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1、Chapter 3.2Measurement Systems Analysis测量系统分析测量系统分析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 Measurement2Effects of Measurement ErrorAveragesVariabilitymmmtotalproductmeas.system=+

2、Measurement System BiasMeasurement System VariabilityAccuracyPrecisions s2total = s s2product + s s2meas system3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4Sources of Measurement VariationM easurement VariationHumidityCleanlinessVibrationLine Voltage VariationTemp

3、erature FluctuationOperator TechniqueStandard ProceduresSufficient Work TimeM aintenance StandardCalibration FrequencyOperator TrainingEase of Data EntryAlgorithm InstabiltyElectrical InstabilityWear Mechanical instabilityGageEnvironmentWork MethodsMeasurement VariationHumidityCleanlinessVibrationLi

4、ne 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动6看到的不一看到的不一定真实定真实7Possible Sou

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

6、bility” as these are the primary contributors to measurement error.Reproducibility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9AccuracylAccuracy Does the average of the measurements deviate from the true value?lTrue value:n Theoretically

7、correct valuen NIST standardslBiasn Distance between average value of all measurements and true valuen Amount gage is consistently off targetn Systematic error or offset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

8、离测量值的均值与真值的距离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11BIAS 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 high

9、er level (e.g., metrology lab) of measuring equipment. ObservedAverageValueReferenceValueBIAS DefinitionBIAS 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 13X1=0.75mmX6=0.8mmX2=0.75mmX7=0.75mmX3=0.8

10、mmX8=0.75mmX4=0.8mmX9=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 0.7

11、0mm.= 0.75Bias = 0.75-0.8= -0.05% Bias=1000.05/0.70=7.1%This means 7.1% of the process variation is BIASXX=10BIAS EXAMPLE:X1=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=

12、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 实例实例:15PrecisionlTotal variation in the measurement systemlMeasure of natural variation of repeated measurementslTerms: Random Error, Spread, Test/Retest errorlRepeatability and ReproducibilitysssMSGO222=+l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

13、到的过程自然变差l代表名词：重复性（代表名词：重复性（ Repeatability）和再现性（和再现性（Reproducibility）sssMSGO222=+精确度（精确度（Precision)17Precision: 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 o

14、ne part.lEstimated by the pooled standard deviation of the distribution of repeated measurements lRepeatability is less than the total variation of the measurement systemsGsGRd=2*l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

15、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19Precision: ReproducibilitylOperator variability of the measurement systemlVariation in the average of the measurements made by different operators using the same gage when measuring a char

16、acteristic on one partlEstimated by the standard deviation 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*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

17、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21LinearityDifference in the accuracy values of a ga

18、ge through the expected operating range of the gage504030201055453525155StandardTrialsR-Squared = 0.981Y = 0.934227 + 0.994959XRegression Plot504030201055453525155StandardTrialsR-Squared = 0.982Y = 0.245295 + 0.99505XLinearity is N ot G oodGood LinearityBad Linearity线性（线性（ Linearity） 量具在不同测量范围的准确度和精

19、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504030201055453525155S 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23StabilitylThe distribution of measurem

20、ents remains constant and predictable over time for both mean and standard deviationlTotal 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 measuremen

21、t analysis studies over timeTime-1Time-2timeMagnitudeStabilityl在一段时间内，测量结果的分布无在一段时间内，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25Discriminationl The techn

22、ological ability of the measurement system to adequately differentiate between values of a measured parameter.RulerCaliperMicrometer.28.279.2794.28.282.2822.28.282.2819.28.279.279126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

23、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.28.279.2794.28.282.2822.28.282.2819.28.279.279127lGenerally two or three operatorslGenerally 10 units to measurelEach unit is measured 2-3 times by each operatorGage

24、R&R studylDetermine if reproducibility is an issue. If it is, select the number of operators 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 ex

25、pected process variation.lInsure defined gaging procedures are followed.lMeasurements should be made in random order.lStudy must be observed by someone who recognizes the importance of conducting a reliable study.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

26、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29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Aver

27、age 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RA30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+PV

28、2)%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nK3789101.821.741.671.62K1=5.15/d2*AV计算中，如根号下出现负值，AV取值031EV= Equipment Variation (Repeatability)仪器变差仪器变差(重复性重复性)AV= Appraiser Variation (Reproducibility)测量人变差测量人变差(再现性再现性)R&R= R

29、epeatability & Reproducibility重复性与再现性重复性与再现性PV= Part Variation零件变差零件变差TV= Total Variation of R&R and PV总变差总变差K1-Trial, K2-Operator, & K3-Part ConstantsGR&R研究中的名词研究中的名词32GR&R sheetR&R = (EV)2 + (AV)2P/T = 100 x (R&R) / Tolerance% R&R = 100 x(R&R)/TVLong Method 0.10

30、19.1318.91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15.325.325.320.005.345.345.360.025.305.345.300.045.3325.445.405.440.045.465.465.480.025.465.405.420.065.4435.485.485.500.025.505.465.480.045.505.505.500.005.4945.205.225.200.025.245.265.260.025.225.225.240.025.2355.245.245.240.005.245.245.260.0

31、25.285.245.240.045.2565.525.505.500.025.545.525.560.045.585.545.560.045.5475.385.385.380.005.405.425.440.045.405.365.380.045.3985.345.345.360.025.365.385.380.025.365.345.360.025.3695.445.445.420.025.465.445.440.025.445.465.420.045.44105.405.405.400.005.405.425.400.025.405.425.400.025.40平均值平均值5.385.3

32、75.385.395.395.415.395.385.38RpAverage 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 Tolerance0.5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

33、= (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研究 Excel 运算33R&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.

