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1、Chapter 3.2Measurement Systems Analysis测量系统分析测量系统分析2测量是科学的基础测量是科学的基础“I often say that when you measure what you are speaking about and express it in numbers,you know something about it.”LORD KELVINThe Science of Measurement3Effects of Measurement ErrorAveragesVariabilitymmmtotalproductmeas.system=+M

2、easurement System BiasMeasurement System VariabilityAccuracyPrecisions s2total =s s2product +s s2meas system4测量误差测量误差平均值平均值变差变差mmm总产品测量系统=+测量系统的偏差测量系统的变差准确度精确度s s2total =s s2产品 +s s2测量系统Sources of Measurement VariationM easurement VariationHumidityCleanlinessVibrationLine Voltage VariationTemperatur

3、e FluctuationOperator TechniqueStandard ProceduresSufficient Work TimeM aintenance StandardCalibration FrequencyOperator TrainingEase of Data EntryAlgorithm InstabiltyElectrical InstabilityWear Mechanical instabilityGageEnvironmentWork Methods6Measurement VariationHumidityCleanlinessVibrationLine Vo

4、ltage VariationTemperature FluctuationOperator TechniqueStandard ProceduresSufficient Work TimeMaintenance StandardCalibration FrequencyOperator TrainingEase of Data Entry 电性能不稳定磨损 机械不稳定性量具量具环境环境测量方法测量方法计算不稳定取得数据的难易操作员培训校准频率量具维护标准足够的工作时间标准操作规程操作员技术湿度清洁程度震动线电压波动温度波动7看到的不一看到的不一定真实定真实Possible Sources o

5、f Process VariationLong-termProcess VariationShort-termProcess VariationVariationw/i sampleActual Process VariationStabilityLinearityRepeatability Accuracy Variation dueto gageVariation dueto operatorsMeasurement VariationObserved Process VariationWe will look at“repeatability”and“reproducibility”as

6、 these are the primary contributors to measurement error.Reproducibility9过程变差剖析过程变差剖析长期过程变差短期抽样产生的变差实际过程变差稳定性线性重复性重复性 准确度 量具变差操作员造成的变差测量误差过程变差观测值“重复性”和“再现性”是测量误差的主要来源再现性再现性过程变差AccuracylAccuracy Does the average of the measurements deviate from the true value?lTrue value:n Theoretically correct value

7、n NIST standardslBiasn Distance between average value of all measurements and true valuen Amount gage is consistently off targetn Systematic error or offset11准确度(Accuracy)l准确度准确度(Accuracy)测量的平均值是否与真值吻合测量的平均值是否与真值吻合?l真值真值(True Value):n理论上正确的值理论上正确的值 n国际度量衡标准国际度量衡标准l偏倚（偏倚（Bias)n测量值的均值与真值的距离测量值的均值与真值的距

8、离n测量系统持续地偏离目标测量系统持续地偏离目标n系统错误系统错误BIAS Is the difference between the observed average of the measurement and the reference value.The reference-value is the value that serves as an agreed-upon reference.The reference value can be determined by averaging several measurements with a higher level(e.g.,me

9、trology lab)of measuring equipment.ObservedAverageValueReferenceValueBIAS Definition13BIAS 测量结果的平均值与参考值的差异.参考值（参考值（reference-value）是一个预先认定的参考标准是一个预先认定的参考标准.该标准该标准可用更高一级测量系统测量的平均值来确定可用更高一级测量系统测量的平均值来确定(例如：高例如：高一级计量室一级计量室)观测平均值参考值偏倚偏倚BIAS X1=0.75mmX6=0.8mmX2=0.75mmX7=0.75mmX3=0.8mmX8=0.75mmX4=0.8mmX9=

10、0.75mmX5=0.65mmX10=0.7mmOne Part Measured Ten Times by One AppraiserWhat else do you need to determine BIAS?The reference Value determined by the layout inspection equipment(ensure this equipment went through a Gage R&R)is 0.80mm.The process variation for the part is 0.70mm.=0.75Bias=0.75-0.8=-0.05%

11、Bias=1000.05/0.70=7.1%This means 7.1%of the process variation is BIASXX=10BIAS EXAMPLE:15X1=0.75mmX6=0.8mmX2=0.75mmX7=0.75mmX3=0.8mmX8=0.75mmX4=0.8mmX9=0.75mmX5=0.65mmX10=0.7mm同一操作者对同一工件测量10次如果参考标准是 0.80mm.过程变差为0.70mm=0.75Bias=0.75-0.8=-0.05%Bias=1000.05/0.70=7.1%表明表明 7.1%的过程变差是偏倚的过程变差是偏倚 BIASXX=10偏

