s4quality tools

2008 Prentice Hall, Inc. 5 1

Quality tools for lean Quality tools for lean systemsystem

Dr. R K SinghDr. R K Singh


ExampleExample--Imagine that pump manufacturing Co has started to implement

TPM. After the passage of a week, the maintenance engineerdecides to compute overall equipment effectiveness (OEE) ofa lathe in which shafts are machined. In this regard, themaintenance engineer gathers the following data.

LoadingLoading time/shift=time/shift=480480 mtsmts,,SetSet upup time/shift=time/shift=7575 mtsmtsDownDown time/shift=time/shift=4545 mtsmts,,NumberNumber ofof shaftsshafts machined/shift=machined/shift=2020,,AverageAverage cyclecycle timetime ofof machiningmachining shaft=shaft= 1212 mtsmtsOperatingOperating time/shift=time/shift=480480 mtsmtsNumberNumber ofof shaftsshafts rejected/shift=rejected/shift=55DetermineDetermine thethe OEEOEE ofof thethe lathelathe inin whichwhich thethe shaftsshafts areare

machinedmachined.. AlsoAlso commentcomment byby referringreferring thethe OEEOEE valuevalue ofofmachinemachine..


SolutionSolutionAvailabilityAvailability= (Loading time= (Loading time--set up timeset up time--down time) X100 down time) X100

/loading time/loading time=(480=(480--7575--45)X100/480=75%45)X100/480=75%

Performance Efficiency=Average cycle time cycle time xNumberxNumber of good of good units made during the specific period x100/operating timeunits made during the specific period x100/operating time

=12 x (20=12 x (20--5) x100/480 =37.5%5) x100/480 =37.5%

Rate of quality= (Total units of good products/total units = (Total units of good products/total units produced) x100 =15/20 x100=75produced) x100 =15/20 x100=75

OEE= 0.75x0.375x0.75=0.2109=21.09%OEE= 0.75x0.375x0.75=0.2109=21.09%


What is Quality?What is Quality?

TheThe qualityquality ofof aa productproduct oror serviceservice isisaa customerscustomers perceptionperception ofof thethedegreedegree toto whichwhich thethe productproduct ororserviceservice meetsmeets hishis oror herherexpectationsexpectations..


Key Dimensions of QualityKey Dimensions of Quality

PerformancePerformance FeaturesFeatures ReliabilityReliability ConformanceConformance

DurabilityDurability ServiceabilityServiceability AestheticsAesthetics Perceived qualityPerceived quality ValueValue


MalcomMalcom BaldrigeBaldrige National Quality National Quality Award Award

Applicants are evaluated on:Applicants are evaluated on:Categories PointsLeadership 120Strategic Planning 85Customer & Market Focus 85Measurement, Analysis, and Knowledge Management 90Workforce Focus 85Process Management 85Results 450


CIICII--EXIM Business EXIM Business Excellence Award: Excellence Award: ModelModel

Leadership100

Processes140

PeopleResults

90Customer

Results200

SocietyResults

60

KeyPerformance

Results150

People90

Policy & Strategy

80Partnership &

Resources90

Enablers Results

Innovation & LearningAdopted from: http://www.ciionline.org/Common/201/default.asp?Page=The%20Business%20Excellence%20Model.htm


Quality CostingQuality CostingCategories of Quality CostsCategories of Quality Costs

Control CostsControl Costs Failure CostsFailure Costs

PreventionPrevention AppraisalAppraisal InternalInternal ExternalExternal

Quality CostsQuality Costs


Total Quality ManagementTotal Quality Management

A philosophy that involves everyone A philosophy that involves everyone in an organization in a continual effort in an organization in a continual effort to improve quality and achieve to improve quality and achieve customer satisfaction.customer satisfaction.

TT QQ MM


1.1.Find out what the Find out what the customer wantscustomer wants2.2.Design a product Design a product or service that or service that

meets or exceeds customer wantsmeets or exceeds customer wants3.3.Design processes Design processes that facilitates that facilitates

doing the job right the first timedoing the job right the first time4.4.Keep track of Keep track of resultsresults5.5.Extend these concepts to Extend these concepts to supplierssuppliers

The TQM ApproachThe TQM Approach


Seven Concepts of TQMSeven Concepts of TQM

Continuous improvementContinuous improvement Six SigmaSix Sigma Employee empowermentEmployee empowerment BenchmarkingBenchmarking JustJust--inin--time (JIT)time (JIT) Taguchi conceptsTaguchi concepts Knowledge of TQM toolsKnowledge of TQM tools


