©2003 thomson/south-western 1 chapter 12 – quality improvement slides prepared by jeff heyl,...
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©2003 Thomson/South-Western 1
Chapter 12 –Chapter 12 –
Quality Quality ImprovementImprovement
Slides prepared by Jeff Heyl, Lincoln UniversitySlides prepared by Jeff Heyl, Lincoln University©2003 South-Western/Thomson Learning™
Introduction toIntroduction to Business StatisticsBusiness Statistics, 6e, 6eKvanli, Pavur, KeelingKvanli, Pavur, Keeling
©2003 Thomson/South-Western 2
The Quality GurusThe Quality Gurus
W. Edwards DemingW. Edwards Deming14 Points for Management14 Points for Management
Joseph M. JuranJoseph M. JuranJuran’s TrilogyJuran’s Trilogy
Philip B. CrosbyPhilip B. CrosbyQuality is FreeQuality is Free
©2003 Thomson/South-Western 3
DefinitionsDefinitions Quality product or service: A product or Quality product or service: A product or
service that meets or exceeds the service that meets or exceeds the expectations of the customerexpectations of the customer
Process: Any combination of people, Process: Any combination of people, machinery, material, and methods that is machinery, material, and methods that is intended to produce a product or serviceintended to produce a product or service
Quality Characteristics: Features of a Quality Characteristics: Features of a product that describe its fitness for useproduct that describe its fitness for use
©2003 Thomson/South-Western 4
DefinitionsDefinitions
Statistical Process Control (SPC): The Statistical Process Control (SPC): The application of statistical quality-control application of statistical quality-control methods to measure and analyze the methods to measure and analyze the variation found in a processvariation found in a process
Control Chart: A statistical chart used to Control Chart: A statistical chart used to monitor various aspects of a process monitor various aspects of a process and to determine if the process is in and to determine if the process is in control or out of controlcontrol or out of control
©2003 Thomson/South-Western 5
Malcolm Baldrige National Malcolm Baldrige National Quality Award CriteriaQuality Award Criteria
Leadership SystemLeadership System Strategic PlanningStrategic Planning Customer and Market FocusCustomer and Market Focus Information and AnalysisInformation and Analysis Human Resource FocusHuman Resource Focus Process ManagementProcess Management Business ResultsBusiness Results
©2003 Thomson/South-Western 6
ISO 9000 RegistrationISO 9000 RegistrationBasic approach is to reduce process Basic approach is to reduce process variation throughout the organizationvariation throughout the organization
ISO 9000: 2000 -ISO 9000: 2000 - Quality Management Quality Management Systems - Fundamentals Systems - Fundamentals and Vocabularyand Vocabulary
ISO 9001: 2000 -ISO 9001: 2000 - Quality Management Quality Management Systems - RequirementsSystems - Requirements
ISO 9001: 2000 -ISO 9001: 2000 - Quality Management Quality Management Systems - Guidelines for Systems - Guidelines for Performance ImprovementPerformance Improvement
©2003 Thomson/South-Western 7
Quality Improvement ToolsQuality Improvement Tools
FlowchartsFlowcharts Cause-and-Effect DiagramsCause-and-Effect Diagrams
©2003 Thomson/South-Western 8
Place in queue for Place in queue for next available drivernext available driverPlace in queue for Place in queue for
next available drivernext available driver
Customer arrives Customer arrives with packagewith package
Customer arrives Customer arrives with packagewith package
Customer waits in lineCustomer waits in lineCustomer waits in lineCustomer waits in line
Order is recordedOrder is recordedOrder is recordedOrder is recorded
Directions to final Directions to final destination prepareddestination prepared
Directions to final Directions to final destination prepareddestination prepared
Driver available?Driver available?