12、倚偏倚BIAS 实例实例:PrecisionlTotal variation in the measurement systemlMeasure of natural variation of repeated measurementslTerms:Random Error,Spread,Test/Retest errorlRepeatability and ReproducibilitysssMSGO222=+17l测量系统总变差测量系统总变差l通过重复测量的方法测量到的过程自然变差通过重复测量的方法测量到的过程自然变差l代表名词：重复性（代表名词：重复性（Repeatability）和再现

13、性（和再现性（Reproducibility）sssMSGO222=+精确度（精确度（Precision)Precision:RepeatabilitylThe inherent variability of the measurement systemlVariation in measurements obtained with a gage when used several times by one operator while measuring a characteristic on one part.lEstimated by the pooled standard deviat

14、ion of the distribution of repeated measurements lRepeatability is less than the total variation of the measurement systemsGsGRd=2*19l测量系统内在的变异性测量系统内在的变异性l基于重复测量的数据，用分基于重复测量的数据，用分组后组内的标准偏差来估算组后组内的标准偏差来估算 l小于测量系统的总变差小于测量系统的总变差sGsGRd=2*重复性重复性指同指同一一 人使用同一测量工具对同一对人使用同一测量工具对同一对象（产品）的同一特性进行多次测量中产生的变象（产品）的

15、同一特性进行多次测量中产生的变差，用于估计短期的变差差，用于估计短期的变差Master Value精确度：重复性精确度：重复性Precision:ReproducibilitylOperator variability of the measurement systemlVariation in the average of the measurements made by different operators using the same gage when measuring a characteristic on one partlEstimated by the standard d

16、eviation of the difference in averages,based on measurements taken by different operators lMust be adjusted for gage variationlReproducibility is less than the total variation of the measurement systemsOsORd=2*21精确度：再现性精确度：再现性l测量系统中操作员产生的变异测量系统中操作员产生的变异l基于不同操作者的测量数据，按操基于不同操作者的测量数据，按操作员分组，通过组平均值的差来估作

17、员分组，通过组平均值的差来估。l应扣除量具的因素（组内变差）应扣除量具的因素（组内变差）l比测量系统总变差小比测量系统总变差小sOsORd=2*Inspector AMaster ValueInspector BInspector CInspector AInspector BInspector C再现性再现性指不同的人在对同种特性进行测量指不同的人在对同种特性进行测量时产生的变差时产生的变差LinearityDifference in the accuracy values of a gage through the expected operating range of the gage5

18、04030201055453525155StandardTrialsR-Squared=0.981Y=0.934227+0.994959XRegression Plot504030201055453525155StandardTrialsR-Squared=0.982Y=0.245295+0.99505XLinearity is N ot G oodGood LinearityBad Linearity23线性（线性（Linearity）量具在不同测量范围的准确度和精确度的变化，当测量范围较宽时尤为要关注量具在不同测量范围的准确度和精确度的变化，当测量范围较宽时尤为要关注50403020105

19、5453525155S tandardTrialsR-Squared=0.981Y=0.934227+0.994959XRegression Plot504030201055453525155StandardTrialsR-Squared=0.982Y=0.245295+0.99505XLinearity is N ot G ood好的线性好的线性差的线性差的线性StabilitylThe distribution of measurements remains constant and predictable over time for both mean and standard devi

20、ationlTotal variation in the measurements obtained with a gage,on the same master or master parts,when measuring a single characteristic over an extended time period.lEvaluated using a trend chart or multiple measurement analysis studies over timeTime-1Time-2timeMagnitudeStability25l在一段时间内，测量结果的分布无在

21、一段时间内，测量结果的分布无论是均值还是标准偏差都保持不变论是均值还是标准偏差都保持不变和可预测的和可预测的l通过较长时间内，用被监视的量具通过较长时间内，用被监视的量具对相同的标准或对相同的标准或 标准件的同一特性标准件的同一特性进行测量的总变异来监视进行测量的总变异来监视l可用时间走势图进行分析可用时间走势图进行分析稳定性（稳定性（Stability）时间-1时间-2时间稳定性量值26Discriminationl The technological ability of the measurement system to adequately differentiate between

22、values of a measured parameter.RulerCaliperMicrometer.28.279.2794.28.282.2822.28.282.2819.28.279.279127测量系统的分辨率（测量系统的分辨率（discrimination）l要求不低于过程变差或允许偏差（要求不低于过程变差或允许偏差（tolerance）的十分之一的十分之一l零件之间的差异必须大于最小测量刻度零件之间的差异必须大于最小测量刻度l极差控制图可显示分辨率是否足够极差控制图可显示分辨率是否足够n 看控制限内有多少个数据阶级看控制限内有多少个数据阶级l不同数据等级的计算为不同数据等级的计

