.00
33 44 .04.04
:: :: ::
:: :: ::
2020 1818 .18.18
200200
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p p--Chart Exam ple (cont.)Chart Exam ple (cont.)
UCL = p + z = 0.10 + 3 p(1 - p)
n
0.10(1 - 0.10)
100
UCL = 0.190
LCL = 0.010
LCL = p - z = 0.10 - 3 p(1 - p)
n
0.10(1 - 0.10)
100
= 200 / 20(100) = 0.10total defectives
total sample observations p =
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0.020.02
0.040.04
0.060.06
0.080.08
0.100.10
0.120.12
0.140.14
0.160.16
0.180.18
0.200.20
P r o p o r t i o n d e
f e c t i v e
P r o p o r t i o n d e
f e c t i v e
Sample number Sample number
22 44 66 88 1010 1212 1414 1616 1818 2020
UCL = 0.190
LCL = 0.010
p = 0.10
p p--ChartChartExam pleExam ple(cont.)(cont.)
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cc--ChartChart
UCL = UCL = c c + + z z WWc c
LCL = LCL = c c -- z z WWc c
where
c = number of defects per sample
WWc c = = c c
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cc--Chart (cont.)Chart (cont.)Number of defects in 15 sample roomsNumber of defects in 15 sample rooms
1 121 12
2 82 8
3 163 16
: :: :
: :: :15 1515 15
190190
SAMPLESAMPLE
c c = = 12.67= = 12.67190190
1515
UCLUCL = = c c + + z z WWc c
= 12.67 + 3 12.67= 12.67 + 3 12.67
= 23.35= 23.35
LCLLCL = = c c + + z z WWc c
= 12.67= 12.67 -- 3 12.673 12.67
= 1.99= 1.99
NUMBER
OF
DEFECTS
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33
66
99
1212
1515
1818
2121
2424
N u m b e
r o f d e f e c t s
N u m b e
r o f d e f e c t s
Sample number Sample number
22 44 66 88 1010 1212 1414 1616
UCL = 23.35
LCL = 1.99
c = 12.67
cc--ChartChart(cont.)(cont.)
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Control Charts for Control Charts for
VariablesVariables
Mean chart ( x -Chart )
uses average of a sample
Range chart ( R-Chart )
uses amount of dispersion in a
sample
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xx--bar Chart bar Chart
x x = =
x x 11 + + x x 22 + ...+ ... x x k k
k k
==
UCL = UCL = x x + + A A22R R LCL = LCL = x x -- A A22R R == ==
wherewhere
x x = average of sample means= average of sample means==
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UCL = x + A2R = 5.01 + (0.58)(0.115) = 5.08
LCL =
x
-A
2R
= 5.01 - (0.58)(0.115) = 4.94
=
=
x = = = 5.01 cm= § x
k
50.09
10
xx-- bar Chart bar Chart
Exam ple (cont.)Exam ple (cont.)
Retrieve Factor Value A2
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xx-- bar bar ChartChartExam pleExam ple
(cont.)(cont.)
UCL = 5.08
LCL = 4.94
M e a n
Sample number
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
5.10 ±
5.08 ±
5.06 ±
5.04 ±
5.02 ±
5.00 ±
4.98 ±
4.96 ±
4.94 ±
4.92 ±
x = 5.01=
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R R-- ChartChart
UCL = UCL = DD44R R LCL = LCL = DD33R R
R R = = §§R R
k k
wherewhere
R R = range of each sample= range of each sample
k k = number of samples= number of samples
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R R--Chart Exam pleChart Exam ple
OBSERVATIONS (SLIPOBSERVATIONS (SLIP--RING DIAMETER, CM)RING DIAMETER, CM)
SAMPLE SAMPLE k k 11 2 2 33 44 5 5 x x R R
11 5.025.02 5.015.01 4.944.94 4.994.99 4.964.96 4.984.98 0.080.08
22 5.015.01 5.035.03 5.075.07 4.954.95 4.964.96 5.005.00 0.120.12
33 4.994.99 5.005.00 4.934.93 4.924.92 4.994.99 4.974.97 0.080.0844 5.035.03 4.914.91 5.015.01 4.984.98 4.894.89 4.964.96 0.140.14
55 4.954.95 4.924.92 5.035.03 5.055.05 5.015.01 4.994.99 0.130.13
66 4.974.97 5.065.06 5.065.06 4.964.96 5.035.03 5.015.01 0.100.10
77 5.055.05 5.015.01 5.105.10 4.964.96 4.994.99 5.025.02 0.140.14
88 5.095.09 5.105.10 5.005.00 4.994.99 5.085.08 5.055.05 0.110.1199 5.145.14 5.105.10 4.994.99 5.085.08 5.095.09 5.085.08 0.150.15
1010 5.015.01 4.984.98 5.085.08 5.075.07 4.994.99 5.035.03 0.100.10
50.0950.09 1.151.15
Example 15.3Example 15.3
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R R--Chart Exam ple (cont.)Chart Exam ple (cont.)
Example 15.3Example 15.3
§R k
R = = = 0.1151.1510
UCL = D4R = 2.11(0.115) = 0.243LCL = D3R = 0(0.115) = 0
Retrieve Factor Values DRetrieve Factor Values D33 and Dand D44
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R R--Chart Exam ple (cont.)Chart Exam ple (cont.)
UCL = 0.243
LCL = 0
R a n g e
Sample number
R = 0.115
|
1
|
2
|
3
|
4
|
5
|
6|
7
|
8
|
9
|
10
0.28 ±
0.24 ±
0.20 ±
0.16 ±
0.12 ±
0.08 ±
0.04 ±
0 ±
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Using xUsing x-- bar and R bar and R--ChartsCharts
Together Together
Process average and process variability must be in control.
