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Chapter 3.2Measurement Systems Analysis测量系统分析测量系统分析Chapter 3.2Measurement System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 Measurement2测量是科学的基础“I often say that wheEffects of Measurement ErrorAveragesVariabilitymmmtotalproductmeas.system=+Measurement System BiasMeasurement System VariabilityAccuracyPrecisions s2total =s s2product +s s2meas system3Effects of Measurement ErrorAv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4测量误差平均值变差mmm总产品测量系统=+测量系统的偏差测量Sources of Measurement VariationM easurement VariationHumidityCleanlinessVibrationLine Voltage VariationTemperature FluctuationOperator TechniqueStandard ProceduresSufficient Work TimeM aintenance StandardCalibration FrequencyOperator TrainingEase of Data EntryAlgorithm InstabiltyElectrical InstabilityWear Mechanical instabilityGageEnvironmentWork MethodsSources of Measurement Variati测量误差的原因测量误差的原因Measurement VariationHumidityCleanlinessVibrationLine 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测量误差的原因Measurement Variation看到的不一看到的不一定真实定真实7看到的不一定真实7Possible Sources 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“reproducibility”as these are the primary contributors to measurement error.ReproducibilityPossible Sources of Process Va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9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AccuracylAccuracy Does the average of the measurements deviate from the true value?lTrue value:nTheoretically correct valuenNIST standardslBiasnDistance between average value of all measurements and true valuenAmount gage is consistently off targetnSystematic error or offsetAccuracyAccuracy Does the av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11准确度(Accuracy)准确度(Accuracy)测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.,metrology lab)of measuring equipment.ObservedAverageValueReferenceValueBIAS DefinitionBIAS Is the difference betwBIAS 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.该标该标准可用更高一级测量系统测量的平均值来确定准可用更高一级测量系统测量的平均值来确定(例如：例如：高一级计量室高一级计量室)观测平均值参考值偏倚偏倚BIAS 13BIAS 测量结果的平均值与参考值的差异.参考值（rX1=0.75mmX6=0.8mmX2=0.75mmX7=0.75mmX3=0.8mmX8=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 0.70mm.=0.75Bias=0.75-0.8=-0.05%Bias=1000.05/0.70=7.1%This means 7.1%of the process variation is BIASBIAS EXAMPLE:X1=0.75mmX6=0.8mmOne Part MeX1=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 BIAS偏倚偏倚BIAS 实例实例:15X1=0.75mmX6=0.8mm同一操作者对同一工件测PrecisionlTotal variation in the measurement systemlMeasure of natural variation of repeated measurementslTerms:Random Error,Spread,Test/Retest errorlRepeatability and ReproducibilitysssMSGO222=+PrecisionTotal variation in thl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）和再现性（和再现性（Reproducibility）sssMSGO222=+精确度（精确度（Precision)17测量系统总变差sssMSGO222=+精确度（PrecisiPrecision: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 deviation of the distribution of repeated measurements lRepeatability is less than the total variation of the measurement systemPrecision:RepeatabilityThe il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 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象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差，（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用于估计短期的变差Master Value精确度：重复性精确度：重复性19测量系统内在的变异性 重复性指同一 人使用同一测量工具对同一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 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 systemPrecision:ReproducibilityOper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21精确度：再现性测量系统中操作员产生的变异Inspector LinearityDifference in the accuracy values