2. DoTest the

plan

3. CheckIs the plan working?

4. ActImplement

the plan

1.PlanIdentify the

improvement and make

a plan

Shewharts PDCA ModelShewharts PDCA Model


Six SigmaSix Sigma Originally developed by Motorola, Originally developed by Motorola,

adopted and enhanced by Honeywell and adopted and enhanced by Honeywell and GEGE

Two meaningsTwo meanings Statistical definition of a process that Statistical definition of a process that

is 99.9997% capable, 3.4 defects per is 99.9997% capable, 3.4 defects per million opportunities (DPMO)million opportunities (DPMO)

66


Two meaningsTwo meanings Statistical definition of a process that Statistical definition of a process that

is 99.9997% capable, 3.4 defects per is 99.9997% capable, 3.4 defects per million opportunities (DPMO)million opportunities (DPMO)

A program designed to reduce A program designed to reduce defects, lower costs, and improve defects, lower costs, and improve customer satisfactioncustomer satisfaction

Six SigmaSix Sigma

Mean

Lower limits Upper limits

3.4 defects/million

6

2,700 defects/million

3


Six Sigma ProcessSix Sigma Process DefineDefine MeasureMeasure AnalyzeAnalyze ImproveImprove ControlControl

DMAICDMAIC


Six Sigma Quality (Continued)Six Sigma Quality (Continued)

Six Sigma allows managers to readily describe Six Sigma allows managers to readily describe process performance using a common metric: process performance using a common metric: Defects Per Million Opportunities (DPMO)Defects Per Million Opportunities (DPMO)

1,000,000 x

units of No. x unit

per error for iesopportunit ofNumber

defects ofNumber

DPMO


Six Sigma Quality (Continued)Six Sigma Quality (Continued)Example of Defects Per Million Example of Defects Per Million

Opportunities (DPMO) calculation. Opportunities (DPMO) calculation. Suppose we observe 200 letters Suppose we observe 200 letters delivered incorrectly to the wrong delivered incorrectly to the wrong addresses in a small city during a addresses in a small city during a single day when a total of 200,000 single day when a total of 200,000 letters were delivered. What is the letters were delivered. What is the DPMO in this situation?DPMO in this situation?

000,1 1,000,000 x

200,000 x 1

200DPMO

So, for every one million letters delivered this citys postal managers can expect to have 1,000 letters incorrectly sent to the wrong address.

Cost of Quality: What might that DPMO mean in terms of over-time employment to correct the errors?


JustJust--inin--Time (JIT)Time (JIT)

Pull system of production scheduling Pull system of production scheduling including supply managementincluding supply management Production only when signaledProduction only when signaled

Allows reduced inventory levelsAllows reduced inventory levels Inventory costs money and hides process Inventory costs money and hides process

and material problemsand material problems

Encourages improved process and Encourages improved process and product qualityproduct quality


JustJust--InIn--Time (JIT) ExampleTime (JIT) Example

ScrapUnreliable VendorsCapacity

Imbalances

Work in process inventory level

(hides problems)


JustJust--InIn--Time (JIT) ExampleTime (JIT) Example

Reducing inventory revealsReducing inventory revealsproblems so they can be solvedproblems so they can be solved

ScrapUnreliable VendorsCapacity

Imbalances


Taguchi ConceptsTaguchi Concepts Engineering and experimental Engineering and experimental

design methods to improve product design methods to improve product and process designand process design Identify key component and process Identify key component and process

variables affecting product variationvariables affecting product variation

Taguchi ConceptsTaguchi ConceptsQuality robustnessQuality robustnessQuality loss functionQuality loss functionTargetTarget--oriented qualityoriented quality


Quality RobustnessQuality Robustness

Ability to produce products Ability to produce products uniformly in adverse manufacturing uniformly in adverse manufacturing and environmental conditionsand environmental conditionsRemove the effects of adverse Remove the effects of adverse

conditionsconditionsSmall variations in materials and Small variations in materials and

process do not destroy product process do not destroy product qualityquality


Unacceptable

Poor

GoodBest

Fair

Quality Loss FunctionQuality Loss FunctionHigh lossHigh loss

Loss (to Loss (to producing producing organization, organization, customer, customer, and society)and society)

Low lossLow loss

FrequencyFrequency

LowerLower TargetTarget UpperUpperSpecificationSpecification

TargetTarget--oriented quality oriented quality yields more product in yields more product in the best categorythe best category

TargetTarget--oriented quality oriented quality brings product toward brings product toward the target valuethe target valueConformanceConformance--oriented oriented quality keeps products quality keeps products within 3 standard within 3 standard deviationsdeviations

L = DL = D22CCwherewhere

L =L = loss to societyloss to societyD =D = distance from distance from

target valuetarget valueC =C = cost of deviationcost of deviation


Service QualityService Quality

ConvenienceConvenience ReliabilityReliability ResponsivenessResponsiveness TimeTime AssuranceAssurance CourtesyCourtesy TangiblesTangibles


Examples of Service QualityExamples of Service Quality

Dimension Examples1. Convenience Was the service center conveniently located?

