MeasurementSystemsAnalysis

測量系統分析1WarmupExercise熱身練習TheNecessityofTrainingFarmHandsforFirstClassFarmsintheFatherlyHandlingofFarmLiveStockisForemostintheEyesofFarmOwners.SincetheForefathersoftheFarmOwnersTrainedtheFarmHandsforFirstClassFarmsintheFatherlyHandlingofFarmLiveStock,theFarmOwnersFeeltheyshouldcarryonwiththeFamilyTraditionofTrainingFarmHandsofFirstClassFarmersintheFatherlyHandlingofFarmLiveStockBecausetheyBelieveitistheBasisofGoodFundamentalFarmManagement.Task:Youhave60secondstocountthenumberoftimesthe6thletterofthealphabetappearsattherightparagraph.Areyouready?Go!給你60秒的時間數出右邊段落中第六個字母的出現次數.WarmupExerciseDocumentyouransweronascrapnoteAswereadtheanswers,typethemintoaMinitabdatasheet.RunahistogramontheresultsWhatareyourobservations?ObservedVariationWhichprocessisbest?

Observed(Total)2TotalVariability(Observedvariability)ProcessAProcessBMeasurementVariationWhichprocessisbest?=

Meas.System2

Observed(Total)2MeasurementVariabilityTotalVariability(Observedvariability)ProcessAProcessBPartVariationWhichprocessisbest?+

Actual(Part)2=PartVariability

(Actualvariability)

Meas.System2

Observed(Total)2ProcessAProcessBTotalVariability(Observedvariability)MeasurementVariabilityLSLUSLGoodPartsRejected?MeasurementUncertaintyWhatIsAnMSA?Scientificandobjectivemethodofanalyzingthevalidityofameasurementsystem一種科學客觀的方法，用于有效的分析測量系統A“tool”whichquantifies:一種工具，它量化：EquipmentVariation設備波動Appraiser(Operator)Variation評估者波動TheTotalVariationofaMeasurementSystem

測量系統總的波動MSAisNOTjustCalibration測量系統分析不僅僅是校準MeasurementSystemAnalysisisoftena“projectwithinaproject”測量系統分析經常是”項目中的項目”MainSourcesOfVariationMaterials材料Methods方法Machines機器People人員Environment環境Measures測量Measurementsystemsarethemostneglected測量系統經常被忽視

測量系統：是用來對被測特性定量測量或定性評價的儀器或量具、標準、操作、方法、夾具、軟件、人員、環境和假設的集合；用來獲得測量結果的整個過程。(MSA手冊第三版定義)MeasurementSystemAsAProcessCleanlinessTemperatureDimensionWeightCorrosionHardnessConductivityDensitySequenceTimingPositioningLocationSet-upPreparationCleanlinessTemperatureDesignPrecisionCalibrationResolutionStabilityWearCleanlinessVibrationAtmosphericpressureLightingTemperatureHumidityCompliance-procedureFatigueAttentionCalculationerrorInterpretationSpeedCoordinationVisionKnowledge-instrumentDexterityPeopleEnvironmentMeasurementErrorMethodMaterialMachineComponentsOfMeasurementErrorResolution/Discrimination分辨率Accuracy(biaseffects)準確度（偏離）Linearity線性Stability(consistency)穩定性（一致性）Repeatability(Precision)重復性（精度）Reproducibility(Precision)再現性（精度）Eachcomponentofmeasurementerrorcancontributetovariation,causingwrongdecisionstobemade測量誤差的每一項都可能對變差造成影響而使我們做出錯誤的決策CategoriesOfMeasurementErrorWhichAffectLocation影響位置的測量誤差Accuracy/BiasLinearityStabilityCategoriesOfMeasurementErrorWhichAffectSpread影響分布的測量誤差RepeatabilityReproducibilityPrecisionResolution/Discrimination分辨率Canchangebedetected?能偵測到改變嗎？Resolution?Accuracy/Bias?Linearity?Stability?Precision(R&R)?OKOKOKOKResolutionDefinitions分辨率定義Resolution/Discrimination分辨率Capabilitytodetectthesmallesttolerablechanges

可以偵測最小變化的能力InadequateMeasurementUnits不充分的度量單位Measurementunitstoolargetodetectvariationpresent度量單位過大而不能偵測到變化Guideline:“10BucketRule”