of a gage through the expected operating range of the gageGood LinearityBad LinearityLinearityDifference in the ac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好的线性好的线性差的线性差的线性23线性（Linearity）量具在不同测量范围的准确度和StabilitylThe distribution of measurements 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 measurement analysis studies over timeTime-1Time-2timeMagnitudeStabilityStabilityThe distribution of ml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25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Discriminationl The technological ability of the measurement system to adequately differentiate between values of a measured parameter.RulerCaliperMicrometer.28.279.2794.28.282.2822.28.282.2819.28.279.279126Discrimination The technologi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.28.279.2794.28.282.2822.28.282.2819.28.279.279127测量系统的分辨率（discrimination）要求不低于lGenerally 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 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 expected 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.Generally two or three operato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计量型数据的GR&R研究均值-极差（X-R）法是确定测量系统计算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计算A测的所有样品同样方法计算对每个样品由三个人所测得的计算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nK3789101.821.741.671.62K1=5.15/d2*AV计算中，如根号下出现负值，AV取值031测量系统分析R=(RA+RB+RC)/3n=样品个数rK12EV=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=Repeatability&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32EV=Equipment Variation(Repea卡尺的R&R研究 Excel 运算33卡尺的R&R研究33R&R 对过程能力计算的影响对过程能力计算的影响70%60%50%40%30%10%R&R Effect on Capability34R&R 对过程能力计算的影响70%60%50%40%30%1Guidelines%R&RResults5%No issues 10%Gage is OK10%30%Maybe acceptable based upon importanceof application,and cost factorOver 30%Gage system needs improvement/correctiveactionVariable Gage R&RGuidelines%R&RResultsVaria%R&RResults 30%测量系统需要改进Gage R&R 判断原则判断原则36%R&RResultsGage R&R 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 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 R37 StdDev Study Var%Study VMinitab 计算计算GR&R图解数据图解数据38Minitab 计算GR&R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%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 97.71 101.29 Total Variation 0.100644 0.518317 100.00 103.66 Number of Distinct Categories=6Minitab 计算计算GR&R-ANOVA 法法在Method of Analysis中选择ANOVA39%ContributionMinitab 计算GR&R-AMeasurement Variation Vs.TolerancelPrecision to Tolerance RatiolAddresses what percent of the ToleranceTolerance is taken up by measurement error.lBest case:10%Acceptable:30%lIncludes both repeatability and reproducibilityOperator x Unit x Trial experimentP/T Ratios are required by certain customersUsually expressed as percentTolerance=USL-LSLNote:5.15 standard deviations accounts for 99%of MS variation.The use of 5.15 is an industry standard.40Measurement Variation Vs.ToleMeasurement Variation Vs.Process(Analytical)lPercent Repeatability&Reproducibility(%R&R)lAddresses what percent of the Total Variation Total Variation is taken up by measurement error.lBest case:10%Acceptable:30%lIncludes both repeatability and reproducibilitynOperator 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=ss100MSs41Measurement Variation Vs.ProcP/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:nP/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）更适合于研究过程的能力与过程更适合于研究过程的能力与过程改进。改进。PTTolerance（容差）测量系统/.