2. Reliability Was the problem fixed?

3. Responsiveness Were customer service personnel willing and able to answer questions?

4. Time How long did the customer wait?

5. Assurance Did the customer service personnel seem knowledgeable about the repair?

6. Courtesy Were customer service personnel and the cashier friendly and courteous?

7. Tangibles Were the facilities clean, personnel neat?


Tools of TQMTools of TQMCheck sheetsCheck sheetsScatter diagramsScatter diagramsCauseCause--andand--effect diagramseffect diagramsPareto chartsPareto chartsFlowchartsFlowchartsHistogramHistogramStatistical process control chartStatistical process control chart


//

/ / /// /// ///// ////

//////

HourDefect 1 2 3 4 5 6 7 8

ABC

////

/

Seven Tools of TQMSeven Tools of TQM(a)(a) Check Sheet: Check Sheet: An organized method of An organized method of

recording datarecording data


Seven Tools of TQMSeven Tools of TQM(b)(b) Scatter Diagram: Scatter Diagram: A graph of the value A graph of the value

of one variable vs. another variableof one variable vs. another variable

AbsenteeismAbsenteeism

Prod

uctiv

ityPr

oduc

tivity


Seven Tools of TQMSeven Tools of TQM(c)(c) CauseCause--andand--Effect Diagram: Effect Diagram: A tool that A tool that

identifies process elements (causes) that identifies process elements (causes) that might effect an outcomemight effect an outcome

CauseCauseMaterialsMaterials MethodsMethods

ManpowerManpower MachineryMachinery

EffectEffect


Seven Tools of TQMSeven Tools of TQM(d)(d) Pareto Chart: Pareto Chart: A graph to identify and plot A graph to identify and plot

problems or defects in descending order of problems or defects in descending order of frequencyfrequencyFr

eque

ncy

Freq

uenc

y

Perc

ent

Perc

ent

AA BB CC DD EE


Seven Tools of TQMSeven Tools of TQM(e)(e) Flowchart (Process Diagram): Flowchart (Process Diagram): A chart that A chart that

describes the steps in a processdescribes the steps in a process


Flow ChartsFlow ChartsMRI FlowchartMRI Flowchart1.1. Physician schedules MRIPhysician schedules MRI2.2. Patient taken to MRIPatient taken to MRI3.3. Patient signs inPatient signs in4.4. Patient is preparedPatient is prepared5.5. Technician carries out MRITechnician carries out MRI6.6. Technician inspects filmTechnician inspects film

7.7. If unsatisfactory, repeatIf unsatisfactory, repeat8.8. Patient taken back to roomPatient taken back to room9.9. MRI read by radiologistMRI read by radiologist10.10. MRI report transferred to MRI report transferred to

physicianphysician11.11. Patient and physician discussPatient and physician discuss

1111

1010

20%20%

99

8880%80%

11 22 33 44 55 66 77


Seven Tools of TQMSeven Tools of TQM(f)(f) Histogram: Histogram: A distribution showing the A distribution showing the

frequency of occurrences of a variablefrequency of occurrences of a variableDistributionDistribution

Repair time (minutes)Repair time (minutes)

Freq

uenc

yFr

eque

ncy


Seven Tools of TQMSeven Tools of TQM(g)(g) Statistical Process Control Chart: Statistical Process Control Chart: A chart with A chart with

time on the horizontal axis to plot values of a time on the horizontal axis to plot values of a statisticstatistic

Upper control limitUpper control limit

Target valueTarget value

Lower control limitLower control limit

TimeTime


Quality Assurance using SPCQuality Assurance using SPC

Designed StandardDesigned Standard

Centre of specification Centre of specification limits (Target)limits (Target)

Upper Specification Limit Upper Specification Limit (USL)(USL)

Lower Specification Limit Lower Specification Limit (LSL)(LSL)

(USL (USL LSL): Desired LSL): Desired tolerancetoleranceThis represents the voice This represents the voice of the customerof the customer

Status of processStatus of process

Centre of the process Centre of the process (Process Average)(Process Average)

