This document provides an overview of statistical process control (SPC) techniques. It discusses the basics of SPC and how it is used to monitor production processes to detect and prevent poor quality. Different types of control charts are introduced for attributes (p-charts and c-charts) and variables (x-bar charts and R-charts). Examples of each type of control chart are provided and explained. The document also discusses how SPC can be applied to service industries and where control charts are most useful.
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SPC Basics & Control Charts Guide
1. Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc.
Beni AsllaniBeni Asllani
University of Tennessee at ChattanoogaUniversity of Tennessee at Chattanooga
Statistical Process ControlStatistical Process Control
Operations Management - 5th
EditionOperations Management - 5th
Edition
Chapter 4Chapter 4
Roberta Russell & Bernard W. Taylor, IIIRoberta Russell & Bernard W. Taylor, III
2. Copyright 2006 John Wiley & Sons, Inc. 4-2
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
3. Copyright 2006 John Wiley & Sons, Inc. 4-3
Basics of StatisticalBasics of Statistical
Process ControlProcess Control
Statistical Process ControlStatistical Process Control
(SPC)(SPC)
monitoring production processmonitoring production process
to detect and prevent poorto detect and prevent poor
qualityquality
SampleSample
subset of items produced tosubset of items produced to
use for inspectionuse for inspection
Control ChartsControl Charts
process is within statisticalprocess is within statistical
control limitscontrol limits
UCLUCL
LCLLCL
4. Copyright 2006 John Wiley & Sons, Inc. 4-4
VariabilityVariability
RandomRandom
common causescommon causes
inherent in a processinherent in a process
can be eliminatedcan be eliminated
only throughonly through
improvements in theimprovements in the
systemsystem
Non-RandomNon-Random
special causesspecial causes
due to identifiabledue to identifiable
factorsfactors
can be modifiedcan be modified
through operator orthrough operator or
management actionmanagement action
5. Copyright 2006 John Wiley & Sons, Inc. 4-5
SPC in TQMSPC in TQM
SPCSPC
tool for identifying problems andtool for identifying problems and
make improvementsmake improvements
contributes to the TQM goal ofcontributes to the TQM goal of
continuous improvementscontinuous improvements
6. Copyright 2006 John Wiley & Sons, Inc. 4-6
Quality MeasuresQuality Measures
AttributeAttribute
a product characteristic that can bea product characteristic that can be
evaluated with a discrete responseevaluated with a discrete response
good – bad; yes - nogood – bad; yes - no
VariableVariable
a product characteristic that is continuousa product characteristic that is continuous
and can be measuredand can be measured
weight - lengthweight - length
7. Copyright 2006 John Wiley & Sons, Inc. 4-7
Nature of defect is different in servicesNature of defect is different in services
Service defect is a failure to meetService defect is a failure to meet
customer requirementscustomer requirements
Monitor times, customer satisfactionMonitor times, customer satisfaction
Applying SPC toApplying SPC to
ServiceService
8. Copyright 2006 John Wiley & Sons, Inc. 4-8
Applying SPC toApplying SPC to
Service (cont.)Service (cont.)
HospitalsHospitals
timeliness and quickness of care, staff responses to requests,timeliness and quickness of care, staff responses to requests,
accuracy of lab tests, cleanliness, courtesy, accuracy ofaccuracy of lab tests, cleanliness, courtesy, accuracy of
paperwork, speed of admittance and checkoutspaperwork, speed of admittance and checkouts
Grocery StoresGrocery Stores
waiting time to check out, frequency of out-of-stock items,waiting time to check out, frequency of out-of-stock items,
quality of food items, cleanliness, customer complaints,quality of food items, cleanliness, customer complaints,
checkout register errorscheckout register errors
AirlinesAirlines
flight delays, lost luggage and luggage handling, waiting timeflight delays, lost luggage and luggage handling, waiting time
at ticket counters and check-in, agent and flight attendantat ticket counters and check-in, agent and flight attendant
courtesy, accurate flight information, passenger cabincourtesy, accurate flight information, passenger cabin
cleanliness and maintenancecleanliness and maintenance
9. Copyright 2006 John Wiley & Sons, Inc. 4-9
Applying SPC toApplying SPC to
Service (cont.)Service (cont.)
