测量系统分析-ppt课件.ppt（71页）

1、Chapter 3.2Measurement Systems Analysis测量系统分析2022-3-192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 Measurement2022-3-193Effects of Measurement ErrorAveragesVariabilitymmmtotalproduct

2、meas.system=+Measurement System BiasMeasurement System VariabilityAccuracyPrecisions s2total = s s2product + s s2meas system2022-3-194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

3、Voltage VariationTemperature FluctuationOperator TechniqueStandard ProceduresSufficient Work TimeM aintenance StandardCalibration FrequencyOperator TrainingEase of Data EntryAlgorithm InstabiltyElectrical InstabilityWear Mechanical instabilityGageEnvironmentWork Methods2022-3-196Measurement Variatio

4、nHumidityCleanlinessVibrationLine Voltage 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

5、动2022-3-197看到的不一看到的不一定真实定真实Possible Sources of Process VariationLong-termProcess VariationShort-termProcess VariationVariationw/i sampleActual Process VariationStabilityLinearityRepeatability Accuracy Variation dueto gageVariation dueto operatorsMeasurement VariationObserved Process VariationWe will

6、 look at “repeatability” and “reproducibility” as these are the primary contributors to measurement error.Reproducibility2022-3-199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AccuracyAccuracy Does the average of the measurements deviate from th

7、e true value?True value: Theoretically correct value NIST standardsBias Distance between average value of all measurements and true value Amount gage is consistently off target Systematic error or offset2022-3-1911准确度准确度(Accuracy)准确度(Accuracy) 测量的平均值是否与真值吻合?真值(True Value): 理论上正确的值 国际度量衡标准偏倚（Bias) 测量

8、值的均值与真值的距离 测量系统持续地偏离目标 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., metr

9、ology lab) of measuring equipment. ObservedAverageValueReferenceValueBIAS Definition2022-3-1913BIAS 测量结果的平均值与参考值的差异. 参考值（reference-value）是一个预先认定的参考标准. 该标准可用更高一级测量系统测量的平均值来确定(例如：高一级计量室)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=0.75mmX5=0.65mmX10=0.7mmOne Part Mea

10、sured 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% Bias=1000.05/0.70=7.1%This m

11、eans 7.1% of the process variation is BIASXX=10BIAS EXAMPLE:2022-3-1915X1=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偏倚偏倚BIAS 实例

12、实例:PrecisionTotal variation in the measurement systemMeasure of natural variation of repeated measurementsTerms: Random Error, Spread, Test/Retest errorRepeatability and ReproducibilitysssMSGO222=+2022-3-1917测量系统总变差通过重复测量的方法测量到的过程自然变差代表名词：重复性（ Repeatability）和再现性（Reproducibility）sssMSGO222=+精确度（精确度（P

13、recision)Precision: RepeatabilityThe inherent variability of the measurement systemVariation in measurements obtained with a gage when used several times by one operator while measuring a characteristic on one part.Estimated by the pooled standard deviation of the distribution of repeated measuremen

14、ts Repeatability is less than the total variation of the measurement systemsGsGRd=2*2022-3-1919测量系统内在的变异性基于重复测量的数据，用分组后组内的标准偏差来估算 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: Reproducib

15、ilityOperator variability of the measurement systemVariation in the average of the measurements made by different operators using the same gage when measuring a characteristic on one partEstimated by the standard deviation of the difference in averages, based on measurements taken by different opera

16、tors Must be adjusted for gage variationReproducibility is less than the total variation of the measurement systemsOsORd=2*2022-3-1921精确度：再现性测量系统中操作员产生的变异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。 应扣除量具的因素（组内变差）比测量系统总变差小sOsORd=2*Inspector AMaster ValueInspector BInspector CInspector AInspector BInspector C再现性再

17、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 gage504030201055453525155StandardTrialsR-Squared = 0.981Y = 0.934227 + 0.994959XRegression Plot504030201055453525155StandardTrialsR-Squared = 0.982Y = 0.245295