Upper Control Limit (UCL)Upper Control Limit (UCL) Lower Control Limit (LCL)Lower Control Limit (LCL) (UCL (UCL LCL): Spread of the LCL): Spread of the

processprocess

This represents the voice This represents the voice of the processof the process


VariabilityVariability

RandomRandom common causescommon causes inherent in a inherent in a

processprocess can be eliminated can be eliminated

only through only through improvements in improvements in the systemthe system

NonNon--RandomRandom special causesspecial causes due to identifiable due to identifiable

factorsfactors can be modified can be modified

through operator or through operator or management actionmanagement action


Quality MeasuresQuality Measures

AttributeAttribute a product characteristic that can be a product characteristic that can be

evaluated with a evaluated with a discrete responsediscrete response good good bad; yes bad; yes -- nono

VariableVariable a product characteristic that is a product characteristic that is

continuouscontinuous and can be measuredand can be measured weight weight -- lengthlength


Applying SPC to Service (cont.)Applying SPC to Service (cont.) HospitalsHospitals

timeliness and quickness of care, staff responses to timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and accuracy of paperwork, speed of admittance and checkoutscheckouts

Grocery StoresGrocery Stores waiting time to check out, frequency of outwaiting time to check out, frequency of out--ofof--stock stock

items, quality of food items, cleanliness, customer items, quality of food items, cleanliness, customer complaints, checkout register errorscomplaints, checkout register errors

AirlinesAirlines flight delays, lost luggage and luggage handling, waiting flight delays, lost luggage and luggage handling, waiting

time at ticket counters and checktime at ticket counters and check--in, agent and flight in, agent and flight attendant courtesy, accurate flight information, attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenancepassenger cabin cleanliness and maintenance


Applying SPC to Service (cont.)Applying SPC to Service (cont.) FastFast--Food RestaurantsFood Restaurants

waiting time for service, customer complaints, waiting time for service, customer complaints, cleanliness, food quality, order accuracy, cleanliness, food quality, order accuracy, employee courtesyemployee courtesy

Insurance CompaniesInsurance Companies billing accuracy, timeliness of claims processing, billing accuracy, timeliness of claims processing,

agent availability and response timeagent availability and response time


Control ChartsControl Charts

A graph that A graph that establishes control establishes control limits of a processlimits of a process

Control limitsControl limits upper and lower bands upper and lower bands

of a control chartof a control chart

Types of chartsTypes of charts Attributes

pp--chartchart cc--chartchart

Variables range (Rrange (R--chart)chart) mean (x bar mean (x bar

chart)chart)


Characteristics for process controlCharacteristics for process controlSome examplesSome examples

Sl. No. Type of Applications Characteristic for Measurement

1 Component Manufacturing Conformance of physical measurements of components and sub-assemblies to specifications

Conformance to operating characteristics of machines and other resources involved in the process

2 Final Assembly Number of defects in the product Conformance to test specifications Number of missing elements

3 Process Industries Temperature, Pressure and Heat specifications Conformance to product specifications Conformance to equipment specifications Vibrations and other variations in equipments

and sub-systems Conformance to specifications of the

automation & control system

4 Service Systems Number of defects in various business processes

Errors in processing documents Conformance to waiting time/lead time related

specifications


Population and Sampling Population and Sampling DistributionsDistributions

Distribution of Distribution of sample meanssample means

Standard Standard deviation of deviation of the sample the sample meansmeans

= = xx ==

nn

Mean of sample means = xMean of sample means = x

| | | | | | |

--33xx --22xx --11xx xx ++11xx ++22xx ++33xx

99.73%99.73% of all xof all xfall within fall within 33xx

95.45%95.45% fall within fall within 22xx


Control Charts for VariablesControl Charts for Variables

For variables that have For variables that have continuous dimensionscontinuous dimensions Weight, speed, length, Weight, speed, length,

strength, etc.strength, etc.

xx--charts are to control charts are to control the central tendency of the processthe central tendency of the process

RR--charts are to control the dispersion of charts are to control the dispersion of the processthe process

These two charts must be used togetherThese two charts must be used together


Setting Chart LimitsSetting Chart LimitsFor xFor x--Charts when we know Charts when we know

Upper control limit Upper control limit (UCL)(UCL) = x + z= x + zxxLower control limit Lower control limit (LCL)(LCL) = x = x -- zzxx

wherewhere xx == mean of the sample means or a target mean of the sample means or a target value set for the processvalue set for the process

zz == number of normal standard deviationsnumber of normal standard deviationsxx == standard deviation of the sample meansstandard deviation of the sample means

== / n/ n == population standard deviationpopulation standard deviationnn == sample sizesample size