23、算为 零件的标准偏差零件的标准偏差/总的量具偏差总的量具偏差*1.41.直尺直尺卡尺卡尺千分尺千分尺.28.279.2794.28.282.2822.28.282.2819.28.279.2791lGenerally two or three operatorslGenerally 10 units to measurelEach unit is measured 2-3 times by each operatorGage R&R studylDetermine if reproducibility is an issue.If it is,select the number of oper

24、ators to participate.lOperators selected should normally use the measurement system.lSelect samples that represent the entire operating range.lGage must have graduations that allow at least one-tenth of the expected process variation.lInsure defined gaging procedures are followed.lMeasurements shoul

25、d be made in random order.lStudy must be observed by someone who recognizes the importance of conducting a reliable study.29计量型数据的计量型数据的GR&RGR&R研究研究均值-极差（X-R）法是确定测量系统的重复性和再现性的数学方法，步骤如下：1 选择三个测量人（A,B,C）和10个测量样品。测量人应有代表性，代表经常从事此项测量工作的QC人员或生产线人员 10个样品应在过程中随机抽取，可代表整个过程的变差，否则会严重影响研究结果。2 校准量具3 测量，让三个测量人对1

26、0个样品的某项特性进行测试，每个样品每人测量 三次，将数据填入表中。试验时遵循以下原则：盲测原则1：对10个样品编号，每个人测完第一轮后，由其他人对这10个样品进行随机的重新编号后再测，避免主观偏向。盲测原则2：三个人之间都互相不知道其他人的测量结果。4 计算30测试人BC样品号第一次第二次第三次极差第一次第二次第三次极差第一次第二次第三次极差 样品均值12345678910平均值平均值Average XARAAverage XBRBAverage XCRCRpA计算A测的所有样品的总平均值XA。同样方法计算RB,XB,RC,Xc对每个样品由三个人所测得的9个测试值求平均值，计算这些均值的极差

27、Rp计算A对每个样品三次测试结果的极差，然后计算10 个样品的极差的均值RA31测量系统分析测量系统分析R=(RA+RB+RC)/3XDIFF=MaxXA,XB,XC-MinXA,XB,XC重复性-设备变差 EV=RK1 再现性-测验人变差 AV=(XDIFF K2)2-(EV2/nr)过程变差 PV=RP K3R&R=(EV2+AV2)总变差 TV=(R&R2+PV2)%EV=EV/TV%AV=AV/TV%R&R=R&R/TV%PV=PV/TVP/T=R&R/Tolerancen=样品个数r=每个人对每个样品的试验次数rK1234.453.05K2233.652.70测试人数nK378910

28、1.821.741.671.62K1=5.15/d2*AV计算中，如根号下出现负值，AV取值032lEV=Equipment Variation(Repeatability)仪器变差仪器变差(重复性重复性)lAV=Appraiser Variation(Reproducibility)测量人变差测量人变差(再现性再现性)lR&R=Repeatability&Reproducibility重复性与再现性重复性与再现性lPV=Part Variation零件变差零件变差lTV=Total Variation of R&R and PV总变差总变差lK1-Trial,K2-Operator,&K3-

29、Part ConstantsGR&R研究中的名词研究中的名词33GR&R sheetR&R=(EV)2+(AV)2P/T=100 x(R&R)/Tolerance%R&R=100 x(R&R)/TVLong Method 0.1019.1318.91测试人ABC样品号第1次第2次第3次极差第1次第2次第3次极差第1次第2次第3次极差样品均值15.325.325.320.005.345.345.360.025.305.345.300.045.3325.445.405.440.045.465.465.480.025.465.405.420.065.4435.485.485.500.025.505.

30、465.480.045.505.505.500.005.4945.205.225.200.025.245.265.260.025.225.225.240.025.2355.245.245.240.005.245.245.260.025.285.245.240.045.2565.525.505.500.025.545.525.560.045.585.545.560.045.5475.385.385.380.005.405.425.440.045.405.365.380.045.3985.345.345.360.025.365.385.380.025.365.345.360.025.3695.44

31、5.445.420.025.465.445.440.025.445.465.420.045.44105.405.405.400.005.405.425.400.025.405.425.400.025.40平均值平均值5.385.375.385.395.395.415.395.385.38RpAverage XA5.37RA0.01Average XB5.40RB0.03Average XC5.39RC0.030.307R=0.02UCLR=(R)X(D4)#trial D4 X diff.=0.02UCLR2=0.07823.27UCLR3=0.06232.58Total Tolerance0