Select driver Select driver from poolfrom pool
Select driver Select driver from poolfrom pool
Relay package and delivery Relay package and delivery instructions/directionsinstructions/directions
Relay package and delivery Relay package and delivery instructions/directionsinstructions/directions
Driver loads package Driver loads package into vehicleinto vehicle
Driver loads package Driver loads package into vehicleinto vehicle
Package is deliveredPackage is deliveredPackage is deliveredPackage is delivered
NoNo
YesYes
FlowchartFlowchart
Figure 12.2Figure 12.2
©2003 Thomson/South-Western 9
Cause-and-Effect DiagramCause-and-Effect Diagram
Figure 12.3Figure 12.3
Problem to be resolvedProblem to be resolvedProblem to be resolvedProblem to be resolved
Secondary causeSecondary cause
Main Main causecause
Main Main causecause
Main Main causecause
Main Main causecause
©2003 Thomson/South-Western 10
Metro Delivery ServiceMetro Delivery Service
Scheduling too many Scheduling too many deliveries per rundeliveries per run
Recording wrong addressRecording wrong address
Language/accent difficultiesLanguage/accent difficulties
Insufficient number of Insufficient number of orders takenorders taken
Recording poor directionsRecording poor directions
Illegible handwritingIllegible handwriting
Making sure package recipient Making sure package recipient will be present at deliverywill be present at delivery
Package stolen from carPackage stolen from car
Had to fill gas tankHad to fill gas tank
Flat tireFlat tire
Engine troubleEngine trouble
Vehicle too small for large Vehicle too small for large package–had to change package–had to change vehiclevehicle
Got lostGot lost
Speeding ticketSpeeding ticket
Couldn’t follow directionsCouldn’t follow directions
Loaded the wrong Loaded the wrong packagepackage
None available None available when neededwhen needed
Impaired due to Impaired due to alcohol/drugsalcohol/drugs
Poor driving caused Poor driving caused an accidentan accident
Wait for funeral processionWait for funeral procession
Long distance to goLong distance to go
Encountering an accidentEncountering an accident
Wait for trainWait for train
Couldn’t find parking spotCouldn’t find parking spot
Hazardous roads due to bad Hazardous roads due to bad weatherweather
Package arrived latePackage arrived latePackage arrived latePackage arrived late
Taking the orderTaking the orderTaking the orderTaking the order Delivery vehiclesDelivery vehiclesDelivery vehiclesDelivery vehicles
DriverDriverDriverDriver Traffic conditionsTraffic conditionsTraffic conditionsTraffic conditions
Figure 12.4Figure 12.4
©2003 Thomson/South-Western 11
Statistical Process Control, Statistical Process Control, Process Variation and Process Variation and
Control ChartsControl Charts
MachineryMachinery PeoplePeople MaterialsMaterials Production MethodsProduction Methods The EnvironmentThe Environment
©2003 Thomson/South-Western 12
Statistical Process Control, Statistical Process Control, Process Variation and Process Variation and
Control ChartsControl Charts
A stable system exhibits chance A stable system exhibits chance causes of variationcauses of variation
Variations outside this stable Variations outside this stable pattern are called assignable pattern are called assignable causes of variationcauses of variation
©2003 Thomson/South-Western 13
Deming Funnel Experiment: Deming Funnel Experiment: StrategiesStrategies
Strategy 1: Do not react to this Strategy 1: Do not react to this random variation and do not move random variation and do not move the funnelthe funnel
Strategy 2: Measure the distance Strategy 2: Measure the distance from the marble’s resting place to from the marble’s resting place to the bull’s-eyethe bull’s-eyeMove the funnel and equal distance, Move the funnel and equal distance, but in the opposite directionbut in the opposite direction