Setting Control LimitsSetting Control LimitsHour 1Hour 1

SampleSample Weight ofWeight ofNumberNumber Oat FlakesOat Flakes

11 171722 131333 161644 181855 171766 161677 151588 171799 1616

MeanMean 16.116.1 == 11

HourHour MeanMean HourHour MeanMean11 16.116.1 77 15.215.222 16.816.8 88 16.416.433 15.515.5 99 16.316.344 16.516.5 1010 14.814.855 16.516.5 1111 14.214.266 16.416.4 1212 17.317.3

n = 9n = 9

LCLLCLxx = x = x -- zzxx = = 16 16 -- 3(1/3) = 15 3(1/3) = 15

For For 99.73%99.73% control limits, z control limits, z = 3= 3

UCLUCLxx = x + z= x + zxx = 16 + 3(1/3) = 17 = 16 + 3(1/3) = 17


17 = UCL17 = UCL

15 = LCL15 = LCL

16 = Mean16 = Mean

Setting Control LimitsSetting Control LimitsControl Chart Control Chart for sample of for sample of 9 boxes9 boxes

Sample numberSample number

|| || || || || || || || || || || ||11 22 33 44 55 66 77 88 99 1010 1111 1212

Variation due Variation due to assignable to assignable

causescauses

Variation due Variation due to assignable to assignable

causescauses

Variation due to Variation due to natural causesnatural causes

Out of Out of controlcontrol

Out of Out of controlcontrol


Setting Chart LimitsSetting Chart Limits

For xFor x--Charts when we dont know Charts when we dont know

Lower control limit Lower control limit (LCL)(LCL) = x = x -- AA22RR

Upper control limit Upper control limit (UCL)(UCL) = x + A= x + A22RR

wherewhere RR == average range of the samplesaverage range of the samplesAA22 == control chart factor found in Table.1 control chart factor found in Table.1 xx == mean of the sample meansmean of the sample means


Control Chart FactorsControl Chart Factors

Table 1Table 1

Sample Size Sample Size Mean Factor Mean Factor Upper Range Upper Range Lower RangeLower Rangen n AA22 DD44 DD3322 1.8801.880 3.2683.268 0033 1.0231.023 2.5742.574 0044 .729.729 2.2822.282 0055 .577.577 2.1152.115 0066 .483.483 2.0042.004 0077 .419.419 1.9241.924 0.0760.07688 .373.373 1.8641.864 0.1360.13699 .337.337 1.8161.816 0.1840.184

1010 .308.308 1.7771.777 0.2230.2231212 .266.266 1.7161.716 0.2840.284


Setting Control LimitsSetting Control LimitsProcess average x Process average x = 12= 12 ouncesouncesAverage range R Average range R = .25= .25Sample size n Sample size n = 5= 5


Setting Control LimitsSetting Control Limits

UCLUCLxx = x + A= x + A22RR= 12 + (.577)(.25)= 12 + (.577)(.25)= 12 + .144= 12 + .144= 12.144 = 12.144 ouncesounces

Process average x Process average x = 12= 12 ouncesouncesAverage range R Average range R = .25= .25Sample size n Sample size n = 5= 5

From From Table.1Table.1



UCLUCLxx = x + A= x + A22RR= 12 + (.577)(.25)= 12 + (.577)(.25)= 12 + .144= 12 + .144= 12.144 = 12.144 ouncesounces

LCLLCLxx = x = x -- AA22RR= 12 = 12 -- .144.144= 11.857 = 11.857 ouncesounces

Process average x Process average x = 12= 12 ouncesouncesAverage range R Average range R = .25= .25Sample size n Sample size n = 5= 5

UCL = 12.144UCL = 12.144

Mean = 12Mean = 12

LCL = 11.857LCL = 11.857


R R ChartChart

Type of variables control chartType of variables control chart Shows sample ranges over timeShows sample ranges over time

Difference between smallest and Difference between smallest and largest values in samplelargest values in sample

Monitors process variabilityMonitors process variability Independent from process meanIndependent from process mean


R R Chart Chart

For RFor R--ChartsCharts

Lower control limit Lower control limit (LCL(LCLRR)) = D= D33RR

Upper control limit Upper control limit (UCL(UCLRR)) = D= D44RR

wherewhereRR == average range of the samplesaverage range of the samples

DD33 and Dand D44 == control chart factors from Table.1 control chart factors from Table.1



UCLUCLRR = D= D44RR= (2.115)(5.3)= (2.115)(5.3)= 11.2 = 11.2 poundspounds

LCLLCLRR = D= D33RR= (0)(5.3)= (0)(5.3)= 0 = 0 poundspounds

Average range R Average range R = 5.3 = 5.3 poundspoundsSample size n Sample size n = 5= 5From From Table 1Table 1 DD44 = 2.115, = 2.115, DD33 = 0= 0

