©2003 thomson/south-western 1 chapter 12 – quality improvement slides prepared by jeff heyl,...

©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


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


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


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


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


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


Quality Improvement ToolsQuality Improvement Tools

FlowchartsFlowcharts Cause-and-Effect DiagramsCause-and-Effect Diagrams


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


Cause-and-Effect DiagramCause-and-Effect Diagram


Problem to be resolvedProblem to be resolvedProblem to be resolvedProblem to be resolved

Secondary causeSecondary cause

Main Main causecause





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



Statistical Process Control, Statistical Process Control, Process Variation and Process Variation and

Control ChartsControl Charts

MachineryMachinery PeoplePeople MaterialsMaterials Production MethodsProduction Methods The EnvironmentThe Environment


Statistical Process Control, Statistical Process Control, Process Variation and Process Variation and


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


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


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


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



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



Figure 12.5(c)Figure 12.5(c)


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



Figure 12.5(d)Figure 12.5(d)


4.0 4.0 –

0.0 0.0 –

-4.0 -4.0 –

YY

| | | | |-30-30 -15-15 00 1515 3030

XX



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


General Form of a Control General Form of a Control ChartChart


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


Control ChartControl Chart


ProcessProcess LotLot SampleSample Use data Use data to construct to construct

a control charta control chart

Corrective actionCorrective action


X and R ChartsX and R Charts

XX = = XX11 + + XX22 + ... + + ... + XXmm

mm

==RR

dd22

^̂



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



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



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



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

^̂


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


X Chart for X Chart for Coffee-Can ExampleCoffee-Can Example


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


XX


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


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


R Chart for R Chart for Coffee-Can ExampleCoffee-Can Example


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


RR


Filled Coffee-Can ExampleFilled Coffee-Can Example


20.2320.23

19.9819.98

19.7319.73

|11

|22

|33

|44

|55

|66


X X chartchart


Filled Coffee-Can ExampleFilled Coffee-Can Example



.93 .93 –

.44 .44 –

0 0

|33

|22

|44

|66

|11

|55

R R chartchart


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


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


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



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)




UCLUCL

LCLLCL

AA

BB

CC

AA

BB

CC

UCLUCL

LCLLCL

AA

BB

CC

AA

BB

CC

Pattern 1Pattern 1 Pattern 2Pattern 2




UCLUCL

LCLLCL

AA

BB

CC

AA

BB

CC

UCLUCL

LCLLCL

AA

BB

CC

AA

BB

CC




Figure 12.12(c)Figure 12.12(c)

UCLUCL

LCLLCL

AA

BB

CC

AA

BB

CC

UCLUCL

LCLLCL

AA

BB

CC

AA

BB

CC




Figure 12.12(d)Figure 12.12(d)

UCLUCL

LCLLCL

AA

BB

CC

AA

BB

CC

UCLUCL

LCLLCL

AA

BB

CC

AA

BB

CC



Minitab X ChartMinitab X Chart


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


Cans of Ground CoffeeCans of Ground Coffee





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





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



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


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



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


p Chart for Coffee Can Examplep Chart for Coffee Can Example


.075 .075 –

.032 .032 –

0 0 –

p Chart for Coffee Cansp Chart for Coffee Cans


I1313

I1212

I55

I1010

I1111

I22

I33

I44

I66

I77

I88

I99

I11

I2020

I1919

I1717

I1818

I1414

I1515

I1616

UCLUCL

CenterCenterLineLine

LCLLCL

pp


p Chart for Coffee Can Examplep Chart for Coffee Can Example


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



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


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



c Chart Equationsc Chart Equations

cc = =∑∑ccii

mm

UCLUCL = = cc + 3 + 3 cc

Center LineCenter Line = = cc

LCLLCL = = cc - 3 - 3 cc


Door Panels ExampleDoor Panels Example


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


I I I I I2121 2222 2323 2424 2525


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




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

^̂^̂




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




USLUSLLSLLSL

11.9511.95 12.0512.05


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)


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^


The CThe Cpkpk Ratio Ratio

LSLLSL TargetTarget USLUSL

Process Process centercenter



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


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


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


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´́



31.531.5 31.9231.92 32.532.5

LSLLSL USLUSL





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

©2003 thomson/south-western 1 chapter 12 – quality improvement slides prepared by jeff heyl,...

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