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1、Chapter 3.2Measurement Systems Analysis丈量系统分析1丈量是科学的根底“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=+Measurement Sy

2、stem BiasMeasurement System VariabilityAccuracyPrecisions2total = s2product + s2meas system3丈量误差平均值变差mmm总产品丈量系统=+丈量系统的偏向丈量系统的变差准确度准确度s2total = s2产品 + s2丈量系统4Sources of Measurement VariationMeasurement VariationHumidityCleanlinessVibrationLine Voltage VariationTemperature FluctuationOperator Techniqu

3、eStandard ProceduresSufficient Work TimeMaintenance StandardCalibration FrequencyOperator TrainingEase of Data EntryAlgorithm InstabiltyElectrical InstabilityWear Mechanical instabilityGageEnvironmentWork Methods5丈量误差的缘由Measurement VariationHumidityCleanlinessVibrationLine Voltage VariationTemperatu

4、re FluctuationOperator TechniqueStandard ProceduresSufficient Work TimeMaintenance StandardCalibration FrequencyOperator TrainingEase of Data Entry 电性能不稳定磨损 机械不稳定性量具环境丈量方法计算不稳定获得数据的难易操作员培训校准频率量具维护规范足够的任务时间规范操作规程操作员技术湿度清洁程度震动线电压动摇温度动摇6看到的不一定真实7Possible Sources of Process VariationLong-termProcess Var

5、iationShort-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 t

6、o measurement error.Reproducibility8过程变差分析长期过程变差短期抽样产生的变差实践过程变差稳定性线性反复性 准确度 量具变差操作员呵斥的变差丈量误差过程变差观测值“反复性 和 “再现性 是丈量误差的主要来源再现性过程变差9AccuracyAccuracy Does the average of the measurements deviate from the true value?True value:Theoretically correct valueNIST standardsBiasDistance between average value of

7、 all measurements and true valueAmount gage is consistently off targetSystematic error or offset10准确度(Accuracy)准确度(Accuracy) 丈量的平均值能否与真值吻合?真值(True Value):实际上正确的值 国际度量衡规范偏倚Bias)丈量值的均值与真值的间隔丈量系统继续地偏离目的系统错误11BIAS Is the difference between the observed average of the measurement and the reference value.

8、 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 Definition12BIAS 丈量结果的平均值与参考值的差别. 参考值reference-v

9、alue是一个预先认定的参考规范. 该规范可用更高一级丈量系统丈量的平均值来确定(例如：高一级计量室)观测平均值参考值偏倚BIAS 13X1=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 equip

10、ment (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:14X1=0.75mmX6=0.8mmX2=0.75mmX7=0.75mmX3=0.8mmX8=0.75mmX4=0.8mmX9=0.75mmX5=0.65

11、mmX10=0.7mm同一操作者对同一工件丈量10次假设参考规范是 0.80mm. 过程变差为0.70mm = 0.75Bias = 0.75-0.8= -0.05% Bias=1000.05/0.70=7.1%阐明 7.1% 的过程变差是偏倚 BIAS偏倚BIAS 实例:15PrecisionTotal variation in the measurement systemMeasure of natural variation of repeated measurementsTerms: Random Error, Spread, Test/Retest errorRepeatabilit

12、y and ReproducibilitysssMSGO222=+16丈量系统总变差经过反复丈量的方法丈量到的过程自然变差代表名词：反复性 Repeatability和再现性ReproducibilitysssMSGO222=+准确度Precision)17Precision: RepeatabilityThe inherent variability of the measurement systemVariation in measurements obtained with a gage when used several times by one operator while meas

13、uring a characteristic on one part.Estimated by the pooled standard deviation of the distribution of repeated measurements Repeatability is less than the total variation of the measurement system18丈量系统内在的变异性基于反复丈量的数据，用分组后组内的规范偏向来估算 小于丈量系统的总变差 反复性指同一 人运用同一丈量工具对同一对象产品的同一特性进展多次丈量中产生的变差，用于估计短期的变差Master

14、Value准确度：反复性19Precision: ReproducibilityOperator 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 me

15、asurements taken by different operators Must be adjusted for gage variationReproducibility is less than the total variation of the measurement system20准确度：再现性丈量系统中操作员产生的变异基于不同操作者的丈量数据，按操作员分组，经过组平均值的差来估。 应扣除量具的要素组内变差比丈量系统总变差小Inspector AMaster ValueInspector BInspector CInspector AInspector BInspector