18、 + 0.99505XLinearity is N ot G oodGood LinearityBad Linearity2022-3-1923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504030201055453525155S tandardTrialsR -Squared = 0.981Y = 0.934227 + 0.994959XRegression Plot504030201055453525155StandardTrialsR-Squared = 0.982Y = 0.245295 + 0.99505XLinearity i

19、s N ot G ood好的线性好的线性差的线性差的线性StabilityThe distribution of measurements remains constant and predictable over time for both mean and standard deviationTotal variation in the measurements obtained with a gage, on the same master or master parts, when measuring a single characteristic over an extended t

20、ime period.Evaluated using a trend chart or multiple measurement analysis studies over timeTime-1Time-2timeMagnitudeStability2022-3-1925在一段时间内，测量结果的分布无论是均值还是标准偏差都保持不变和可预测的通过较长时间内，用被监视的量具对相同的标准或 标准件的同一特性进行测量的总变异来监视可用时间走势图进行分析稳定性（Stability）时间-1时间-2时间稳定性量值2022-3-1926Discriminationl The technological ab

21、ility of the measurement system to adequately differentiate between values of a measured parameter.RulerCaliperMicrometer.28.279.2794.28.282.2822.28.282.2819.28.279.27912022-3-1927测量系统的分辨率（ discrimination）要求不低于过程变差或允许偏差（ tolerance）的十分之一零件之间的差异必须大于最小测量刻度极差控制图可显示分辨率是否足够 看控制限内有多少个数据阶级不同数据等级的计算为 零件的标准偏差

22、/ 总的量具偏差* 1.41.直尺直尺卡尺卡尺千分尺千分尺.28.279.2794.28.282.2822.28.282.2819.28.279.2791Generally two or three operatorsGenerally 10 units to measureEach unit is measured 2-3 times by each operatorGage R&R studylDetermine if reproducibility is an issue. If it is, select the number of operators to participate.l

23、Operators 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 should be made in random or

24、der.lStudy must be observed by someone who recognizes the importance of conducting a reliable study.2022-3-1929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10个样品的某项特性进行

25、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2022-3-1930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

26、的极差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RA2022-3-1931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

27、.70测试人数nK3789101.821.741.671.62K1=5.15/d2*AV计算中，如根号下出现负值，AV取值02022-3-1932EV= Equipment Variation (Repeatability)仪器变差(重复性)AV= Appraiser Variation (Reproducibility)测量人变差(再现性)R&R= Repeatability & Reproducibility重复性与再现性PV= Part Variation零件变差TV= Total Variation of R&R and PV总变差K1-Trial, K2-Operator, & K3

28、-Part ConstantsGR&R研究中的名词研究中的名词2022-3-1933GR&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15.325.325.320.005.345.345.360.025.305.345.300.045.3325.445.405.440.045.465.465.480.025.465.405.420.065.443

29、5.485.485.500.025.505.465.480.045.505.505.500.005.4945.205.225.200.025.245.265.260.025.225.225.240.025.2355.245.245.240.005.245.245.260.025.285.245.240.045.2565.525.505.500.025.545.525.560.045.585.545.560.045.5475.385.385.380.005.405.425.440.045.405.365.380.045.3985.345.345.360.025.365.385.380.025.3

30、65.345.360.025.3695.445.445.420.025.465.445.440.025.445.465.420.045.44105.405.405.400.005.405.425.400.025.405.425.400.025.40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 =0.07823.27UCLR

31、3 =0.06232.58Total Tolerance0.5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

32、差-Total Variation(TV)TV= (R&R2+PV2)TV=0.506卡尺的R&R研究 Excel 运算2022-3-1934R&R 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 i

33、s OK10% 30%Maybe acceptable based upon importanceof application, and cost factorOver 30%Gage system needs improvement/correctiveactionVariable Gage R&R2022-3-1936% R&RResults 30%测量系统需要改进Gage R&R 判断原则判断原则2022-3-1937 StdDev Study Var %Study Var %ToleranceSource (SD) (5.15*SD) (%SV) (SV/Toler) Total Ga

34、ge R&R 1.85E-02 0.095449 18.87 19.09 Repeatability 1.42E-02 0.073006 14.44 14.60 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