1/10原則Incrementsinthemeasurementsystemshouldbeone-tenththeproductspecificationorprocessvariation

測量系統必須精確到產品范圍或過程變差的1/10Sameprocessoutputbeingmeasured12345BetterDiscrimination12345PoorDiscrimination1.31Resolution/Discrimination分辨率Resolution分辨率OnHoldcomplaintsperhour每小時的投訴Complaint

NumberTransfers50Disputes 210Information 143Other 12 Total 415Whatisthecustomer’sbiggestcomplaint?OnHoldcomplaintsperhourComplaint

NumberTransfers 50SetuporMaintenanceDisputes 70ServiceReceivedDisputes 60BillingAmountDisputes 80UpdateAccountInformation 115RequestInformation 28Other 12Total 415Whatisthecustomer’sbiggestcomplaint?ResolutionAccuracy/Bias準確性/偏離Measurementsare“shifted”from“true”value測量值偏離真值Resolution?Accuracy/Bias?Linearity?Stability?Precision(R&R)?OKOKOKOKDifferencebetweentheobservedaveragevalueofmeasurementsandthemastervalue測量平均值與基準值之間的差異MasterValue(ReferenceStandard)AverageValueMastervalueisanaccepted,traceablereferencestandard基準值是公認的標準值Accuracy/Bias準確性/偏離xxxxxxxxxxxxxxxxxxLessaccurateMoreaccurateAccuracy/Bias準確性/偏離Linearity線性Measurementisnot“true”and/orconsistentacrosstherangeofthe“gage”測量系統在測量范圍內與儀器范圍的不一致性Resolution?Accuracy/Bias?Linearity?Stability?Precision(R&R)?OKOKOKOKLinearityFullRangeofGageReferenceValueNoBiasObservedAverageValueBiasLinearity-AttributeExampleSurveyscoring:__ SuperOutstanding! 10__ Outstanding! 9__ Incredible 8__ Excellent 7__ Great 6__ VeryGood 5__ Good 4__ OK 3__ Fair 2__ Poor 1Isthisafairscale?Stability穩定性Measurementdrifts測量系統偏移Resolution?Accuracy/Bias?Linearity?Stability?Precision(R&R)?OKOKOKOKStability穩定性Measurementsremainconstantandpredictableovertime

測量系統隨時間保持一致性與可預見性Forbothmeanandstandarddeviation

含均值與標準偏差Evaluatedusingcontrolcharts

可用控制圖來檢查Time2Time1MasterValue(ReferenceStandard)Precision精確性RepeatabilityandReproducibility重復性與再現性Resolution?Accuracy/Bias?Linearity?Stability?Precision(R&R)?OKOKOKOKPrecision精確性

2total=

2product/process+

2repeatability+

2reproducibility

GoodPrecisionPoorPrecisionMasterValueABAlsoknownasGageR&RRepeatability重復性VariationthatoccurswhenrepeatedmeasurementsaremadeofthesameitemunderabsolutelyidenticalconditionsSame:OperatorSet-upUnitsEnvironmentalconditions重復性：同一個人使用同樣的設備、同樣的儀器在同樣的條件下測量同一個樣品的差異Repeatability重復性MasterValuemeanmeanGoodRepeatabilityBadRepeatabilityMasterValueReproducibility再現性VariationthatoccurswhendifferentoperatorsmakethemeasurementsunderabsolutelyidenticalconditionsSame:Set-upsTestunitsEnvironmentalconditionsLocationsCompanies

再現性：不同的人使用同樣的儀器，在同樣的條件下測量同一個樣本之間的差異Reproducibility再現性評價者

A評價者B評價者

C評價者

C評價者

A評價者

BGoodReproducibilityBadReproducibilityMasterValueABCMasterValueABCR&R重復性與再現性TheBigPicture:LinkingThemAllTogether

2Total=

2R&R +

2Processoutput

2Total=

2Repeat+

2Reproducibility+

2Processoutput

2Total=

2Repeat+

2Oper+

2Oper?Processoutput+

2ProcessoutputMeasurementErrorMatchingExerciseMatchthemeasurementelementtothepicturethatbestdescribesit12345A.AccuracyB.StabilityC.LinearityD.ResolutionE.PrecisionTime2Time11.2.3.4.5.ReferenceValueObservedAverageValue

Type1GageStudy

類型1量具分析35PurposeOfType1GageStudyTodeterminehowmuchofyourobservedprocessvariationisduetomeasurementsystemvariation.