16、 C再现性指不同的人在对同种特性进展丈量时产生的变差21LinearityDifference in the accuracy values of a gage through the expected operating range of the gageGood LinearityBad Linearity22线性 Linearity 量具在不同丈量范围的准确度和准确度的变化，当丈量范围较宽时尤为要关注好的线性差的线性23StabilityThe distribution of measurements remains constant and predictable over time

17、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 time period.Evaluated using a trend chart or multiple measurement analysis studies over timeTime-1Time-2timeMagnit

18、udeStability24在一段时间内，丈量结果的分布无论是均值还是规范偏向都坚持不变和可预测的经过较长时间内，用被监视的量具对一样的规范或 规范件的同一特性进展丈量的总变异来监视可用时间走势图进展分析稳定性Stability时间-1时间-2时间稳定性量值25Discrimination The technological ability of the measurement system to adequately differentiate between values of a measured parameter.RulerCaliperMicrometer.28.279.2794.

19、28.282.2822.28.282.2819.28.279.279126丈量系统的分辨率 discrimination要求不低于过程变差或允许偏向 tolerance的非常之一零件之间的差别必需大于最小丈量刻度极差控制图可显示分辨率能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 零件的规范偏向/ 总的量具偏向* 1.41.直尺卡尺千分尺.28.279.2794.28.282.2822.28.282.2819.28.279.279127Generally two or three operatorsGenerally 10 units to measureEach unit is me

20、asured 2-3 times by each operatorGage R&R studyDetermine if reproducibility is an issue. If it is, select the number of operators to participate.Operators selected should normally use the measurement system.Select samples that represent the entire operating range.Gage must have graduations that allo

21、w at least one-tenth of the expected process variation.Insure defined gaging procedures are followed.Measurements should be made in random order.Study must be observed by someone who recognizes the importance of conducting a reliable study.28计量型数据的GR&R研讨均值-极差X-R法是确定丈量系统的反复性和再现性的数学方法，步骤如下：1 选择三个丈量人A,

22、 B,C和10个丈量样品。 丈量人应有代表性，代表经常从事此项丈量任务的QC人员或消费线人员 10个样品应在过程中随机抽取，可代表整个过程的变差，否那么会严重影响研讨结果。2 校准量具3 丈量，让三个丈量人对10个样品的某项特性进展测试，每个样品每人丈量 三次，将数据填入表中。实验时遵照以下原那么： 盲测原那么1：对10个样品编号，每个人测完第一轮后，由其他人对这10个样品进展随机的重新编号后再测，防止客观偏向。 盲测原那么2：三个人之间都相互不知道其他人的丈量结果。4 计算29计算A测的一切样品的总平均值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

23、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丈量系统分析R=(RA+RB+RC)/3XDIFF=MaxXA,XB,XC-MinXA,XB,XC反复性-设备变差 EV=RK1 再现性-检验人变差 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实验次数rK1234.453.05K2233.652.70测试人数

24、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(反复性)AV= Appraiser Variation (Reproducibility)丈量人变差(再现性)R&R= Repeatability & Reproducibility反复性与再现性PV= Part Variation零件变差TV= Total Variation of R&R and PV总变差K1-Trial, K2-Operator, & K3-Part ConstantsG

25、R&R研讨中的名词32卡尺的R&R研讨 Excel 运算33R&R 对过程才干计算的影响70%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 improvement/correctiveactionVariable Gage R&R35% R&RResults 30%

26、丈量系统需求改良Gage R&R 判别原那么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 9.82

27、E-02 0.505735 100.00 101.15 Number of distinct categories = 7Minitab 计算GR&RXbar-R 均值极差法注：运用同组数据Discrim98.218.9=sspms=*.227.3MinitabStatQuality ToolsGage StudyGage R&R Study (Crossed)在Method of Analysis中选择 Xbar and R37Minitab 计算GR&R图解数据38 %ContributionSource VarComp (of VarComp) Total Gage R&R 0.0004

28、59 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 22.0

29、7 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

30、= 6Minitab 计算GR&R-ANOVA 法在Method of Analysis中选择ANOVA39Measurement Variation Vs. TolerancePrecision to Tolerance RatioAddresses what percent of the Tolerance is taken up by measurement error.Best case: 10% Acceptable: 30%Includes both repeatability and reproducibilityOperator x Unit x Trial experimen

31、tP/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. Process (Analytical)Percent Repeatability & Reproducibility (%R&R)Address