©2003 Thomson/South-Western 14
Deming Funnel Experiment: Deming Funnel Experiment: StrategiesStrategies
Strategy 3: Measure the distance Strategy 3: Measure the distance from the marble’s resting place to from the marble’s resting place to the bull’s-eyethe bull’s-eyeMove the funnel this distance, in Move the funnel this distance, in the opposite direction, starting at the opposite direction, starting at the bull’s-eyethe bull’s-eye
©2003 Thomson/South-Western 15
Deming Funnel ExperimentDeming Funnel Experiment
Figure 12.5(a)Figure 12.5(a)
MarbleMarble
Target paper Target paper with bull’s eyewith bull’s eye
Funnel Funnel ApparatusApparatus
©2003 Thomson/South-Western 16
Deming Funnel ExperimentDeming Funnel Experiment
Figure 12.5(b)Figure 12.5(b)
CONTROL STRATEGY 1CONTROL STRATEGY 1
4.0 4.0 –
0.0 0.0 –
-4.0 -4.0 –
YY
| | | | |-5.0-5.0 -2.5-2.5 0.00.0 2.52.5 5.05.0
XX
©2003 Thomson/South-Western 17
Deming Funnel ExperimentDeming Funnel Experiment
Figure 12.5(c)Figure 12.5(c)
CONTROL STRATEGY 2CONTROL STRATEGY 2
4.0 4.0 –
0.0 0.0 –
-4.0 -4.0 –
YY
| | | | |-5.0-5.0 -2.5-2.5 0.00.0 2.52.5 5.05.0
XX
©2003 Thomson/South-Western 18
Deming Funnel ExperimentDeming Funnel Experiment
Figure 12.5(d)Figure 12.5(d)
CONTROL STRATEGY 3CONTROL STRATEGY 3
4.0 4.0 –
0.0 0.0 –
-4.0 -4.0 –
YY
| | | | |-30-30 -15-15 00 1515 3030
XX
©2003 Thomson/South-Western 19
Control ChartsControl Charts
A process is in control if the observed A process is in control if the observed variation is due to inherent or natural variation is due to inherent or natural variationvariationThis variability is the cumulative effect This variability is the cumulative effect of many small, essentially of many small, essentially uncontrollable, causesuncontrollable, causes
A process in out of control if a relatively A process in out of control if a relatively large variation is introduced that can be large variation is introduced that can be traced to an assignable causetraced to an assignable cause
©2003 Thomson/South-Western 20
General Form of a Control General Form of a Control ChartChart
Figure 12.6Figure 12.6
Upper control limitUpper control limit
Lower control limitLower control limit
Center lineCenter line
|11
|22
|33
|44
|55
|66
|77
|88 ......
Sample numberSample number
UCLUCL
CLCL
LCLLCL
©2003 Thomson/South-Western 21
Control ChartControl Chart
Figure 12.7Figure 12.7
ProcessProcess LotLot SampleSample Use data Use data to construct to construct
a control charta control chart
Corrective actionCorrective action
©2003 Thomson/South-Western 22
X and R ChartsX and R Charts
XX = = XX11 + + XX22 + ... + + ... + XXmm
mm
==RR
dd22
^̂
©2003 Thomson/South-Western 23
X and R ChartsX and R Charts
Table 12.2Table 12.2
Preliminary sample resultsPreliminary sample results
SampleSample 11 22 33 44 55 66 77 88 99 1010
XX 20.0020.00 19.9819.98 19.8819.88 19.9419.94 20.0420.04 20.0620.06 20.0220.02 19.8219.82 20.0220.02 20.0620.06
RR .4.4 .5.5 .5.5 .4.4 .6.6 .3.3 .4.4 .4.4 .5.5 .7.7
Sample Sample 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
XX 19.9419.94 19.8619.86 19.9019.90 20.1220.12 19.9219.92 20.0420.04 20.0620.06 19.9819.98 19.8819.88 20.0820.08
RR .4.4 .3.3 .2.2 .5.5 .5.5 .4.4 .3.3 .5.5 .6.6 .4.4
©2003 Thomson/South-Western 24
X and R ChartsX and R Charts
Factors for constructing an Factors for constructing an RR chart chart
nn dd22 dd33 DD33 DD44
22 1.1281.128 .853.853 00 3.2673.26733 1.6931.693 .888.888 00 2.5742.57444 2.0592.059 .880.880 00 2.2822.28255 2.3262.326 .864.864 00 2.1142.11466 2.5342.534 .848.848 00 2.0042.00477 2.7042.704 .833.833 .076.076 1.9241.92488 2.8472.847 .820.820 .136.136 1.8641.86499 2.9702.970 .808.808 .184.184 1.8161.816
1010 3.0783.078 .797.797 .223.223 1.7771.777
Table 12.3Table 12.3
