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1、Chapter 3.2Measurement Systems Analysis测量系统分析,2022/12/8,2,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 KELVIN,The Science of Measurement,2022/12/8,3,Effects of Measurement Error,Averages,Variability,Measurement
2、System Bias,Measurement System Variability,Accuracy,Precision,s2total = s2product + s2meas system,2022/12/8,4,测量误差,平均值,变差,测量系统的偏差,测量系统的变差,准确度,精确度,s2total = s2产品 + s2测量系统,Sources of Measurement Variation,2022/12/8,6,测量误差的原因,M,e,a,s,u,r,e,m,e,n,t,V,a,r,i,a,t,i,o,n,H,u,m,i,d,i,t,y,C,l,e,a,n,l,i,n,e,s,s
3、,V,i,b,r,a,t,i,o,n,L,i,n,e,V,o,l,t,a,g,e,V,a,r,i,a,t,ion,T,e,m,p,e,r,a,t,u,r,e,F,l,u,c,t,u,a,tion,O,p,e,r,a,t,o,r,T,e,c,h,n,i,q,u,e,S,t,a,n,d,a,r,d,P,r,o,c,e,d,u,r,e,s,S,u,f,f,i,c,i,e,n,t,W,o,r,k,T,i,m,e,M,a,i,n,t,e,n,a,n,c,e,S,t,a,n,d,a,r,d,C,a,l,i,b,r,a,t,i,o,n,F,r,e,q,u,e,n,cy,O,p,e,r,a,t,o,r,T,r
4、,a,i,n,i,n,g,E,a,s,e,o,f,D,a,t,a,E,n,t,r,y,电性能不稳定,磨损,机械不稳定性,量具,环境,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,2022/12/8,7,看到的不一定真实,Possible Sources of Process Variation,Long-term,Process Variation,Short-term,Process Variation,Variation,w/i sample,Actual Process Va
5、riation,Stability,Linearity,Repeatability,Accuracy,Variation due,to gage,Variation due,to operators,Measurement Variation,Observed Process Variation,We will look at “repeatability” and “reproducibility” as these are the primary contributors to measurement error.,Reproducibility,2022/12/8,9,过程变差剖析,长期
6、,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,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,过程变差,Accuracy,Accuracy Does the average of the measurements deviate from the true value?True value:Theoretically correct valueNIST standardsBiasDistance between average value of all measurements and true v
7、alueAmount gage is consistently off targetSystematic error or offset,2022/12/8,11,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-
8、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.,ObservedAverageValue,ReferenceValue,BIAS Definition,2022/12/8,13,BIAS 测量结果的平均值与参考值的差异. 参考值（reference-v
9、alue）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BIAS,X1=0.75mmX6=0.8mmX2=0.75mmX7=0.75mmX3=0.8mmX8=0.75mmX4=0.8mmX9=0.75mmX5=0.65mmX10=0.7mm,One Part Measured Ten Times by One Appraiser,What else do you need to determine BIAS?,The reference Value determined by the layout inspection
10、equipment (ensure this equipment went through a Gage R&R) is 0.80mm. The process variation for the part is 0.70mm.,= 0.75,Bias = 0.75-0.8= -0.05,% Bias=1000.05/0.70=7.1%,This means 7.1% of the process variation is BIAS,BIAS EXAMPLE:,2022/12/8,15,X1=0.75mmX6=0.8mmX2=0.75mmX7=0.75mmX3=0.8mmX8=0.75mmX4
11、=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,= 0.75,Bias = 0.75-0.8= -0.05,% Bias=1000.05/0.70=7.1%,表明 7.1% 的过程变差是偏倚 BIAS,偏倚BIAS 实例:,Precision,Total variation in the measurement systemMeasure of natural variation of repeated measurementsTerms: Random Error, Spread, T
12、est/Retest errorRepeatability and Reproducibility,s,s,s,MS,G,O,2,2,2,=,+,2022/12/8,17,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）,s,s,s,MS,G,O,2,2,2,=,+,精确度（Precision),Precision: Repeatability,The inherent variability of the measurement systemVariation in measurements obt
13、ained 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 measurements Repeatability is less than the total variation of the measurement system,2022/12/8,19,测量系统内在的变异性基于重复测量的数据，用分组
14、后组内的标准偏差来估算 小于测量系统的总变差,精确度：重复性,Precision: Reproducibility,Operator 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 ave