32、es what percent of the Total Variation is taken up by measurement error.Best case: 10% Acceptable: 30%Includes both repeatability and reproducibilityOperator x Unit x Trial experimentAgain, the stability in the repeated measurements as well as the degree of discrimination could affect the validity o

33、f the calculation.%R&R is required by certain customersUsually expressed as percent%&RRMSTotal=ss100MSs41P/T 与 %R&R将丈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. 产品规范的制定有时会太紧，有时又太松。 普通来说，当丈量系统只是用来检验消费线样品能否合格时， P/T 是很有效的。由于这时候，即使过程才干(Cpk)缺乏， P/T 也可以给他足够的自信心来判别产品的好坏丈量系统变差与过程变差的比较%R&R更适宜于研讨过程的才干与过程改良。PT

34、Tolerance容差丈量系统/.*=515sTolerance = USL - LSL%&RR丈量系统总过程变差=ss10042%R&R = 20%R&R = 50%过程实践的变差%R&R = 100%产品的容差LSLUSL丈量系统变差P/T = 20%P/T = 50%P/T = 100%43%R&R = 25%R&R = 50%过程实践变差%R&R = 100%产品容差ToleranceLSLUSL丈量系统变差P/T = 50%P/T = 100%P/T = 200%44%R&R = 20%R&R = 40%R&R = 100%产品容差 ToleranceLSLUSL丈量系统变差P/T

35、= 10%P/T = 20%P/T = 50%过程实践变差45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GR&R短期方式d常数表允差Tolerance = 20= 最大值-最小值RRRRR46短期方式练习Average range = R = ( + + + + )/_ = _ / _Gage Error = 5.

36、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方式用消费设备 用消费操作员快速 - 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不能指点改良的方向可用于破坏性测试长期方式用消费设备 用消费操作员较多样品 (5)要求反复 Replicates (3)估计总的变差 (Total Gage R&R)可以区分 A

37、V 和EV为丈量系统的改良提供指点48正常规范方法Part ABTest 1Test 2Operator对同样的样品进展反复丈量(称之为交叉设计 Crossed Designed)巢式设计 Nested DesignCTest 1Test 2Test 1Test 2OperatorIOperatorIIOperatorIII样品来自同一总体PartTestABC121212DEF121212GHI121212IIIIII破坏性丈量和不可反复的丈量49破坏性丈量和不可反复的丈量与可反复丈量的丈量系统比较 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

38、展的破坏性测试的次数 每组样品来自过程中延续的产出, 默许该组内各样品之间是没有差别的 MinitabStatQuality ToolsGage StudyGage R&R Study (Nested) 结果中只能看到丈量系统的反复性 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 Variatio

39、n 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运用前面

40、一样的数据51NO-GOGOErrorOperator 2Operator 1定性数据(Attribute Data)的丈量系统52定性数据(Attribute Data)的丈量系统的可靠性 Go-No Go 数据方式人为要素主导，情况复杂 统计模型多种多样 统计学上各家争鸣，尚无定论 实际中采用何种方式，取决于实例与统计模型的接近程度53对于以“是和“不是为计数根底的定性数据，其 GR&R调查的概念是与定量数据一样的。但方法上完全不同.定性数据丈量系统的才干取决于操作员判别的有效性，即将“合格判别成合格，将“不合格判别成不合格的程度.计数型丈量系统才干分析方法例如54以下为判别所用的目的 有

41、效性 Effectiveness(E) - 即判别“合格与“不合格的准确性 E= 实践判别正确的次数/能够判别正确的时机次数. 漏判的几率 Probability of miss(P-miss) - 将“不合格判为合格的时机 P(miss)=实践漏判的次数 / 漏判的总时机数.误判的几率 Probability of false alarm(P-FA) - 将“合格判为不合格的时机. P(false alarm)=实践误判次数 / 误判的总时机数.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 BQual

42、ity 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

43、 0.288675 2.76546 0.002862ICC等级关联络数Intraclass Correlation Coefficient当产品的质量断定不仅仅是合格与不合格两种性质，而是进展多个等级的区分时ICC针对不同情行下的丈量系统进展评价ICC运用平方和 Sums of Square来进展评价任务实例：某公司建立评价系统来丈量采购订单(PO)完成的质量程度，选了三个高级采购员对个订单的完成好坏进展打分评价，分代表很差，分代表很好，结果如下63PO#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 BBuye