©2003 Thomson/South-Western 25
Tail Area in Normal CurveTail Area in Normal Curve
33-3-3
Shaded area isShaded area is.00135 + .00135 = .0027.00135 + .00135 = .0027
Area is .49865Area is .49865
Area is .00135Area is .00135
ZZ
Figure 12.8Figure 12.8
©2003 Thomson/South-Western 26
X and R ChartsX and R ChartsProcess for Estimating Process for Estimating
1.1. Determine the average of the m values Determine the average of the m values of Rof R
2.2. Select the values of dSelect the values of d22 from from Table 12.3Table 12.3
using the corresponding sample size, nusing the corresponding sample size, n
3.3. Estimate Estimate using: using:
==RR
dd22
^̂
©2003 Thomson/South-Western 27
X and R ChartsX and R ChartsControl LimitsControl Limits
UCLUCL = = XX + 3 = + 3 = XX + 3 + 3
Center LineCenter Line = = XX
LCLLCL = = XX - 3 = - 3 = XX - 3 - 3 nn
^̂
nn
^̂ ((RR / / dd22))
nn
((RR / / dd22))
nn
©2003 Thomson/South-Western 28
X Chart for X Chart for Coffee-Can ExampleCoffee-Can Example
Figure 12.9Figure 12.9
20.2320.23
19.9819.98
19.7319.73
UCLUCL
CLCL
LCLLCL
|11
|1010
|22
|33
|44
|55
|66
|77
|88
|99
|1212
|1111
|1313
|1414
|1515
|1616
|1717
|1818
|1919
|2020
Sample numberSample number
XX
©2003 Thomson/South-Western 29
The R ChartThe R Chart
ssRR = = RRdd33
dd22
UCL = UCL = RR + 3 + 3ssRR = = RR + 3 + 3RR = 1 + 3 = 1 + 3 RRdd33
dd22
dd33
dd22
UCL = UCL = RR - 3 - 3ssRR = = RR - 3 - 3RR = 1 - 3 = 1 - 3 RRdd33
dd22
dd33
dd22
©2003 Thomson/South-Western 30
The R ChartThe R Chart
By definingBy defining
DD33 = 1 - 3 and = 1 - 3 and DD44 = 1 + 3 = 1 + 3dd33
dd22
dd33
dd22
UCLUCL = = DD44RR
Center LineCenter Line = = RR
LCLLCL = = DD33RR
©2003 Thomson/South-Western 31
R Chart for R Chart for Coffee-Can ExampleCoffee-Can Example
Figure 12.10Figure 12.10
1.0 1.0 –
.8 .8 –
.6 .6 –
.4 .4 –
.2 .2 –
0 0 –
UCL = .98UCL = .98
RR = .44 = .44
LCL = 0LCL = 0
|
|1010
|22
|
|44
|
|66
|
|88
|
|1212
|
|
|1414
|
|1616
|
|1818
|
|2020
Sample numberSample number
RR
©2003 Thomson/South-Western 32
Filled Coffee-Can ExampleFilled Coffee-Can Example
Figure 12.11(a)Figure 12.11(a)
20.2320.23
19.9819.98
19.7319.73
|11
|22
|33
|44
|55
|66
Sample numberSample number
X X chartchart
©2003 Thomson/South-Western 33
Filled Coffee-Can ExampleFilled Coffee-Can Example
Figure 12.11(b)Figure 12.11(b)
Sample numberSample number
.93 .93 –
.44 .44 –
0 0
|33
|22
|44
|66
|11
|55
R R chartchart
©2003 Thomson/South-Western 34
Steps for Making X and R Steps for Making X and R ChartsCharts
1.1. Collect m samples of data, each of size nCollect m samples of data, each of size n
2.2. Compute the average of each subgroupCompute the average of each subgroup
3.3. Compute the range for each subgroupCompute the range for each subgroup
4.4. Find the overall meanFind the overall mean
5.5. Find the average rangeFind the average range
6.6. Estimate Estimate
©2003 Thomson/South-Western 35
Steps for Making X and R Steps for Making X and R ChartsCharts
8.8. Compute the 3-sigma control limits for RCompute the 3-sigma control limits for R7.7. Compute the 3-sigma control limits for XCompute the 3-sigma control limits for X
9.9. Construct the control charts by plotting X Construct the control charts by plotting X and R points for each subgroup on the and R points for each subgroup on the same vertical linesame vertical line
©2003 Thomson/South-Western 36
Pattern Analysis for X ChartsPattern Analysis for X Charts
Pattern analysis is concerned with Pattern analysis is concerned with recognizing systematic or nonrandom recognizing systematic or nonrandom patterns in an X control chart and patterns in an X control chart and identifying the source of such identifying the source of such process variationprocess variation
Each chart is divided into zonesEach chart is divided into zones
Zone AZone AZone BZone BZone CZone C