34、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 Capability34Guidelines% R&RResults5%No issues 10%Gage is OK10% 30%Maybe acceptable based upon importanceof application, and cost factorOver 30%Gage system needs impr

35、ovement/correctiveactionVariable Gage R&R% R&RResults 30%测量系统需要改进Gage R&R 判断原则判断原则36 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 14.60 Reproducibility 1.19E-02 0.061486

36、 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Method of Analysis中选择 Xbar and

37、R37Roy 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 15.65.55.45.35.2Part NoOperatorOper

38、ator*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 MeasurementMinitab 计

39、算计算GR&R图解数据图解数据38 %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 Var %Tol

40、eranceSource (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

41、 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ANOVA39Measurement Variation Vs. TolerancelPrecision to Tolerance RatiolAddresses what percent of the is taken up by measurem

42、ent error.lBest case: 10% Acceptable: 30%lIncludes both repeatability and reproducibility Operator x Unit x Trial experiment P/T Ratios are required by certain customersUsually expressed as percentP TToleranceMS/.*=515sTolerance = USL - LSLNote: 5.15 standard deviations accounts for 99% of MS variat

43、ion. The use of 5.15 is an industry standard.40Measurement 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 Operato

44、r x Unit x Trial experimentlAgain, the 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=ss100MSs41P/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

45、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

46、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/.*=515sTolerance = USL - LSL% &RR测量系统总过程变差=ss10042%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%43%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

47、%44%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45零件操作员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 /

48、 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）短期模式）d常数表常数表允差Tolerance = 20= 最大值-最小值RRRRR46短期模式练习短期模式练习PartOperator A Operator BRange1201203220319832062074198201

49、5203199Sum 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 - 21547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

50、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48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 2OperatorIOperatorIIOpera

51、torIII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49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 50Gage R&R

52、 %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 15.19 Repeatabi

53、lity 0.015202 0.091214 15.19 Reproducibility 0.000000 0.000000 0.00Part-To-Part 0.098898 0.593386 98.84Total Variation 0.100059 0.600355 100.00Number of Distinct Categories = 9使用前面一样的数据51NO-GOGOErrorOperator 2Operator 1定性数据定性数据(Attribute Data)的测量系统的测量系统52定性数据定性数据(Attribute Data)的测量系统的可靠性的测量系统的可靠性 Go

54、-No Go 数据模式人为因素主导，情况复杂 统计模型多种多样 统计学上各家争鸣，尚无定论 实践中采用何种形式，取决于实例与统计模型的接近程度53 对于以“是”和“不是”为计数基础的定性数据，其 GR&R考察的概念是与定量数据一样的。但方法上完全不同. 定性数据测量系统的能力取决于操作员判断的有效性，即将“合格”判断成合格，将“不合格”判断成不合格的程度.计数型测量系统能计数型测量系统能力分析方法示例力分析方法示例54以下为判断所用的指标以下为判断所用的指标 有效性有效性 Effectiveness(E) - 即判断“合格”与“不合格”的准确性 E= 实际判断正确的次数/可能判断正确的

55、机会次数. 漏判的几率漏判的几率 Probability of miss(P-miss) - 将“不合格”判为合格的机会 P(miss)=实际漏判的次数 / 漏判的总机会数.误判的几率误判的几率 Probability of false alarm(P-FA) - 将“合格”判为不合格的机会. P(false alarm)=实际误判次数 / 误判的总机会数.偏倚偏倚 Bias(B) - 指漏判或误判的偏向. B=P(false alarm) / P(miss) B=1, 无偏倚 B1, 偏向误判 B0.90.8-0.90.8P(FA)0.1P(miss)0.05B0.8-1.20.5-0.81

56、.5测量系统好坏的判据测量系统好坏的判据 E, P(FA), P(miss) and B在中可以进行这样的计算Attribute Chart59Kappa-如果不知道标准样品如果不知道标准样品Kappa 用来分析操作者之间的一致性, 但不说明真实的对错Kappa=(Pobserved-Pchance)/(1-Pchance)Pobserved为操作员实际判断一致的比例=(Pass Pass+Fail Fail)/总的检验次数Pchance 为在随机状态下操作员判断一致的机会=(Pass Pass+Fail Pass)*(Pass Pass+Pass Fail/总检验次数之平方+(Pass Fa

57、il+Fail Fail)*(Fail Pass+Fail Fail)/总的检验次数之方对于两个操作员60例如两个检验员目测12来料样品样品样品123456789101112QC1PPPPPFPPPFPFQC2PPPFPFPPPFPFP代表合格, F代表不合格PassFailPass80Fail13Pobserved=(8+3)/12=11/12Pchance=(8+0)*(8+1)/144+(1+3)*(0+3)/144=7/12Kappa=(11-7)/(12-7)=0.8一般要求Kappa 大于0.75, 小于0.4则表示很差QC1QC261测量系统一致性在测量系统一致性在Minitab 中的计算中的计算MinitabQuality ToolsAttribute Agreement AnalysisBetween Appraisers Assessment Agreement# Inspected # Matched Percent 95 % CI 12 11 91.67 (61.52, 99.79)# Matched: All appraisers assessments agree with each other.Fleiss Kappa StatisticsResponse Kappa SE Kappa Z P(vs 0)F 0.798319 0.2