確定觀測到的過程變異有多少是由于測量系統本身的變異Tocombinedeffectsofbiasandrepeatabilitybasedonmultiplemeasurementsfromasinglepart.

通過對單個產品的多次測量來計算偏倚和重復性的影響Type1GageStudyshouldbedonepriortoconductingothergagerepeatabilityandreproducibilitystudies.Todetermineifcalibrationisneed量具的分析應該在做重復性和再現性之前做,來確定是否量具需要校準。SampleRuleOnemastersample(knownreferencevalue)取一個已知標準值的標準樣品Referencevaluescanbedeterminedinmanyways,dependingonindustrystandardsandcompanyandcustomerexpectations.Someofthebasesforreferencevaluesare:標準值可以通過多種方法獲得，根據行業和公司標準及客戶的期望。

1)averageofrepeatedmeasurementsfrommoreaccuratemeasuringequipment用更準確的測量設備測量多次取平均值2)valuesendorsedbyaprofessionalgroup專業機構認可的值3)valuesagreeduponbytheaffectedparties客戶認可的值4)valuesdefinedbylaw法律規定的值Tomeasurethemastersample25timesinsameconditionatleast,recordthemeasurements.

在相同條件下重復測量標準樣品至少25次，記錄每次測量數據StudyMethod在此處輸入測量數據在此處輸入標準值在此處輸入測量值的公差規格ExampleofType1GageStudy1OpentheworksheetSHAFT.MTW.2ChooseStat>QualityTools>GageStudy>Type1GageStudy.3InMeasurementdata,enterDiameter.4InReference,type12.305.5UnderTolerance,chooseUpperspec-lowerspecandtype0.05.ClickOK.ExampleofType1GageStudy1）分析結果顯示偏倚量是-0.00231，P值等于0說明測量系統的偏倚是統計顯著的

同樣從圖上可以看出大部分的測量數據都低于標準值。2）Cg是公差和測量變異進行比較，CgK是公差和測量變異及偏倚量兩者進行比較

Cg和CgK越大，表示測量系統的變異相對公差來說越小。通常Cg和CgK要求大于1.333）%Var(repeatability)由于Cg來確定，%Var(repeatabilityandbias)由Cgk來確定.%Var值小表示測量值變異相對公差而言小.能力指標1.33相當于%Var＝15%.AttributeMeasurementSystemStudies

離散型數據

測量系統研究41PurposeOfAttributeMSAAssessstandardsagainstcustomers’requirements

對顧客要求的標準進行評定Determineifallappraisersusethesamecriteria

確定所有的檢驗者使用相同的標準Quantifyrepeatabilityandreproducibilityofoperators

量化操作者的重復性與再現性Identifyhowwellmeasurementsystemconformstoa“knownmaster”

確定測量系統對已知標準的符合程度Discoverareaswhere:發現一些領域：

Trainingisneeded需要培訓Proceduresarelacking缺少規程Standardsarenotdefined標準定義不清晰SampleRule30samplesatleast,

3appraisersandtwicetests

需要3個測量者，最少30個樣本與每個樣本2次測試40%~45%forpasssamples

40%~45%的好樣本40%~45%forfailsamples

40%~45%的壞樣本10%forequivocalsamples(ifpossible)

10%的邊緣樣本Thecriteriaforsamplesshouldbedeterminedinadvance.樣本的好壞標準需提前確定下來Makesuretherandomizationforthetest