Fast-Food RestaurantsFast-Food Restaurants
waiting time for service, customer complaints,waiting time for service, customer complaints,
cleanliness, food quality, order accuracy, employeecleanliness, food quality, order accuracy, employee
courtesycourtesy
Catalogue-Order CompaniesCatalogue-Order Companies
order accuracy, operator knowledge and courtesy,order accuracy, operator knowledge and courtesy,
packaging, delivery time, phone order waiting timepackaging, delivery time, phone order waiting time
Insurance CompaniesInsurance Companies
billing accuracy, timeliness of claims processing,billing accuracy, timeliness of claims processing,
agent availability and response timeagent availability and response time
10. Copyright 2006 John Wiley & Sons, Inc. 4-10
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 itProcess is particularly harmful and costly if it
goes out of controlgoes out of control
ExamplesExamples
at the beginning of a process because it is a waste ofat the beginning of a process because it is a waste of
time and money to begin production process with badtime and money to begin production process with bad
suppliessupplies
before a costly or irreversible point, after which productbefore a costly or irreversible point, after which product
is difficult to rework or correctis difficult to rework or correct
before and after assembly or painting operations thatbefore and after assembly or painting operations that
might cover defectsmight cover defects
before the outgoing final product or service is deliveredbefore the outgoing final product or service is delivered
11. Copyright 2006 John Wiley & Sons, Inc. 4-11
Control ChartsControl Charts
A graph that establishesA graph that establishes
control limits of acontrol limits of a
processprocess
Control limitsControl limits
upper and lower bands ofupper and lower bands of
a control charta control chart
Types of chartsTypes of charts
AttributesAttributes
p-chartp-chart
c-chartc-chart
VariablesVariables
range (R-chart)range (R-chart)
mean (x bar – chart)mean (x bar – chart)
12. Copyright 2006 John Wiley & Sons, Inc. 4-12
Process ControlProcess Control
ChartChart
11 22 33 44 55 66 77 88 99 1010
Sample numberSample number
UpperUpper
controlcontrol
limitlimit
ProcessProcess
averageaverage
LowerLower
controlcontrol
limitlimit
Out of controlOut of control
13. Copyright 2006 John Wiley & Sons, Inc. 4-13
Normal DistributionNormal Distribution
µµ=0=0 11σσ 22σσ 33σσ-1-1σσ-2-2σσ-3-3σσ
95%
99.74%
14. Copyright 2006 John Wiley & Sons, Inc. 4-14
A Process Is inA Process Is in
Control If …Control If …
1. … no sample points outside limits
2. … most points near process average
3. … about equal number of points above
and below centerline
4. … points appear randomly distributed
15. Copyright 2006 John Wiley & Sons, Inc. 4-15
Control Charts forControl Charts for
AttributesAttributes
p-charts
uses portion defective in a sample
c-charts
uses number of defects in an item
16. Copyright 2006 John Wiley & Sons, Inc. 4-16
p-Chartp-Chart
UCL = p + zσp
LCL = p - zσp
z = number of standard
deviations from process average
p = sample proportion
defective; an estimate of process average
σp = standard deviation of sample
proportion
σσpp ==
pp(1 -(1 - pp))
nn
17. Copyright 2006 John Wiley & Sons, Inc. 4-17
p-Chart Examplep-Chart Example
20 samples of 100 pairs of jeans20 samples of 100 pairs of jeans
NUMBER OFNUMBER OF PROPORTIONPROPORTION
SAMPLESAMPLE DEFECTIVESDEFECTIVES DEFECTIVEDEFECTIVE
11 66 .06.06
22 00 .00.00
33 44 .04.04
:: :: ::
:: :: ::
2020 1818 .18.18
200200
18. Copyright 2006 John Wiley & Sons, Inc. 4-18
p-Chart Example (cont.)p-Chart Example (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) = 0.10
total defectives
total sample observations
p =
20. Copyright 2006 John Wiley & Sons, Inc. 4-20
c-Chartc-Chart
UCL =UCL = cc ++ zzσσcc
LCL =LCL = cc -- zzσσcc
where
c = number of defects per sample
σσcc == cc
21. Copyright 2006 John Wiley & Sons, Inc. 4-21
c-Chart (cont.)c-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
cc = = 12.67= = 12.67
190190
1515
UCLUCL == cc ++ zzσσcc
= 12.67 + 3 12.67= 12.67 + 3 12.67
= 23.35= 23.35
LCLLCL == cc ++ zzσσcc
= 12.67 - 3 12.67= 12.67 - 3 12.67
= 1.99= 1.99
NUMBER
OF
DEFECTS
22. Copyright 2006 John Wiley & Sons, Inc. 4-22
33
66
99
1212
1515
1818
2121
2424
NumberofdefectsNumberofdefects
Sample numberSample number
22 44 66 88 1010 1212 1414 1616
UCL = 23.35
LCL = 1.99
c = 12.67
c-Chartc-Chart
(cont.)(cont.)
23. Copyright 2006 John Wiley & Sons, Inc. 4-23
Control Charts forControl Charts for
VariablesVariables
Mean chart ( x -Chart )
uses average of a sample
Range chart ( R-Chart )
uses amount of dispersion in a
sample
24. Copyright 2006 John Wiley & Sons, Inc. 4-24
x-bar Chartx-bar Chart
xx ==
xx11 ++ xx22 + ...+ ... xxkk
kk
==
UCL =UCL = xx ++ AA22RR LCL =LCL = xx -- AA22RR== ==
wherewhere
xx = average of sample means= average of sample means
==
28. Copyright 2006 John Wiley & Sons, Inc. 4-28
R- ChartR- Chart
UCL =UCL = DD44RR LCL =LCL = DD33RR
RR ==
∑RR
kk
wherewhere
RR = range of each sample= range of each sample
kk = number of samples= number of samples
30. Copyright 2006 John Wiley & Sons, Inc. 4-30
R-Chart Example (cont.)R-Chart Example (cont.)