UCL = 11.2UCL = 11.2

Mean = 5.3Mean = 5.3

LCL = 0LCL = 0


Mean and Range ChartsMean and Range Charts(a)(a)These These sampling sampling distributions distributions result in the result in the charts belowcharts below

(Sampling mean is (Sampling mean is shifting upward but shifting upward but range is consistent)range is consistent)

RR--chartchart(R(R--chart does not chart does not detect change in detect change in mean)mean)

UCLUCL

LCLLCL

xx--chartchart(x(x--chart detects chart detects shift in central shift in central tendency)tendency)

UCLUCL

LCLLCL


Mean and Range ChartsMean and Range Charts

RR--chartchart(R(R--chart detects chart detects increase in increase in dispersion)dispersion)

UCLUCL

LCLLCL

(b)(b)These These sampling sampling distributions distributions result in the result in the charts belowcharts below

(Sampling mean (Sampling mean is constant but is constant but dispersion is dispersion is increasing)increasing)

xx--chartchart(x(x--chart does not chart does not detect the increase detect the increase in dispersion)in dispersion)

UCLUCL

LCLLCL


Control Charts for AttributesControl Charts for Attributes

For variables that are categoricalFor variables that are categoricalGood/bad, yes/no, Good/bad, yes/no,

acceptable/unacceptableacceptable/unacceptable

Measurement is typically counting Measurement is typically counting defectivesdefectives

Charts may measureCharts may measurePercent defective (pPercent defective (p--chart)chart)Number of defects (cNumber of defects (c--chart)chart)


Control Limits for pControl Limits for p--ChartsCharts

Population will be a binomial distribution, Population will be a binomial distribution, but applying the Central Limit Theorem but applying the Central Limit Theorem

allows us to assume a normal distribution allows us to assume a normal distribution for the sample statisticsfor the sample statistics

UCLUCLpp = p + z= p + zpp^^

LCLLCLpp = p = p -- zzpp^^wherewhere pp == mean fraction defective in the samplemean fraction defective in the sample

zz == number of standard deviationsnumber of standard deviationspp == standard deviation of the sampling distributionstandard deviation of the sampling distributionnn == sample sizesample size^^

pp(1 (1 -- pp))nnpp ==^^


pp--Chart for Data EntryChart for Data Entry(Sample size=100)(Sample size=100)

SampleSample NumberNumber FractionFraction SampleSample NumberNumber FractionFractionNumberNumber of Errorsof Errors DefectiveDefective NumberNumber of Errorsof Errors DefectiveDefective

11 66 .06.06 1111 66 .06.0622 55 .05.05 1212 11 .01.0133 00 .00.00 1313 88 .08.0844 11 .01.01 1414 77 .07.0755 44 .04.04 1515 55 .05.0566 22 .02.02 1616 44 .04.0477 55 .05.05 1717 1111 .11.1188 33 .03.03 1818 33 .03.0399 33 .03.03 1919 00 .00.00

1010 22 .02.02 2020 44 .04.04Total Total = 80= 80

(.04)(1 (.04)(1 -- .04).04)100100pp = = = .02= .02^^

p p = = .04= = .048080

(100)(20)(100)(20)


.11 .11

.10 .10

.09 .09

.08 .08

.07 .07

.06 .06

.05 .05

.04 .04

.03 .03

.02 .02

.01 .01

.00 .00


Frac

tion

defe

ctiv

eFr

actio

n de

fect

ive

| | | | | | | | | |22 44 66 88 1010 1212 1414 1616 1818 2020

pp--Chart for Data EntryChart for Data EntryUCLUCLpp = p + z= p + zpp = .04 + 3(.02) = .10= .04 + 3(.02) = .10^^

LCLLCLpp = p = p -- zzpp = .04 = .04 -- 3(.02) = 03(.02) = 0^^

UCLUCLpp = 0.10= 0.10

LCLLCLpp = 0.00= 0.00

p p = 0.04= 0.04


.11 .11

.10 .10

.09 .09

.08 .08

.07 .07

.06 .06

.05 .05

.04 .04

.03 .03

.02 .02

.01 .01

.00 .00


Frac

tion

defe

ctiv

eFr

actio

n de

fect

ive

| | | | | | | | | |22 44 66 88 1010 1212 1414 1616 1818 2020

UCLUCLpp = p + z= p + zpp = .04 + 3(.02) = .10= .04 + 3(.02) = .10^^

LCLLCLpp = p = p -- zzpp = .04 = .04 -- 3(.02) = 03(.02) = 0^^

UCLUCLpp = 0.10= 0.10

LCLLCLpp = 0.00= 0.00

p p = 0.04= 0.04

pp--Chart for Data EntryChart for Data Entry

Possible assignable

causes present


Control Limits for cControl Limits for c--ChartsCharts

Population will be a Poisson distribution, Population will be a Poisson distribution, but applying the Central Limit Theorem but applying the Central Limit Theorem

allows us to assume a normal distribution allows us to assume a normal distribution for the sample statisticsfor the sample statistics

wherewhere cc == mean number defective in the samplemean number defective in the sample