保證樣本測試的隨機性

AttributeMSA-ExcelMethodAllowsforR&Ranalysiswithinandbetweenappraisers

可以分析評估者之間的R&RTestforeffectivenessagainststandard

對標準判斷的有效性Limitedtonominaldataattwolevels

只能用于兩個水平的名義性數據DATE:1/4/2001AttributeLegend5(usedincomputations)NAME:AcmeEmployee1PassPRODUCT:Widgets2FailBUSINESS:EarthProductsKnownPopulationSample#AttributeTry#1Try#2Try#1Try#2Try#1Try#21PassPassPassPassPassPassPass2PassPassPassPassPassPassPass3PassPassPassPassPassPassPass4PassPassPassPassPassFailPass5FailFailFailFailFailPassFail6FailPassPassPassPassPassPass7PassPassPassPassPassPassPass8PassPassPassPassPassPassPass9FailFailFailFailFailFailFail10PassPassPassPassPassPassPass11PassPassPassPassPassPassPass12PassPassPassPassPassPassPass13PassPassPassPassPassPassPass14PassPassPassPassPassFailPass15FailFailFailFailFailPassFail16PassPassPassPassPassPassPass17PassPassPassPassPassPassPass18PassPassPassPassPassPassPass19FailFailFailFailFailFailFail20PassPassPassPassPassPassPass21PassPassPassPassPassPassPass22PassFailFailPassPassPassPass23PassPassPassPassPassPassPass24PassPassPassPassPassFailPass25FailFailFailFailFailFailFail26PassPassPassPassPassPassPass27PassPassPassPassPassPassPass28PassPassPassPassPassPassPass29FailFailFailFailFailFailFail30PassPassPassPassPassPassPassOperator#1Operator#2Operator#3AttributeMSAExampleOpenScoringExample100%istargetforallscores<100%indicatestrainingrequired%Appraiserscore=repeatabilityScreen%EffectivenessScore=reproducibility%Scorevs.AttributeindividualerroragainstaknownpopulationScreen%Effectivevs.AttributeTotalerroragainstaknownpopulation100.00%100.00%83.33%93.33%96.67%80.00%SCREEN%EFFECTIVESCORE->80.00%SCREEN%EFFECTIVESCOREvs.ATTRIBUTE->76.67%%APPRAISERSCORE->%SCOREVS.ATTRIBUTE->StatisticalReportStatisticalReportStatisticalReport-ContMINITABMethod-DataEntrySamedataasExcelexample

與Excel例中相同的數據Arrangedinmultiplecolumns

數據存放在多欄中Datacanalsobestackedinsinglecolumn

數據也可以堆疊在單獨一欄中AttributeStudy-MINITABAnalysisAttributeStudy-MINITABAnalysis1.Select“MultipleColumns”ifdataisun-stacked2.Enternumberofappraisersandtrials3.Enternameofcolumnwith“Known”4.SelectOK1.Select“SingleColumn”ifdataisstackedMINITABGraphicalOutputLowervariationwithinappraiserHighervariationwithinappraiserLowervariationappraiservs.standardHighervariationappraiservs.standardNotincludedifno“Known”MINITABSessionWindowResultsEachAppraiservs.StandardAssessmentAgreementAppraiser#Inspected#MatchedPercent(%)95.0%CIBob302893.3(77.9,99.2)Sue302996.7(82.8,99.9)Tom302480.0(61.4,92.3)#Matched:Appraiser'sassessmentacrosstrialsagreeswithstandard.AssessmentDisagreementAppraiser#Pass/FailPercent(%)#Fail/PassPercent(%)#MixedPercent(%)Bob114.2914.3500.0Sue114.2900.000.0Tom114.2900.0516.7#Pass/Fail:Assessmentsacrosstrials=Pass/standard=Fail.#Fail/Pass:Assessmentsacrosstrials=Fail/standard=Pass.#Mixed:Assessmentsacrosstrialsarenotidentical.BetweenAppraisersAssessmentAgreement#Inspected#MatchedPercent(%)95.0%CI302480.0(61.4,92.3)#Matched:Allappraisers'assessmentsagreewitheachother.AllAppraisersvs.StandardAssessmentAgreement#Inspected#MatchedPercent(%)95.0%CI302376.7(57.7,90.1)#Matched:Allappraisers'assessmentsagreewithstandard.Individualvs.StandardDisagreementassessment(repeatability)Betweenappraisers(reproducibility)Totalagreement(againstknown)AttributeMSAExercise5人一組,選3人為檢查員,一人為記時員,一人為數據錄入員。發給每組3份AttributeGageR&R樣本。每份樣本包含20個方盒，每個方盒包含25個字母或數字.如果方盒包含任何數字即被認為是有缺陷的（FAIL）。讓3個檢查員獨立地評估手中的第一份樣本并判斷每一個方盒是否有缺陷每個方盒只給5秒的時間做判斷。當3位檢查員完成第1份樣本后，將被提供第2份樣本并重復以上步驟。數據錄入員將小組答案錄入AttributeR&R.xls全部完成后，老師將提供標準答案。小組將標準答案錄入，得到R&R的最終分數.每組展示自己的AttributeGageR&Rscore。VariablesMeasurementSystemStudies