©2003 Thomson/South-Western 37
Pattern Analysis for X ChartsPattern Analysis for X Charts
PatternPattern DescriptionDescription
11One point beyond zone AOne point beyond zone A
22Nine points in a row in zone C or beyond, all on Nine points in a row in zone C or beyond, all on one side of the center lineone side of the center line
33Six points in a row, all increasing or decreasingSix points in a row, all increasing or decreasing
44Fourteen points in a row, alternating up and downFourteen points in a row, alternating up and down
55Two out of three points in a row in zone A or Two out of three points in a row in zone A or beyondbeyond
66Four out of five points in zone B or beyond (on one Four out of five points in zone B or beyond (on one side of center line)side of center line)
77Fifteen points in a row in zones C (above or below Fifteen points in a row in zones C (above or below center line)center line)
88Eight points in a row beyond zones C (above or Eight points in a row beyond zones C (above or below center line)below center line)
©2003 Thomson/South-Western 38
Pattern Analysis for X ChartsPattern Analysis for X Charts
Figure 12.12(a)Figure 12.12(a)
UCLUCL
LCLLCL
AA
BB
CC
AA
BB
CC
UCLUCL
LCLLCL
AA
BB
CC
AA
BB
CC
Pattern 1Pattern 1 Pattern 2Pattern 2
©2003 Thomson/South-Western 39
Pattern Analysis for X ChartsPattern Analysis for X Charts
Figure 12.12(b)Figure 12.12(b)
UCLUCL
LCLLCL
AA
BB
CC
AA
BB
CC
UCLUCL
LCLLCL
AA
BB
CC
AA
BB
CC
Pattern 3Pattern 3 Pattern 4Pattern 4
©2003 Thomson/South-Western 40
Pattern Analysis for X ChartsPattern Analysis for X Charts
Figure 12.12(c)Figure 12.12(c)
UCLUCL
LCLLCL
AA
BB
CC
AA
BB
CC
UCLUCL
LCLLCL
AA
BB
CC
AA
BB
CC
Pattern 5Pattern 5 Pattern 6Pattern 6
©2003 Thomson/South-Western 41
Pattern Analysis for X ChartsPattern Analysis for X Charts
Figure 12.12(d)Figure 12.12(d)
UCLUCL
LCLLCL
AA
BB
CC
AA
BB
CC
UCLUCL
LCLLCL
AA
BB
CC
AA
BB
CC
Pattern 7Pattern 7 Pattern 8Pattern 8
©2003 Thomson/South-Western 42
Minitab X ChartMinitab X Chart
Figure 12.13Figure 12.13
15 15 –
10 10 –
5 5 –
X-bar Chart for CALLSX-bar Chart for CALLS
|00
|1010
|2020
|3030
|4040
|5050
Sample NumberSample Number
3.0SL=14.653.0SL=14.65
2.0SL=13.072.0SL=13.07
1.0SL=11.501.0SL=11.50
X=9.925X=9.925
-1.0SL=8.351-1.0SL=8.351
-2.0SL=6.778-2.0SL=6.778
-3.0SL=5.204-3.0SL=5.204
Sam
ple
Me
anS
amp
le M
ean
©2003 Thomson/South-Western 43
Cans of Ground CoffeeCans of Ground Coffee
Figure 12.14Figure 12.14
©2003 Thomson/South-Western 44
Cans of Ground CoffeeCans of Ground Coffee
Figure 12.15Figure 12.15
2.5 2.5 –
2 2 –
1.5 1.5 –
1.01.0 –
0.5 0.5 –
0 0 –
R Chart for Coffee CansR Chart for Coffee Cans
UCLUCL
LCLLCLI I II I I I I I I I I I I II I I I I11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
Sample NumberSample Number
©2003 Thomson/South-Western 45
Cans of Ground CoffeeCans of Ground Coffee
Figure 12.16Figure 12.16
50.8 50.8 –
50.6 50.6 –
50.4 50.4 –
50.250.2 –
50 50 –
49.8 49.8 –
49.649.6 –
49.4 49.4 –
49.2 49.2 –
49 49 –
48.848.8 –
X-Bar Chart for Coffee CansX-Bar Chart for Coffee Cans
UCLUCL
LCLLCL
I I II I I I I I I I I I I II I I I I11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
Sample NumberSample Number
©2003 Thomson/South-Western 46
Control Charts for Control Charts for Attribute DataAttribute Data
1.1. Quality measurements are not possibleQuality measurements are not possible
2.2. Quality measurements are not practicalQuality measurements are not practical
3.3. Many characteristics on each part are Many characteristics on each part are being judged during inspectionbeing judged during inspection
4.4. The main question of interest is: “Will The main question of interest is: “Will the process be able to produce the process be able to produce conforming products over time?”conforming products over time?”