35、.9=sspms=*.227.3MinitabStatQuality ToolsGage StudyGage R&R Study (Crossed)在Method of Analysis中选择 Xbar and R2022-3-1938Roy ChenJuly 1999CaliperMisc:Tolerance:Reported by:Date of study:Gage name:5.65.55.45.35.2321Xbar Chart by OperatorSample MeanMean=5.386UCL=5.411LCL=5.3620.070.060.050.040.030.020.01

36、0.00321R Chart by OperatorSample RangeR=0.024UCL=0.06178LCL=010 9 8 7 6 5 4 3 2 15.65.55.45.35.2Part 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-

37、to-PartReprodRepeatGage R&R100500Components of VariationPercentGR&R Study to Dimension MeasurementMinitab 计算计算GR&R图解数据图解数据2022-3-1939 %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 N

38、o 0.000111 1.09 Part-To-Part 0.009670 95.47 Total Variation 0.010129 100.00 StdDev Study Var %Study Var %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 0.0

39、10834 0.055793 10.76 11.16 Operator*Part No 0.010525 0.054205 10.46 10.84 Part-To-Part 0.098336 0.506430 97.71 101.29 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ANOVA2022-3-1940Measureme

40、nt Variation Vs. TolerancelPrecision to Tolerance RatiolAddresses what percent of the is taken up by measurement error.lBest case: 10% Acceptable: 30%lIncludes both repeatability and reproducibility Operator x Unit x Trial experimentP/T Ratios are required by certain customersUsually expressed as pe

41、rcentP TToleranceMS/.*=515sTolerance = USL - LSLNote: 5.15 standard deviations accounts for 99% of MS variation. The use of 5.15 is an industry standard.2022-3-1941Measurement Variation Vs. Process (Analytical)Percent Repeatability & Reproducibility (%R&R)Addresses what percent of the is taken up by

42、 measurement error.Best case: 10% Acceptable: 30%Includes both repeatability and reproducibility Operator x Unit x Trial experimentAgain, the stability in the repeated measurements as well as the degree of discrimination could affect the validity of the calculation.%R&R is required by certain custom

43、ersUsually expressed as percent% &RRMSTotal=ss100MSs2022-3-1942P/T 与 %R&R将测量系统的变差与产品容差比较是最常用的方法: P/T 可以表达与产品规范比较时的好坏程度. 产品规范的制订有时会太紧，有时又太松。 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 是很有效的。因为这时候，即使过程能力(Cpk)不足， P/T 也可以给你足够的信心来判断产品的好坏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程改进。PTTolerance（容差）测量系统/.*=515sTolerance = USL

44、 - LSL% &RR测量系统总过程变差=ss1002022-3-1943%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%2022-3-1944%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%2022-3-1945%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

45、/T = 20%P/T = 50%过程实际变差2022-3-1946零件操作员1操作员2范围(R)14222341367145725981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11.411.912.2421.281.812.1531.231.772.12

46、41.211.752.1151.191.742.161.181.732.0971.171.732.0981.171.722.0891.161.722.08101.161.722.08快速快速GR&R（短期模式）短期模式）d常数表常数表允差Tolerance = 20= 最大值-最小值RRRRR2022-3-1947短期模式练习短期模式练习PartOperator A Operator BRange12012032203198320620741982015203199Sum of RangesAverage RangeAverage range = R = ( + + + + )/_ = _ /

47、 _Gage Error = 5.15 / d * R = 5.15 /_ * R = _ * R = _ * _ = _% Gage R&R = Gage Error / Tolerance = _ / _ * 100 %) = _%Spec range = 185 - 2152022-3-1948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

48、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2022-3-1949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 1Test 2Test 1Test 2OperatorIOperatorIIOperatorIII样品来自同一总体样品来自同一总体PartTestABC121212DEF121212GHI121212IIIIII破坏性

49、测量和不可重复的测量2022-3-1950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) 结果中只能看到测量系统的重复性 2022-3-1951Gage R&R %ContributionSource VarComp (of VarComp)Total Gage R&R

50、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 15.19 Repeatability 0.015202 0.091214 15.19 Reproducibility 0.000000 0.000000 0