15、rages, based on measurements taken by different operators Must be adjusted for gage variationReproducibility is less than the total variation of the measurement system,2022/12/8,21,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,Linearity,Difference in the accuracy value
16、s of a gage through the expected operating range of the gage,Good Linearity,Bad Linearity,2022/12/8,23,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,好的线性,差的线性,Stability,The distribution of measurements remains constant and predictable over time for both mean and standard deviationTotal variation
17、 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 time,Time-1,Time-2,time,Magnitude,Stability,2022/12/8,25,在一段时间内，测量结果的分布无论是均值还
18、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）,量值,2022/12/8,26,Discrimination,The technological ability of the measurement system to adequately differentiate between values of a measured parameter.,2022/12/8,27,测量系统的分辨率（ discrimination）,要求不低于过程变差或允许偏差（ tolerance）
19、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/ 总的量具偏差* 1.41.,Generally two or three operatorsGenerally 10 units to measureEach unit is measured 2-3 times by each operator,Gage R&R study,Determine if reproducibility is an issue. If it is, select the number of operators to parti
20、cipate.Operators selected should normally use the measurement system.Select samples that represent the entire operating range.Gage must have graduations that allow at least one-tenth of the expected process variation.Insure defined gaging procedures are followed.Measurements should be made in random
21、 order.Study must be observed by someone who recognizes the importance of conducting a reliable study.,2022/12/8,29,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
22、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,2022/12/8,30,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RA,2022/12/8,31,测量系统分析,R=(RA+RB+RC)/3XDIFF=MaxXA,XB,XC-MinXA,XB
23、,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/Tolerance,n=样品个数r=每个人对每个样品的试验次数,r,K1,23,4.453.05,K2,23,3.652.70,测试人数,n,K3,78910,1.821.741.671.62,K1=5.15/d2,*AV计算中，如根号下出现负值，AV取值0,2022/12/8,32,EV= Equipment
24、 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-Part Constants,GR&R研究中的名词,2022/12/8,33,卡尺的R&R研究 Excel 运算,2022/12/8,34,R&R 对过程能力计算的影响,
25、70%,60%,50%,40%,30%,10%,R&R Effect on Capability,Guidelines,% R&RResults5%No issues 10%Gage is OK10% 30%Maybe acceptable based upon importanceof application, and cost factorOver 30%Gage system needs improvement/correctiveaction,Variable Gage R&R,2022/12/8,36,% R&RResults 30%测量系统需要改进,Gage R&R 判断原则,20
26、22/12/8,37,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 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
27、100.00 101.15 Number of distinct categories = 7,Minitab 计算GR&R,Xbar-R 均值极差法,注：使用同组数据,MinitabStatQuality ToolsGage StudyGage R&R Study (Crossed)在Method of Analysis中选择 Xbar and R,2022/12/8,38,Minitab 计算GR&R,图解数据,2022/12/8,39,%ContributionSource VarComp (of VarComp) Total Gage R&R 0.000459 4.53 Repeata
28、bility 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
29、 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 = 6,Minitab 计算G
30、R&R-ANOVA 法,在Method of Analysis中选择ANOVA,2022/12/8,40,Measurement Variation Vs. Tolerance,Precision 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 customers,Note: 5.15 standard deviations accounts for 99% of MS variation. The use of 5.15 is an industry standard.,2022/12/8,41,Measurement Variation Vs. Process (Analytical),Percent Repeatability & Reproducibility (%R&R)Addresses what percent of the Total Variat
32、ion 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 of the calculation.%R&R is required