*=515sTolerance=USL-LSL%&RR测量系统总过程变差=ss10042P/T 与%R&R将测量系统的变差与产品容差比较是最常用的%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=20%R&R=50%过程实际的变差%R&%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%44%R&R=25%R&R=50%过程实际变差%R&R%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%R&R=20%R&R=40%R&R=100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%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平均范围=(2+1+1+2+1)/5=7短期模式练习短期模式练习Average range=R=(+)/_=_ /_Gage Error=5.15/d*R=5.15/_*R=_*R=_*_=_%Gage R&R=Gage Error/Tolerance=_/_*100%)=_%Spec range=185-21547短期模式练习Average range=R=(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短期与长期方法的比较短期模式长期模式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 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49正常标准方法Part ABTest 1Operator对同样破坏性测量和不可重复的测量破坏性测量和不可重复的测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 50破坏性测量和不可重复的测量与可重复测量的测量系统比较50Gage 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 15.19 Repeatability 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51Gage R&R 使用前面一样的数据51NO-GOGOErrorOperator 2Operator 1定性数据定性数据(Attribute Data)的测量系的测量系统统52NO-GOGOErrorOperator 2Operator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-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定性数据(Attribute Data)的测量系统的可靠性 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对于以“是”和“不是”为计数基础的定性数据，其 GR&R考察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 BQuality 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 0.288675 2.76546 0.0028P 0.798319 0.288675 2.76546 0.002862测量系统一致性在Minitab 中的计算MinitabQuICC等级关联系数Intraclass Correlation Coefficient当产品的质量判定不仅仅是合格与不合格两种性质，而是进行多个等级的区分时ICC针对不同情行下的测量系统进行评估ICC使用平方和 Sums of Square来进行评估工作实例：某公司建立评估系统来测量采购订单(PO)完成的质量水平，选了三个高级采购员对个订单的完成好坏进行打分评估，分代表很差，分代表很好，结果如下63ICC等级关联系数当产品的质量判定不仅仅是合格与不合格两种PO#Buyer ABuyer BBuyer C15762654344344545765667778988988955610678定义如下平方和项BMS=Between mean square EMS=Error mean squareJMS=Judge mean squareWMS=Within mean squareTMS=Total mean square64PO#Buyer ABuyer BBuyer C157626PO#Buyer ABuyer BBuyer CSS21576183242654152253443111214454131695765183246677204007898256258988256259556162561067821441S6063591823510S236003969348111050Sum of all squared:1182Average of all:6.07Sum X average=6.07X182=1110.81Degree of freedomBuyers=3-1=2Between PO=10-1=9Total=30-1=29Within PO=10X(3-1)=20Error=29-9-2=1865PO#Buyer ABuyer BBuyer CSS2157BMS=SS between POs/DF of POs=(3510/3-1110.81)/9=6.57JMS=SS of Buyers/DF of Buyers=(11050/10-1110.81)/2=2.9TMS=SS of all/DF of total=(1182-1110.81)/29=2.45WMS=(SS total-SS between POs)/DF within POs =(1182-1110.81)-(3510/3-1110.81)/20=0.6EMS=(SS total-SS between PO-SS buyers)/DF of Error =(1182-1110.81)-(3510/2-1110.81)-(11050/10-1110.81)/18 =(71.19-59.19-5.81)/18=0.34466BMS=SS between POs/DF of POs=(三种情形下的ICC计算1.任意从很多采购员中取3个人来对1个PO打分,下一个PO又重复同样的事,任意取3 人来打分,每次打分的采购员可能不相同2.每个采购员的可信度为：(k代表采购员的个数）3.ICC=(BMS-WMS)/BMS+(k-1)WMS4.=(6.57-0.6)/(6.57+2*0.6)5.=0.776.采购员的平均可信度为7.ICC=(BMS-WMS)/BMS8.=(6.57-0.6)/6.579.=0.9167三种情形下的ICC计算672.任意从很多采购员中取3人来对10个PO进行打分,鉴定10个PO 的采购员是一样的3人每个采购员的可信度为：（n代表的个数）ICC=(BMS-EMS)/BMS+(k-1)EMS+k(JMS-EMS)/n =(6.57-0.344)/6.57+2*0.344+3*(2.9-0.344)/10 =0.78采购员的平均可信度为ICC=(BMS-EMS)/BMS+(JMS-EMS)/n =(6.57-0.344)/6.57+(2.9-0.344)/10 =0.91682.任意从很多采购员中取3人来对10个PO进行打分,鉴定3.固定了3个采购员对10个PO进行打分每个采购员的可信度为ICC=(BMS-EMS)/BMS+(k-1)EMS =(6.57-0.344)/6.57+(3-1)*0.344 =0.86采购员的平均可信度为ICC=(BMS-EMS)/BMS =(6.57-0.344)/6.57 =0.95ICC的接收下限为0.7,0.9以上比较好693.固定了3个采购员对10个PO进行打分ICC的接收下限为0练习某食品公司生产辣酱，其产品的辣度由专业品辣员来担当。辣度分为微辣(M)辣(H)很辣(VH)受不了(SH)为了保证辣度的测量是可靠的，找了两个品辣员对个样品进行品味，结果如下70练习某食品公司生产辣酱，其产品的辣度由专业品辣员来担当。辣度SauceTaster 1Taster 21MM2MH3SHVH4VHSH5HVH6VHVH7HM8HH9SHVH10MH计算三种情形下的该公司辣度测量系统如何？71SauceTaster 1Taster 21MM2MH3SH
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