statistical thinking ans applications

7/30/2019 statistical thinking ans applications

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Chapter9

StatisticalThinking

andApplications


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StatisticalThinking

StatisticalThinkingisaphilosophyoflearningandactionbasedonthefollowing

fundamentalprinciples:

Allworkoccursinasystemofinterconnectedprocesses

Variationexistsinallprocesses

Understandingandreducingvariationarethekeystosuccess


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Inputs Outputs

Suppliers Customers

S I P O C

Process

Aseriesofactivitiesthatconvertsinputsinto

outputs

Process


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SYSTEM

External

Supplier

External

CustomerProcessA ProcessB ProcessC

Supplier Supplier Supplier Supplier

Customer Customer Customer Customer


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Average Target

VariationandTargets

Variationcanbethoughtofas:

1. Deviationsaroundtheoverallaverage,or

Average

2. Adeviationoftheoverallaveragefromadesired

target


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Variation

Manysourcesofuncontrollablevariation

exist(commoncauses)

Special(assignable)causesofvariationcanberecognizedandcontrolled

Failuretounderstandthesedifferences

canincreasevariationinasystem


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Definitions

CommonCause

Variationaprocesswouldexhibitif

behavingatitsbestSpecialCause

Variationfrominterventionofsources

externaltotheprocess

StructuralCause

Inherentprocessvariation(likecommon

cause)thatlookslikespecialcause

Hasapredictableonset


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CommonCauses

Numerous

Repetitive

Originatefrommanysources

Commontoallthedata

Predictableintermsofabandofvariation


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SpecialCauses

Sporadicinoccurrence

Onsetoftennotpredictable

OriginatefromfewsourcesIncreasetotalvariationoverandabove

existingcommoncauses Canbeonetimeupsets,or

PermanentchangestotheprocessMayenterorexitaprocessviaprocess

inputs(outsidesources)orthrough

conversionactivities


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Improvementfor

CommonCauses

Allthedataarerelevant Notjustthebadoroutofspecpoints

AfundamentalchangeisrequiredThreeimprovementstrategies: Stratify Disaggregate

Designedexperimentation

Managementshouldinitiateand

leadthechangeeffort


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Improvementfor

SpecialCauses

Worktogetverytimelydata

Immediatelysearchforcause

whencontrolchartgivesasignal

Nofundamentalprocesschanges

Seekwaystochangesomehigher

levelprocess Maintaingoodspecialcauses Preventrecurrenceofundesirable

specialcauses


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QuestionstoHelpDistinguishBetween

SpecialandCommonCauses

Didthishappenbecausewegotcaughtand

wereunlucky,ordidsomethingorsomeone

specificallycauseit?Unlucky=CommonCause

Specificevent=SpecialCause

Couldithaveelsewhere,atanothertime,to

someoneelse,withdifferentmaterials?Yes=CommonCause

No=SpecialCause

Wasitspecifictoaperson,material,condition

ortime?Yes=SpecialCause

No=CommonCause


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StructuralCausesofVariability

Variationthatispartofthesystem

butlookslikeaspecialcause

Consistentdifference(acrossspace)Amonginjectionmoldercavities

Acrossacoatedorextrudedroll

AroundapartStructureovertimeMachinewear

Consistentcyclicdata

Coatingrollpatterns


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DealingWithStructural

Variation

RemovestructureifpossibleRequireschangetotheprocess

Use3-ChartmethodStructureonlyaffectstheRange

chart

ModelstructureandremoveeffectRequiresdataanalysis

Doesnotreduceprocessvariability

Allowsbetterassessmentofother

sourcesofvariation


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Robustness-AnUnderused

Concept

KeyaspectofStatisticalThinking;

Reducetheeffectsof

uncontrollablevariationin:

Productdesign

Processdesign

Managementpractices

Anticipatevariationandreduceits

effects

R b f P d d


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RobustnessofProductandProcessDesign

Anotherwaytoreducevariation;

Anticipatevariation Designtheprocessorproducttobe

insensitivetovariation

Arobustprocessorproductismorelikelytoperformasexpected

100%inspectioncannotprovide robustness

Designprocesstobeinsensitive

tofactorsuncontrollablevariation


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ImprovetheSystem:

ReduceCommon

CauseVariation

AnticipateVariation:

DesignRobust

ProcessesandProducts

Quality

Improvement

ThreeWaystoReduce

VariationandImproveQuality

ControltheProcess:

EliminateSpecial

CauseVariation


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TwoFundamental

ManagementMistakes

1. Treatingasaspecialcauseanyfault,

complaint,mistake,breakdown,accident

orshortagewhenitactuallyisduetocommoncauses

2. Attributingtocommoncausesanyfault,

complaint,mistake,breakdown,accidentorshortagewhenitactuallyisduetoa

specialcause


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StatisticalProcess Control (SPC)SPC is the methodology for monitoring and optimizing

the process output, mainly in terms of variability, and

for judging when changes (engineering actions) are

required to bring the process back to a state of

control. This strategy of control differs from the

engineering process control (EPC) where the process isallowed to adapt by automatic control devices etc.


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SamplingMethods

Simplerandomsampling

SystematicsamplingStratifiedsampling

Clustersampling

Judgmentsampling


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SamplingError

Samplingerror(statisticalerror)

Nonsamplingerror(systematicerror) Factorstoconsider:

Samplesize

Appropriatesampledesign


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ProcessCapability

Therangeoverwhichthenaturalvariation

ofaprocessoccursasdeterminedbythe

systemofcommoncauses

Measuredbytheproportionofoutputthat

canbeproducedwithindesign

specifications


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TypesofCapabilityStudies

Peakperformancestudy-howaprocess

performsunderidealconditions

Processcharacterizationstudy-howa

processperformsunderactualoperatingconditions

Componentvariabilitystudy-relative

contributionofdifferentsourcesofvariation

(e.g.,processfactors,measurementsystem)


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ProcessCapabilityStudy

1.