UCLUCLcc = c + = c + 33 cc LCLLCLcc = c = c -- 33 cc


cc--Chart for Cab CompanyChart for Cab Companyc c = 54= 54 complaintscomplaints/9/9 days days = 6 = 6 complaintscomplaints//dayday

|1

|2

|3

|4

|5

|6

|7

|8

|9

DayDay

Num

ber d

efec

tive

Num

ber d

efec

tive14 14

12 12 10 10 8 8 6 6 4 2 0 0

UCLUCLcc = c + = c + 33 cc= 6 + 3 6= 6 + 3 6= 13.35= 13.35

LCLLCLcc = c = c -- 33 cc= 6 = 6 -- 3 63 6= 0= 0

UCLUCLcc = 13.35= 13.35

LCLLCLcc = 0= 0

c c = 6= 6


Which Control Chart to UseWhich Control Chart to Use

Using an xUsing an x--chart and Rchart and R--chart:chart:Observations are variablesObservations are variablesCollect Collect 20 20 -- 2525 samples of n samples of n = 4= 4, or n , or n = =

55, or more, each from a stable process , or more, each from a stable process and compute the mean for the xand compute the mean for the x--chart chart and range for the Rand range for the R--chartchart

Track samples of n observations eachTrack samples of n observations each

Variables DataVariables Data



Using the pUsing the p--chart:chart:Observations are attributes that can Observations are attributes that can

be categorized in two states be categorized in two states We deal with fraction, proportion, or We deal with fraction, proportion, or

percent defectivespercent defectivesHave several samples, each with Have several samples, each with

many observationsmany observations

Attribute DataAttribute Data



Using a cUsing a c--Chart:Chart:Observations are attributes whose Observations are attributes whose

defects per unit of output can be defects per unit of output can be countedcounted

The number counted is a small part of The number counted is a small part of the possible occurrencesthe possible occurrences

Defects such as number of blemishes Defects such as number of blemishes on a desk, number of typos in a page on a desk, number of typos in a page of text, flaws in a bolt of clothof text, flaws in a bolt of cloth

Attribute DataAttribute Data


Process CapabilityProcess Capability

The natural variation of a process The natural variation of a process should be small enough to produce should be small enough to produce products that meet the standards products that meet the standards requiredrequired

A process in statistical control does not A process in statistical control does not necessarily meet the design necessarily meet the design specificationsspecifications

Process capability is a measure of the Process capability is a measure of the relationship between the natural relationship between the natural variation of the process and the design variation of the process and the design specificationsspecifications


Process Capability RatioProcess Capability Ratio

CCpp = = Upper Specification Upper Specification -- Lower SpecificationLower Specification

66

A capable process must have a A capable process must have a CCpp of at of at least least 1.01.0

Does not look at how well the process Does not look at how well the process is centered in the specification range is centered in the specification range

Often a target value of Often a target value of CCpp = 1.33 = 1.33 is used is used to allow for offto allow for off--center processescenter processes

Six Sigma quality requires aSix Sigma quality requires a CCpp = 2.0= 2.0




66

Insurance claims processInsurance claims process

Process mean x Process mean x = 210.0= 210.0 minutesminutesProcess standard deviation Process standard deviation = .516= .516 minutesminutesDesign specification Design specification = 210 = 210 33 minutesminutes




66



= = 1.938= = 1.938213 213 -- 2072076(.516)6(.516)




66



= = 1.938= = 1.938213 213 -- 2072076(.516)6(.516) Process is capable


Process Capability IndexProcess Capability Index

A capable process must have a A capable process must have a CCpkpk of at of at least least 1.01.0

A capable process is not necessarily in the A capable process is not necessarily in the center of the specification, but it falls within center of the specification, but it falls within the specification limit at both extremesthe specification limit at both extremes

CCpkpk = minimum of ,= minimum of ,UpperUpperSpecification Specification -- xxLimitLimit

33

LowerLowerx x -- SpecificationSpecification

LimitLimit33


Process Capability IndexProcess Capability IndexNew Cutting MachineNew Cutting Machine

New process mean x New process mean x = .250 inches= .250 inchesProcess standard deviation Process standard deviation = .0005 inches= .0005 inchesUpper Specification Limit Upper Specification Limit = .251 inches= .251 inchesLower Specification LimitLower Specification Limit = .249 inches= .249 inches