連續型數據

測量系統研究56StepVariablesMSAStep1:Randomlyselect10samples.Inaddition,identifytheoperatorswhousethisinstrumentdaily.第一步:隨機選取10個能夠代表過程變異的樣品,指定常用該檢驗裝置的操作員來做檢查人員Step2:Calibratethegageorverifythelastcalibrationdateisvalid.第二步:檢驗儀器,確認儀器在校準合格期以內Step3:SetuptheMinitabdatacollectionsheetfortheR&Rstudy.第三步:用Minitab設定做GR&R分析的數據收集表格Step4:Askthefirstoperatortomeasureallthesamplesonceinrandomorder.Blindsampling,inwhichtheoperatordoesnotknowtheidentityofeachpartshouldbeusedtoreducehumanbias.第四步:要求第一個操作員隨機測量所有樣品一次,注意不能讓操作員知道樣品的編號,以減少人為偏差.Step5:Havethesecondoperatormeasureallthesamplesonceinrandomorderandcontinueuntilalloperatorshavemeasuredthesamplesonce(thisistrial1)第五步:讓第二個操作員隨機測量所有樣品一次,繼續直到所有操作員都測量樣品一次.這算完成第一輪測量.StepVariablesMSAStep6:Repeatsteps4&5fortherequirednumberoftrials.Itisbestifthesemeasurementscanbedoneoverseveraldays.第六步:重復第4和第5步直到完成需要的輪次.如果可能,測量最好是在跨時間段完成.Step7:EnterthedataandtoleranceinformationintoMinitab

第七步:把數據和公差信息輸入到Minitab中Step8:Analyzetheresultsbyassessingthequalityofthemeasurementsystembasedontheguidelinesonthefollowingpage.Determinefollow-upactions.第八步:根據后續的測量系統評估指標的指導原則來分析測量系統是否可以接受,決定采取必要的行動.SAMPLESELECTIONOption1:ifprocessvariabilityisknown,thesamplesselectedshouldberepresentativeofthenormalprocess/productvariationOption2:ifprocessvariabilityisunknown,thesamplesselectedshoulduniformlyspanbeyondthewidthofthespecs樣品選擇的原則:1)如果過程變異已知,那么樣品要盡量展現正常過程/產品的變異范圍

2)如果過程變異未知,那么樣品要盡量在規格范圍內均勻取樣.TrialsAndDataCollectionGenerallytwotothreeoperators

一般選取2到3個操作者Generally5-10processoutputstomeasure

選取5到10個樣本進行測量Eachprocessoutputismeasured2-3times(replicated)byeachoperator

每個操作者測量每個樣本2到3次RandomizationisCritical隨機很關鍵GR&REvaluateGuideline%Contribution=×100%%StudyVariation=×100%%Tolerance=×100%Numberofdistinctcategories=Round{×1.41}部品散布(σpart)測定散布(σMS)σ2MSσ2TotalσMSσTotal5.15×σMSTolerance

(*Tolerance=USL-LSL)區分%Contribution%StudyVariation或%Tolerance辨別范周良好<1%<10%>10費用/考慮重要性1~10%10~30%5~9不可使用>10%>30%<5AcceptabilitySummaryTabularMethod%Contribution1%10%Process

Control

%StudyVariation10%30%Product

Control

%Tolerance10%30%Numberof

Distinct

Categories105DesirabletoHaveAll4IndicatorsSay“Go”VariablesMSA-MINITABExampleOpenthefileVariableMSA.mtwUSL=1.0LSL=0.5Replicate1Replicate2(Randomizedorder)MSAUsingMINITAB10ProcessOutputs3Operators2ReplicatesHaveOperator1measureallsamplesonce(asshownintheoutlinedblock)Then,haveOperator2measureallsamplesonceContinueuntilalloperatorshavemeasuredsamplesonce(thisisReplicate1)RepeatthesestepsfortherequirednumberofReplicatesEnterdataintoMINITABin3columnsasshownUSL=1.5LSL=0.5Replicate1Replicate2(Randomizedorder)ManipulateTheDataYourdatainMINITABshouldinitiallylooklikethis.YouwillneedtoSTACKyourdatasothatalllikedataisinonecolumnonlyNowyouarereadytorunthemacrofordataanalysisUsethecommands >Data