33、by certain customers,2022/12/8,42,P/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。,2022/12/8,43,%R&R = 20%,%R&R = 50%,%R&R = 100%,测量系统变差,P/T = 20%,P/T =
34、50%,P/T = 100%,2022/12/8,44,%R&R = 25%,%R&R = 50%,%R&R = 100%,测量系统变差,P/T = 50%,P/T = 100%,P/T = 200%,2022/12/8,45,%R&R = 20%,%R&R = 40%,%R&R = 100%,测量系统变差,P/T = 10%,P/T = 20%,P/T = 50%,过程实际变差,2022/12/8,46,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%
35、Gage R&R = 量具误差Gage Error / 允差Tolerance = 6.1 / 20 * 100 % = 30.5%,快速GR&R（短期模式）,d常数表,允差Tolerance = 20,= 最大值-最小值,2022/12/8,47,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
36、 = 185 - 215,2022/12/8,48,短期与长期方法的比较,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,2022/12/8,49,正常标准方法,Part,A,B,Test 1Test 2,Operator,对同样的样品进行重复测量(称之为交叉设计 Cross
37、ed Designed),巢式设计 Nested Design,C,Test 1Test 2,Test 1Test 2,OperatorI,OperatorII,OperatorIII,样品来自同一总体,PartTest,I,II,III,破坏性测量和不可重复的测量,2022/12/8,50,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 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 StudyG
38、age R&R Study (Nested) 结果中只能看到测量系统的重复性,2022/12/8,51,Gage 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) (
39、%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,2022/12/8,52,NO-GO,GO,定性数据(Attribute Data)的测量系统,2022/12/8,53,
40、定性数据(Attribute Data)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,2022/12/8,54,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.,计数型测量系统能力分析方法示例,2022/12/8,55,以下为判断所用的指标 有效性 Effectiveness(E) - 即判断“合格”与“不合格”的准
41、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 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 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 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 B1, 偏向漏判,2022/12/8,56,样品大小的规定样品的选择 由专家
42、或可作标准的人员选定样品 1/3 合格 1/3 不合格 1/3 模糊 (50% 接近合格， 50% 接近不合格) 随机地给操作员检验.,2022/12/8,57,实例: 由主管选取14 个样品（其中 8 个合格， 6 个不合格） 三个操作员对每个样品测三次 记录中 A= 接受（accept）， R= 拒收（reject）,2022/12/8,58,计算判断的指标,检验结果总结,2022/12/8,59,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 Chart,2022/12/8,60,Kappa-如果不知道标准样品,Kappa 用
43、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 Fail+Fail Fail)*(Fail Pass+Fail Fail)/总的检验次数之方,对于两个操作员,2022/12/8,61,例如两个检验员目测12来料样品,P代表合格, F代表不合格,Pobs
44、erved=(8+3)/12=11/12,Pchance=(8+0)*(8+1)/144+(1+3)*(0+3)/144=7/12,Kappa=(11-7)/(12-7)=0.8,一般要求Kappa 大于0.75, 小于0.4则表示很差,QC1,QC2,2022/12/8,62,测量系统一致性在Minitab 中的计算,MinitabQuality ToolsAttribute Agreement Analysis,Between Appraisers Assessment Agreement# Inspected # Matched Percent 95 % CI 12 11 91.67 (
45、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 0.0028,2022/12/8,63,ICC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
46、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,2022/12/8,64,定义如下平方和项BMS=Between mean square EMS=Error mean squareJMS=Judge mean squareWMS=Within mean squareTMS=Total mean square,2022/12/8,65,Sum of all squared: 1182Average of all: 6.0
47、7Sum X average=6.07X182=1110.81,Degree of freedomBuyers=3-1=2Between PO=10-1=9Total=30-1=29Within PO=10X(3-1)=20Error=29-9-2=18,2022/12/8,66,BMS=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=(
48、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=0.344,2022/12/8,67,三种情形下的ICC计算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每个
49、采购员的可信度为： (k代表采购员的个数）ICC=(BMS-WMS)/BMS+(k-1)WMS=(6.57-0.6)/(6.57+2*0.6)=0.77采购员的平均可信度为ICC=(BMS-WMS)/BMS=(6.57-0.6)/6.57=0.91,2022/12/8,68,2. 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
50、度为ICC=(BMS-EMS)/BMS+(JMS-EMS)/n =(6.57-0.344)/6.57+(2.9-0.344)/10 =0.91,2022/12/8,69,3.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 =0.95,ICC的接收下限为0.7, 0.9以上比较好,2022/12/8,70,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。辣度分为