Proportion Nonconforming: p ChartProportion Nonconforming: p ChartReasons for Using a p ChartReasons for Using a p Chart
©2003 Thomson/South-Western 47
Steps for Making p ChartsSteps for Making p Charts
5.5. Draw the control lines and plot the Draw the control lines and plot the values of pvalues of pii
4.4. Compute the 3-sigma control limitsCompute the 3-sigma control limits
3.3. Find p, the overall proportion Find p, the overall proportion nonconformingnonconforming
2.2. Determine the proportion nonconforming Determine the proportion nonconforming for each samplefor each sample
1.1. Collect m samples of data, each of size nCollect m samples of data, each of size n
©2003 Thomson/South-Western 48
p Chart Equations p Chart Equations
ppii = =TTii
nnpp = =
∑∑TTii
mnmn
pp = = total number of nonconforming unitstotal number of nonconforming units
total sample sizetotal sample size
UCLUCL = = pp + 3 + 3
CLCL = = pp
LCLLCL = = pp - 3 - 3
pp(1 - (1 - pp))
nn
pp(1 - (1 - pp))
nn
©2003 Thomson/South-Western 49
p Chart for Coffee Can Examplep Chart for Coffee Can Example
Figure 12.17Figure 12.17
.075 .075 –
.032 .032 –
0 0 –
p Chart for Coffee Cansp Chart for Coffee Cans
Sample NumberSample Number
I1313
I1212
I55
I1010
I1111
I22
I33
I44
I66
I77
I88
I99
I11
I2020
I1919
I1717
I1818
I1414
I1515
I1616
UCLUCL
CenterCenterLineLine
LCLLCL
pp
©2003 Thomson/South-Western 50
p Chart for Coffee Can Examplep Chart for Coffee Can Example
Figure 12.18Figure 12.18
0.08 0.08 –
0.07 0.07 –
0.06 0.06 –
0.050.05 –
0.04 0.04 –
0.03 0.03 –
0.020.02 –
0.010.01 –
00 –
p Chart for Coffee Cansp Chart for Coffee Cans
UCLUCL
LCLLCLI I II I I I I I I I I I I II I I I I11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
Sample NumberSample Number
©2003 Thomson/South-Western 51
Control Charts for Control Charts for Attribute DataAttribute Data
1.1. One or more types of nonconformitiesOne or more types of nonconformities
2.2. Poisson distributionPoisson distribution
Number Nonconforming per Unit: c ChartNumber Nonconforming per Unit: c ChartReasons for Using a c ChartReasons for Using a c Chart
©2003 Thomson/South-Western 52
The c Chart ConstructionThe c Chart Construction
5.5. Construct the chartConstruct the chart
4.4. Compute the 3-sigma control limitsCompute the 3-sigma control limits
3.3. Find the average number of Find the average number of nonconformities per unit, cnonconformities per unit, c
2.2. Determine the number of Determine the number of nonconformities for the ith unit. nonconformities for the ith unit. Call this value cCall this value cii
1.1. Collect m samples of data, each of size nCollect m samples of data, each of size n
©2003 Thomson/South-Western 53
c Chart Equationsc Chart Equations
cc = =∑∑ccii
mm
UCLUCL = = cc + 3 + 3 cc
Center LineCenter Line = = cc
LCLLCL = = cc - 3 - 3 cc
©2003 Thomson/South-Western 54
Door Panels ExampleDoor Panels Example
Figure 12.19Figure 12.19
9 9 –
8 8 –
7 7 –
6 6 –
55 –
4 4 –
3 3 –
22 –
11 –
00 –
c Chart for Door Panelsc Chart for Door Panels
UCLUCL
LCLLCL
I I II I I I I I I I I I I II I I I I11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
Sample NumberSample Number
I I I I I2121 2222 2323 2424 2525
©2003 Thomson/South-Western 55
Process CapabilityProcess Capability
Specification Limits: process Specification Limits: process requirementsrequirements
Lower spec limit (LSL): the lower limit Lower spec limit (LSL): the lower limit of the process output that meets the of the process output that meets the process requirementsprocess requirements
Upper spec limit (USL): the upper limit Upper spec limit (USL): the upper limit of the process output that meets the of the process output that meets the process requirementsprocess requirements
©2003 Thomson/South-Western 56