32、.5重复性-Equipment Variation(EV)EV=R X K1#trialK124.56EV=0.07333.05%EV=14.47再现性-Appraiser Variation(AV)AV=(Xdiff.x K2)2-(EV)2/(n x r)OperatorK2n=样品个数23.65AV=0.06r=测试次数32.7%AV=12.17过程变差-Process Variation(PV)PV=Rp X K3#PartsK3PV=0.49771.8281.7491.67101.62总变差-Total Variation(TV)TV=(R&R2+PV2)TV=0.506卡尺的R&R

33、研究 Excel 运算34R&R 对过程能力计算的影响对过程能力计算的影响0.01.02.03.04.05.06.00.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0Observed CpActual Cp0%10%20%30%40%50%60%70%R&R70%60%50%40%30%10%R&R Effect on CapabilityGuidelines%R&RResults5%No issues 10%Gage is OK10%30%Maybe acceptable based upon importanceo

34、f application,and cost factorOver 30%Gage system needs improvement/correctiveactionVariable Gage R&R36%R&RResults 30%测量系统需要改进Gage R&R 判断原则判断原则37 StdDev Study Var%Study Var%ToleranceSource (SD)(5.15*SD)(%SV)(SV/Toler)Total Gage R&R 1.85E-02 0.095449 18.87 19.09 Repeatability 1.42E-02 0.073006 14.44 1

35、4.60 Reproducibility 1.19E-02 0.061486 12.16 12.30 Part-to-Part 9.64E-02 0.496646 98.20 99.33 Total Variation 9.82E-02 0.505735 100.00 101.15 Number of distinct categories=7Minitab 计算计算GR&RXbar-R 均值极差法注：使用同组数据Discrim98.218.9=sspms=*.227.3MinitabStatQuality ToolsGage StudyGage R&R Study(Crossed)在Meth

36、od of Analysis中选择 Xbar and R38Roy ChenJuly 1999CaliperMisc:Tolerance:Reported by:Date of study:Gage name:5.65.55.45.35.2321Xbar Chart by OperatorSample MeanMean=5.386UCL=5.411LCL=5.3620.070.060.050.040.030.020.010.00321R Chart by OperatorSample RangeR=0.024UCL=0.06178LCL=010 9 8 7 6 5 4 3 2 15.65.55

37、.45.35.2Part NoOperatorOperator*Part No InteractionAverage1 2 3 3215.65.55.45.35.2OperatorResponse by Operator10 9 8 7 6 5 4 3 2 15.65.55.45.35.2Part NoResponse by Part No%Contribution%Study Var%Tolerance Part-to-PartReprodRepeatGage R&R100500Components of VariationPercentGR&R Study to Dimension Mea

38、surementMinitab 计算计算GR&R图解数据图解数据39%ContributionSource VarComp (of VarComp)Total Gage R&R 0.000459 4.53 Repeatability 0.000231 2.28 Reproducibility 0.000228 2.25 Operator 0.000117 1.16 Operator*Part No 0.000111 1.09 Part-To-Part 0.009670 95.47 Total Variation 0.010129 100.00 StdDev Study Var%Study Va

39、r%ToleranceSource (SD)(5.15*SD)(%SV)(SV/Toler)Total Gage R&R 0.021430 0.110366 21.29 22.07 Repeatability 0.015202 0.078292 15.11 15.66 Reproducibility 0.015105 0.077789 15.01 15.56 Operator 0.010834 0.055793 10.76 11.16 Operator*Part No 0.010525 0.054205 10.46 10.84 Part-To-Part 0.098336 0.506430 97

40、.71 101.29 Total Variation 0.100644 0.518317 100.00 103.66 Number of Distinct Categories=6Minitab 计算计算GR&R-ANOVA 法法sssssTotalrptOpPxOPart22222=+在Method of Analysis中选择ANOVA40Measurement Variation Vs.TolerancelPrecision to Tolerance RatiolAddresses what percent of the is taken up by measurement error.