CCpkpk = minimum of ,= minimum of ,(.251) (.251) -- .250.250

(3).0005(3).0005




CCpkpk = = 0.67= = 0.67.001.001.0015.0015

New machine is NOT capable

CCpkpk = minimum of ,= minimum of ,(.251) (.251) -- .250.250

(3).0005(3).0005.250 .250 -- (.249)(.249)

(3).0005(3).0005

Both calculations result inBoth calculations result in


Interpreting Interpreting CCpkpk

Cpk = negative number

Cpk = zero

Cpk = between 0 and 1

Cpk = 1

Cpk > 1


Acceptance SamplingAcceptance Sampling Form of quality testing used for Form of quality testing used for

incoming materials or finished goodsincoming materials or finished goodsTake samples at random from a lot Take samples at random from a lot

(shipment) of items(shipment) of items Inspect each of the items in the sampleInspect each of the items in the sampleDecide whether to reject the whole lot Decide whether to reject the whole lot

based on the inspection resultsbased on the inspection results

Only screens lots; does not drive Only screens lots; does not drive quality improvement effortsquality improvement efforts


Acceptance SamplingAcceptance Sampling Form of quality testing used for Form of quality testing used for

incoming materials or finished goodsincoming materials or finished goodsTake samples at random from a lot Take samples at random from a lot

(shipment) of items(shipment) of items Inspect each of the items in the sampleInspect each of the items in the sampleDecide whether to reject the whole lot Decide whether to reject the whole lot

based on the inspection resultsbased on the inspection results

Only screens lots; does not drive Only screens lots; does not drive quality improvement effortsquality improvement efforts

Rejected lots can be: Returned to the

supplier Culled for

defectives (100% inspection)


Operating Characteristic Operating Characteristic CurveCurve

Shows how well a sampling plan Shows how well a sampling plan discriminates between good and discriminates between good and bad lots (shipments)bad lots (shipments)

Shows the relationship between Shows the relationship between the probability of accepting a lot the probability of accepting a lot and its quality leveland its quality level


Return whole shipment

The Perfect OC CurveThe Perfect OC Curve

% Defective in Lot% Defective in Lot

P(A

ccep

t Who

le S

hipm

ent)

P(A

ccep

t Who

le S

hipm

ent)

100 100

75 75

50 50

25 25

0 0 | | | | | | | | | | |00 1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

Cut-Off

Keep whole Keep whole shipmentshipment


An OC CurveAn OC Curve

Probability Probability of of

AcceptanceAcceptance

Percent Percent defectivedefective

| | | | | | | | |00 11 22 33 44 55 66 77 88

100 100 95 95

75 75

50 50

25 25

10 10

0 0

= 0.05= 0.05 producers risk for AQLproducers risk for AQL

= 0.10= 0.10

Consumers Consumers risk for LTPDrisk for LTPD

LTPDLTPDAQLAQLBad lotsBad lotsIndifference Indifference zonezone

Good Good lotslots

Figure S6.9Figure S6.9


AQL and LTPDAQL and LTPD

Acceptable Quality Level (AQL)Acceptable Quality Level (AQL)Poorest level of quality we are Poorest level of quality we are

willing to acceptwilling to accept

Lot Tolerance Percent Defective Lot Tolerance Percent Defective (LTPD)(LTPD)Quality level we consider badQuality level we consider badConsumer (buyer) does not want to Consumer (buyer) does not want to

accept lots with more defects than accept lots with more defects than LTPDLTPD


Producers and Consumers Producers and Consumers RisksRisks

Producer's risk Producer's risk (())Probability of rejecting a good lot Probability of rejecting a good lot Probability of rejecting a lot when the Probability of rejecting a lot when the

fraction defective is at or above the fraction defective is at or above the AQLAQL

Consumer's risk Consumer's risk (())Probability of accepting a bad lot Probability of accepting a bad lot Probability of accepting a lot when Probability of accepting a lot when

fraction defective is below the LTPDfraction defective is below the LTPD


SPC and Process VariabilitySPC and Process Variability

(a)(a) Acceptance Acceptance sampling (Some sampling (Some bad units accepted)bad units accepted)

(b)(b) Statistical process Statistical process control (Keep the control (Keep the process in control)process in control)

(c)(c) CCpkpk >1>1 (Design (Design a process that a process that is in control)is in control)

Lower Lower specification specification

limitlimit

Upper Upper specification specification

limitlimit

Process mean, Process mean, mm

s4quality tools

Documents

prentice hall

time x100

rate of quality

lean quality tools

timeloading time

good units

loadingloading timeshift

mtsmtsdowndown timeshift