Process CapabilityProcess Capability
Figure 12.20Figure 12.20
USL = 12.05USL = 12.05
XX = 12.1 = 12.1XX + 3 + 3 = 12.19= 12.19
XX - 3 - 3 = 12.01= 12.01
LSL = 11.95LSL = 11.95
Process must operate in hereProcess must operate in here
Process Process isis operating in here operating in here
^̂^̂
©2003 Thomson/South-Western 57
Process CapabilityProcess Capability
Figure 12.20Figure 12.20
USL = 12.05USL = 12.05
XX = 12.1 = 12.1XX + 3 + 3 = 12.19= 12.19
XX - 3 - 3 = 12.01= 12.01
LSL = 11.95LSL = 11.95
Process must operate in hereProcess must operate in here
Process Process isis operating in here operating in here
^̂^̂
The difference between The difference between 12.01 and 12.19 is referred12.01 and 12.19 is referredto as the process spreadto as the process spread
©2003 Thomson/South-Western 58
Process CapabilityProcess Capability
Figure 12.21Figure 12.21
USLUSLLSLLSL
11.9511.95 12.0512.05
©2003 Thomson/South-Western 59
Process Capability Ratio CProcess Capability Ratio Cpp
Assumptions:Assumptions:
1.1. The process is centered within The process is centered within specificationsspecifications
2.2. The process is normally The process is normally distributeddistributed
3.3. The process is stable (in control)The process is stable (in control)
©2003 Thomson/South-Western 60
Formulas for CFormulas for Cpp
CCpp = =USL - LSLUSL - LSL
66̂^
CCpp = = (upper spec limit only)(upper spec limit only)USL - USL - XX
33̂̂
CCpp = = (lower spec limit only)(lower spec limit only)XX - LSL - LSL
33̂^
©2003 Thomson/South-Western 61
The CThe Cpkpk Ratio Ratio
LSLLSL TargetTarget USLUSL
Process Process centercenter
Figure 12.22Figure 12.22
©2003 Thomson/South-Western 62
Process Capability Ratio CProcess Capability Ratio Cpkpk
Assumptions:Assumptions:
1.1. The process may or may not be The process may or may not be centered in speccentered in spec
2.2. The process is normally distributedThe process is normally distributed
3.3. The process is stableThe process is stable
4.4. Control charts will be used to Control charts will be used to monitor the process over timemonitor the process over time
©2003 Thomson/South-Western 63
Procedure for Finding CProcedure for Finding Cpkpk
1. Determine 1. Determine RRLL = =XX - LSL - LSL
33^̂
2. Determine 2. Determine RRUU = =USL -USL - X X
33^̂
3. 3. CCpkpk = Minimum of = Minimum of RRLL and and RRUU
©2003 Thomson/South-Western 64
Taking CTaking Cpkpk One Step Further One Step FurtherIf the process is capable If the process is capable ((CCpkpk > 1)> 1)
Monitor the processMonitor the process Pursue continual imporvementPursue continual imporvement
If the process is not capable If the process is not capable ((CCpkpk ≤ ≤ 1) 1)
Monitor the processMonitor the process Pursue continual imporvementPursue continual imporvement Invest time, money, and resources to reduce Invest time, money, and resources to reduce
process variationprocess variation Consider removing this product from Consider removing this product from
productionproduction
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Considering the Process Considering the Process Target: Use of CTarget: Use of Cpmpm
ss´ =´ =∑∑((xx - - TT))22
nn - 1 - 1
∑∑((xx - - xx))22
nn - 1 - 1= += +
nn((xx - - TT))22
nn - 1 - 1
= = ss22 + +nn((xx - - TT))22
nn - 1 - 1 CCpmpm = =USL - LSLUSL - LSL
66ss´́
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Process CapabilityProcess Capability
31.531.5 31.9231.92 32.532.5
LSLLSL USLUSL
Figure 12.23Figure 12.23
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Process CapabilityProcess Capability
Table 12.4Table 12.4
Number of Noncomforming UnitsNumber of Noncomforming UnitsCCpkpk per Million Producedper Million Produced
.5.5 133,614133,614
.75.75 24,44824,4481.001.00 2,7002,7001.301.30 96961.501.50 6.86.82.002.00 .002.002