41、lBest case:10%Acceptable:30%lIncludes both repeatability and reproducibilityn Operator x Unit x Trial experimentlP/T Ratios are required by certain customersUsually expressed as percentP TToleranceMS/.*=515sTolerance=USL-LSLNote:5.15 standard deviations accounts for 99%of MS variation.The use of 5.1

42、5 is an industry standard.41Measurement Variation Vs.Process(Analytical)lPercent Repeatability&Reproducibility(%R&R)lAddresses what percent of the is taken up by measurement error.lBest case:10%Acceptable:30%lIncludes both repeatability and reproducibilityn Operator x Unit x Trial experimentlAgain,t

43、he stability in the repeated measurements as well as the degree of discrimination could affect the validity of the calculation.l%R&R is required by certain customersUsually expressed as percent%&RRMSTotal=ss100MSs42P/T 与与%R&Rl将测量系统的变差与产品容差比较是最常用的方法将测量系统的变差与产品容差比较是最常用的方法:n P/T 可以表达与产品规范比较时的好坏程度可以表达与产

44、品规范比较时的好坏程度.n 产品规范的制订有时会太紧，有时又太松。产品规范的制订有时会太紧，有时又太松。n 一般来说，当测量系统只是用来检验生产线样品是否合格时，一般来说，当测量系统只是用来检验生产线样品是否合格时，P/T 是是很有效的。因为这时候，即使过程能力很有效的。因为这时候，即使过程能力(Cpk)不足，不足，P/T 也可以给你也可以给你足够的信心来判断产品的好坏足够的信心来判断产品的好坏l测量系统变差与过程变差的比较（测量系统变差与过程变差的比较（%R&R）更适合于研究过程的能力与过更适合于研究过程的能力与过程改进。程改进。PTTolerance（容差）测量系统/.*=515sTole

45、rance=USL-LSL%&RR测量系统总过程变差=ss10043%R&R=20%R&R=50%过程实际的变差%R&R=100%产品的容差LSLUSL测量系统变差P/T=20%P/T=50%P/T=100%44%R&R=25%R&R=50%过程实际变差%R&R=100%产品容差（Tolerance）LSLUSL测量系统变差P/T=50%P/T=100%P/T=200%45%R&R=20%R&R=40%R&R=100%产品容差（Tolerance）LSLUSL测量系统变差P/T=10%P/T=20%P/T=50%过程实际变差46零件操作员1操作员2范围(R)142223413671457259

46、81范围之和7平均范围1.4平均范围=(2+1+1+2+1)/5=7/5=1.4量具误差=5.15*/d=5.15/1.19*=4.33*=4.33*1.4=6.1%Gage R&R=量具误差Gage Error/允差Tolerance=6.1/20*100%=30.5%零件个数2个操作员3个操作员4个操作员11.411.912.2421.281.812.1531.231.772.1241.211.752.1151.191.742.161.181.732.0971.171.732.0981.171.722.0891.161.722.08101.161.722.08快速快速GR&R（短期模式）短

47、期模式）d常数表常数表允差Tolerance=20=最大值-最小值RRRRR47短期模式练习短期模式练习PartOperator A Operator BRange12012032203198320620741982015203199Sum of RangesAverage RangeAverage range=R=(+)/_=_ /_Gage Error=5.15/d*R=5.15/_*R=_*R=_*_=_%Gage R&R=Gage Error/Tolerance=_/_*100%)=_%Spec range=185-21548短期与长期方法的比较短期与长期方法的比较短期模式短期模式用生

48、产设备 用生产操作员快速-只需几个样品(5)无反复（replicates）估计总的变差(Total Gage R&R)不能区分 AV 和EV不能指导改进的方向可用于破坏性测试长期模式长期模式用生产设备 用生产操作员较多样品(5)要求反复 Replicates(3)估计总的变差(Total Gage R&R)可以区分 AV 和EV为测量系统的改进提供指导49正常标准正常标准方法方法Part ABTest 1Test 2Operator对同样的样品进行重复测量对同样的样品进行重复测量(称之为交叉设计 Crossed Designed)巢式设计巢式设计 Nested DesignCTest 1Tes

49、t 2Test 1Test 2OperatorIOperatorIIOperatorIII样品来自同一总体样品来自同一总体PartTestABC121212DEF121212GHI121212IIIIII破坏性测量和不可重复的测量50破坏性测量和不可重复的测破坏性测量和不可重复的测量量与可重复测量的测量系统比较 样品的个数不是几个(例如10个),而是几组(例如10组),每组内样品的个数等于对该组要进行的破坏性测试的次数 每组样品来自过程中连续的产出,默认该组内各样品之间是没有差异的 MinitabStatQuality ToolsGage StudyGage R&R Study(Nested)

50、结果中只能看到测量系统的重复性 51Gage R&R%ContributionSource VarComp (of VarComp)Total Gage R&R 0.0002311 2.31 Repeatability 0.0002311 2.31 Reproducibility 0.0000000 0.00Part-To-Part 0.0097807 97.69Total Variation 0.0100119 100.00 Study Var%Study VarSource StdDev(SD)(6*SD)(%SV)Total Gage R&R 0.015202 0.091214 15.1