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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