It is possible for samples to have very narrow ranges, but
their averages is beyond control limits.
It is possible for sample averages to be in control, but
ranges might be very large.
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Control Chart PatternsControl Chart Patterns
UCLUCL
LCLLCL
Sample observationsSample observations
consistently above theconsistently above the
center linecenter line
LCLLCL
UCLUCL
Sample observationsSample observations
consistently below theconsistently below thecenter linecenter line
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Control Chart Patterns (cont.)Control Chart Patterns (cont.)
LCLLCL
UCLUCL
Sample observationsSample observations
consistently increasingconsistently increasing
UCLUCL
LCLLCL
Sample observationsSample observations
consistently decreasingconsistently decreasing
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Zones for Pattern TestsZones for Pattern TestsUCL
LCL
Zone A
Zone B
Zone C
Zone C
Zone B
Zone A
Processaverage
3 sigma = x + A2R =
3 sigma = x - A2R =
2 sigma = x + ( A2R )= 2
3
2 sigma = x - ( A2R )= 23
1 sigma = x + ( A2R )= 1
3
1 sigma = x - ( A2R )= 1
3
x =
Sample number
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
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Control Chart PatternsControl Chart Patterns
8 consecutive points on one side of the center line
8 consecutive points up or down across zones
14 points alternating up or down
2 out of 3 consecutive points in zone A but still
inside the control limits
4 out of 5 consecutive points in zone A or B
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Performing a Pattern TestPerforming a Pattern Test
11 4.984.98 BB ²² BB
22 5.005.00 BB UU CC
33 4.954.95 BB DD AA44 4.964.96 BB DD AA
55 4.994.99 BB UU CC
66 5.015.01 ²² UU CC
77 5.025.02 AA UU CC
88 5.055.05 AA UU BB
99 5.085.08 AA UU AA
1010 5.035.03 AA DD BB
SAMPLESAMPLE x x ABOVE /BELOWABOVE /BELOW UP/DOWNUP/DOWN ZONEZONE
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Sam ple SizeSam ple Size
Attribute charts require larger sample sizes
50 to 100 parts in a sample
Variable charts require smaller samples
2 to 10 parts in a sample
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SPC with ExcelSPC with Excel
UCL=0.19
LCL=0.01
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SPC with Excel:SPC with Excel:
FormulasFormulas
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Process Ca pabilityProcess Ca pability
TolerancesTolerances
design specifications reflecting product requirementsdesign specifications reflecting product requirements Process capabilityProcess capability
range of natural variability in a process what werange of natural variability in a process what we
measure with control chartsmeasure with control charts
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Process Ca pabilityProcess Ca pability
(b) Design specifications(b) Design specificationsand natural variation theand natural variation thesame; process is capablesame; process is capableof meeting specificationsof meeting specificationsmost of the time.most of the time.
DesignDesignSpecificationsSpecifications
ProcessProcess
(a) Natural variation(a) Natural variationexceeds designexceeds designspecifications; processspecifications; processis not capable of is not capable of meeting specificationsmeeting specificationsall the time.all the time.
DesignDesignSpecificationsSpecifications
ProcessProcess
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Process Ca pability (cont.)Process Ca pability (cont.)
(c) Design specifications(c) Design specificationsgreater than naturalgreater than naturalvariation; process isvariation; process iscapable of alwayscapable of alwaysconforming toconforming tospecifications.specifications.
DesignDesignSpecificationsSpecifications
ProcessProcess
(d) Specifications greater (d) Specifications greater than natural variation, than natural variation, but process off center;but process off center;capable but some outputcapable but some outputwill not meet upper will not meet upper specification.specification.
DesignDesignSpecificationsSpecifications
ProcessProcess
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Process Ca pability MeasuresProcess Ca pability Measures
Process Capability Ratio
Cp =
=
tolerance range
process range
upper specification limit -lower specification limit
6W
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Com puting CCom puting C p p
Net weight specification = 9.0 oz s 0.5 oz
Process mean = 8.80 oz
Process standard deviation = 0.12 oz
Cp =
= = 1.39
upper specification limit -lower specification limit
6W
9.5 - 8.5
6(0.12)
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Process Ca pability MeasuresProcess Ca pability Measures
Process Capability Ind ex Process Capability Ind ex
C C pk pk = minimum= minimum
x x -- lower specification limitlower specification limit
33WW
==
upper specification limitupper specification limit -- x x
33WW
==
,,
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Com puting CCom puting C pk pk
Net weight specification = 9.0 oz s 0.5 oz
Process mean = 8.80 oz
Process standard deviation = 0.12 oz
Cpk = minimum
= minimum , = 0.83
x - lower specification limit
3W
=
upper specification limit - x
3W
=
,
8.80 - 8.50
3(0.12)
9.50 - 8.80
3(0.12)
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FactFactorsors
n A2 D3 D4
SAMPLE SIZE FACTOR FOR x -CHART FACTORS FOR R -CHART
2 1.88 0.00 3.27
3 1.02 0.00 2.57
4 0.73 0.00 2.28
5 0.58 0.00 2.11
6 0.48 0.00 2.00
7 0.42 0.08 1.928 0.37 0.14 1.86
9 0.44 0.18 1.82
10 0.11 0.22 1.78
11 0.99 0.26 1.74
12 0.77 0.28 1.72
13 0.55 0.31 1.69
14 0.44 0.33 1.6715 0.22 0.35 1.65
16 0.11 0.36 1.64
17 0.00 0.38 1.62
18 0.99 0.39 1.61
19 0.99 0.40 1.61
20 0.88 0.41 1.59
Appendix:
Determining Control Limits for x-bar and R-Charts
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