2.

3.

4.

5.

6.

7.

Choosearepresentativemachineorprocess

Definetheprocessconditions

Selectarepresentativeoperator

Providetherightmaterials

Specifythegaugingormeasurementmethod

Recordthemeasurements

Constructahistogramandcomputedescriptivestatistics:meanandstandarddeviation

8. Compareresultswithspecifiedtolerances


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StatisticalThinkingand

StatisticalMethodsStatisticalthinkingprovidesaphilosophical

frameworkforuseofstatisticalmethods.

Theframeworkfocusesonprocesses,

recognizingvariation,andusingdatato

understandthenatureofthevariation.

Statisticalmethods,whenusedinthecontext

ofstatisticalthinking,canproduceanalyses

thatleadtoactionandresultingimprovement.


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StatisticsandImprovement

Process Variation Data

Statistical

Thinking

Statistical

Methods

Philosophy Analysis Action

Improve-

ment


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ComparisonofStatisticalThinking

andStatisticalMethods

Statistical

Thinking

Statistical

Methods

OverallApproach

DesiredApplication

PrimaryRequirement

LogicalSequence

Conceptual

Universal

Knowledge

Leads

Technical

Targeted

Data

Reinforces


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WithoutaProcessView

Peopledontunderstandtheproblem

andtheirroleinitssolution

Itisdifficulttodefinethescopeoftheproblem

Itisdifficulttogettorootcauses

Peoplegetblamedwhentheprocessistheproblem

Youcantimproveaprocessthatyoudontunderstand


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WithoutData

Everyoneisanexpert:

discussionsproducemoreheat

thanlightHistoricalmemoryispoor

Difficulttogetagreementon

Definitionoftheproblem Definitionofsuccess

Degreeofprogress


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WithoutUnderstanding

Variation

Managementisbythelastdatapoint

Fire-fightingdominates Specialcausemethodsareusedtosolve

commoncauseproblems

Tamperingandmicromanagingabound

Effortstoattaingoalsfail

Processunderstandingishindered Learningisslowed


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WithoutStatisticalThinking

Processmanagementisineffective

Improvementisslowed

Earlyon,wefailedtofocusadequatelyoncore

workprocessesandstatistics.DavidKearnsandDavidNelder,XeroxCorporation

Process Improvement Strategy


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StepsDescribetheprocess

CollectDataonKeyProcessand

OutputMeasures

AssessProcessStability

AddressSpecialCauseVariation

EvaluateProcessCapability

AnalyzeCommonCauseVariation

StudyCause-and-EffectRelationships

PlanandImplementChanges

ToolsFlowchart

ChecksheetDataSheet

Surveys

TimePlot/RunChart

ControlChart

SeeProblemSolvingStrategy

FrequencyPlot/Histogram

Standards

ParetoChart

StatisticalInferenceStratification

Disaggregation

Cause&EffectDiagram

ExperimentalDesign

ScatterPlots

InterrelationshipDigraphModelBuilding

ProcessImprovementStrategy

P bl S l i St t


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DocumenttheProblem

IdentifyPotentialrootCauses

ChooseBestSolutions

Implement/TestSolutions

MeasureResults

ProblemSolved?

Standardize

Checksheet

ParetoChart

ControlChart/TimePlot/RunChartIs/IsNotAnalysis

5Whys

Cause&EffectDiagram

Brainstorming

ScatterPlot

Stratification

InterrelationshipDigraph

Multivoting

AffinityDiagram

DesignofExperiments

Checksheet

ParetoChartControlChart/TimePlot/RunChart

Flowchart

Procedures

TrainingYes

No

ProblemSolvingStrategySteps Sample Tools


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DesignofExperiments

Atestorseriesofteststocomparetwoormoremethodstodeterminewhichisbetter,ortodeterminelevelsofcontrollablefactorstooptimizetheyieldofaprocessorminimizethevariabilityofaresponsevariable.

Factorialexperiment

Analysisofallcombinationsoffactorlevelstounderstandmaineffectsandinteractions


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BenefitsofDOE

MoreInformationfromfewer experiment

EvaluationofPlausibleRelationships

PredictionofFutureResults

OptimizationofResponses

ControlofProcesses


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HistoricalDataorDOE?

Historical

Data

takewhatyoucanget

limitedrange

takenovertime

correlation

Designed

Experiments

controlledconditions

definedrange

focusedtimeframe

causation

Whatisyourobjective?


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AdequateDesign

Hasstatedobjectivewithhypothesis statement

Considers

Replication

Blocking

RangesForm(splitplot,randomization,etc.)


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Considerationsfor

PlannedExperiments

Scopeofvalidity

factors

ranges

responses

NOTE:adequatemeasurementsneededfor

bothfactorsandresponses

ReplicationRandomization

Blocking


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ValueofReplication

Tension

Cure


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ValueofReplication

Tension

Cure


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Replication

Needyardstickforcomparisonso

youknoweffectsriseabovesystem

noise(commoncausevariability)

Makesurereplicatesaredifferent

(e.g.Notrepeatmeasuresonsame

sample)Typically,replicatesarespread

throughoutaseriesofexperiments


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EvaluatingtheResults

Aretheresultssignificant?

Statistically

Practically

Howdoyouknow?

Besureofsignificancebeforelookingatplots!


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SomethingImportant

IsResultSignificant?

LastPeriod ThisPeriod


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Thank you

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statistical thinking ans applications