Example 15.3Example 15.3
∑R
k
R = = = 0.115
1.15
10
UCL = D4R = 2.11(0.115) = 0.243
LCL = D3R = 0(0.115) = 0
Retrieve Factor Values DRetrieve Factor Values D33 and Dand D44
31. Copyright 2006 John Wiley & Sons, Inc. 4-31
R-Chart Example (cont.)R-Chart Example (cont.)
UCL = 0.243
LCL = 0
Range
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 –
32. Copyright 2006 John Wiley & Sons, Inc. 4-32
Using x- bar and R-ChartsUsing x- bar and R-Charts
TogetherTogether
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.
33. Copyright 2006 John Wiley & Sons, Inc. 4-33
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 the
center linecenter line
35. Copyright 2006 John Wiley & Sons, Inc. 4-35
Zones for Pattern TestsZones for Pattern Tests
UCL
LCL
Zone A
Zone B
Zone C
Zone C
Zone B
Zone A
Process
average
3 sigma = x + A2R
=
3 sigma = x - A2R
=
2 sigma = x + (A2R)
= 2
3
2 sigma = x - (A2R)
= 2
3
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
36. Copyright 2006 John Wiley & Sons, Inc. 4-36
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
37. Copyright 2006 John Wiley & Sons, Inc. 4-37
Performing a Pattern TestPerforming a Pattern Test
11 4.984.98 BB —— BB
22 5.005.00 BB UU CC
33 4.954.95 BB DD AA
44 4.964.96 BB DD AA
55 4.994.99 BB UU CC
66 5.015.01 —— 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 xx ABOVE/BELOWABOVE/BELOW UP/DOWNUP/DOWN ZONEZONE
38. Copyright 2006 John Wiley & Sons, Inc. 4-38
Sample SizeSample 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
39. Copyright 2006 John Wiley & Sons, Inc. 4-39
SPC with ExcelSPC with Excel
UCL=0.19
LCL=0.01
40. Copyright 2006 John Wiley & Sons, Inc. 4-40
SPC with Excel:SPC with Excel:
FormulasFormulas
41. Copyright 2006 John Wiley & Sons, Inc. 4-41
Process CapabilityProcess Capability
TolerancesTolerances
design specifications reflecting productdesign specifications reflecting product
requirementsrequirements
Process capabilityProcess capability
range of natural variability in a process whatrange of natural variability in a process what
we measure with control chartswe measure with control charts
42. Copyright 2006 John Wiley & Sons, Inc. 4-42
Process CapabilityProcess Capability
(b) Design specifications(b) Design specifications
and natural variation theand natural variation the
same; process is capablesame; process is capable
of meeting specificationsof meeting specifications
most of the time.most of the time.
DesignDesign
SpecificationsSpecifications
ProcessProcess
(a) Natural variation(a) Natural variation
exceeds designexceeds design
specifications; processspecifications; process
is not capable ofis not capable of
meeting specificationsmeeting specifications
all the time.all the time.
DesignDesign
SpecificationsSpecifications
ProcessProcess
43. Copyright 2006 John Wiley & Sons, Inc. 4-43
Process Capability (cont.)Process Capability (cont.)
(c) Design specifications(c) Design specifications
greater than naturalgreater than natural
variation; process isvariation; process is
capable of alwayscapable of always
conforming toconforming to
specifications.specifications.
DesignDesign
SpecificationsSpecifications
ProcessProcess
(d) Specifications greater(d) Specifications greater
than natural variation, butthan natural variation, but
process off center;process off center;
capable but some outputcapable but some output
will not meet upperwill not meet upper
specification.specification.
DesignDesign
SpecificationsSpecifications
ProcessProcess
44. Copyright 2006 John Wiley & Sons, Inc. 4-44
Process Capability MeasuresProcess Capability Measures
Process Capability Ratio
Cp =
=
tolerance range
process range
upper specification limit -
lower specification limit
6σ
45. Copyright 2006 John Wiley & Sons, Inc. 4-45
Computing CComputing Cpp
Net weight specification = 9.0 oz ± 0.5 oz
Process mean = 8.80 oz
Process standard deviation = 0.12 oz
Cp =
= = 1.39
upper specification limit -
lower specification limit
6σ
9.5 - 8.5
6(0.12)
46. Copyright 2006 John Wiley & Sons, Inc. 4-46
Process Capability MeasuresProcess Capability Measures
Process Capability IndexProcess Capability Index
CCpkpk = minimum= minimum
xx - lower specification limit- lower specification limit
33σσ
==
upper specification limit -upper specification limit - xx
33σσ
==
,,
47. Copyright 2006 John Wiley & Sons, Inc. 4-47
Computing CComputing Cpkpk
Net weight specification = 9.0 oz ± 0.5 oz
Process mean = 8.80 oz
Process standard deviation = 0.12 oz
Cpk = minimum
= minimum , = 0.83
x - lower specification limit
3σ
=
upper specification limit - x
3σ
=
,
8.80 - 8.50
3(0.12)
9.50 - 8.80
3(0.12)
49. Copyright 2006 John Wiley & Sons, Inc. 4-49
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc.
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