工程方法_6sigma_10测量系统分析

1、MSA-Measurement System Analysis (GR&R)测量系统分析(重复性和再现性)主 要 培 训 内 容Learning Objectives学习目的Explain how measurement is a process解释工序中如何进行测量的Effects of Measurement System variability on the process variability测量系统误差对工序误差的影响Basic terms and concepts in MSAMSA的基本术语和内容Analysis of Variable GR&R计量型GRR 的分析Analys

2、is of Attribute GR&R计数型GRR的分析Analysis and Application of Nested GR&R 嵌套式GRR 的分析和应用如果从你座位前的电脑上看上面的图片左边的脸是生气的脸而右边的脸是平静的脸但请你起立往后走35步突然间他们交换位置了!这个幻觉图片是由Glasgow大学的PhillippeG.SchynsandAudeOliva所设计由此证明,我们可能从来没看到过事情的真正面貌。看出来了别忘了回到座位上，呵呵What is a Measurement System?测量系统是什么? 测量: 以确定实体或系统的量值大小为目标的一整套作业测量系统: 由人

3、,量具,测量方法和测量对象构成的过程的整体测量系统分析: 指用统计学的方法来了解测量系统中的各个波动源,以及它们对测量结果的影响,最后给出本测量系统是否合乎使用要求的明确判断.观测值真实值测量系统测量人员测量设备测量物料测量方法测量环境Verify product/ process conformity to specifications验证产品/工序和规格的一直性Assist in continuous improvement activities为连续性的改善活动提供支持Why Worry About Measurement Variation? 为什么担心测量系统误差?Consider

4、the reasons why we analyze the measure system:想一下为何我们要分析测量系统:How might measurementvariation affect these decisions?测量变异影响以上这些决定有多大程度?What if the amount of measurement variation is unknown如果测量误差未知那又到何种程度?Product产品Measurement测量Product产品Measurement测量Measurement variation can make our processes LOOK wor

5、se than they are.测量误差能使我们的工序看起来比实际更差MSA: Warm-up Exercise MSA: 热身练习Line 2拉 2Line 1拉 1From ongoing line monitoring, we conclude that Line 1 and Line 2 are producing similar parts (same spread).从观测结果看,我们认定拉1和拉2生产相同的产品(相同分布)Process variability study工序方差研究s2observed (Equal for both lines)两条拉观测值相同Enginee

6、ring decides to perform a MSA to understand measurement variability, before proceeding with improvement plans在进行改善计划前,工程部决定进行测量系统分析来分析测量变异,Line 拉1Line拉 2Total Variability(observed)全部变异(观测值)Measurement Variability测量变异S2observed观测值s2 MS 1测量系统!s2 MS 2测量系统2MSA: Warm-up Exercise MSA: 热身练习Process variabil

7、ity study工序方差研究Questions问题:1. Are the two lines equivalent ?两条拉一样吗?2. Which measurement system is useful to detect process variability ?哪一个测量系统适用于检测工序变异?3. What would you do next for process improvement for each line ?对于每一条拉的改善行动,你下一步打算做什么?Line拉 1Line拉 2Total Variability(observed)全部变异(观测值)Measuremen

8、t Variability测量变异True Process Variability真实工序变异s2true process(真实状况) + s2MS(测量系统) = s2observed(观测的)MSA: Warm-up Exercise MSA: 热身练习Measurement System Analysis Approach测量系统分析方法There are two types of measurements possible:两种可能的测量Variable计量值Data can be described on a continuous scale数据可以用连续的标尺描述Attribute

9、计数值Data cannot be adequately described on a continuous scale数据不能以连续的标尺描述Pass / Fail, very low counts通过/不通过,好/坏 Each must be approached differently.每一种方法必须用不同的处理方法Variable Measurement System Analysis计量值测量系统分析The ideal measurement system will produce “true” measurements every time it is used (Zero Bia

10、s, Zero Variance).理想的测量系统每次会得出”真”测量值(零偏差,零变异)Study of your measurement system will reveal the relative amount of variation in your data that results from measurement system error.研究你的测量系统可以揭示数据中包含的测量误差的变异量It is also a great tool for comparing two or more measurement devices or two or more operators.

11、它可以是一个很好的工具比较两或更多测量设备或两或两个以上测量员工.MSA should be used as part of the criteria for accepting a new piece of measurement equipment to manufacturing.MSA 应该是制造业的新测量系统的合格接受标准It should be the basis for evaluating a measurement system which is suspect of being deficient.应该为受怀疑的测量系统能力不足提供评估基础It should be part

12、 of the periodic maintenance program.应该是定期维护程序的一部分.Possible Sources of Process Variation测量误差的可能来源To address actual process variability, variation due to the measurement system must first be identified and separated from that of the process为了准确定义实际的工序变异,和测量系统变异,我们必须首先从工序变异中验证和区分它们.Observed Process Va

13、riation观测的工序误差Actual Process Variation实际的工序误差Measurement Variation测量误差Long-term Process Variation长期的工序误差Short-term Process Variation短期的工序误差Variation With Sample样本间误差Variation dueTo instrument测量设备误差Variation dueTo Operators员工操作误差Repeatability重复性Bias偏差Stability稳定性Linearity线性Reproducibility再现性Resolutio

14、n精度MeasurementVariationHumidityCleanlinessVibrationLineVoltageVariationTemperatureFluctuationOperatorTechniqueStandardProceduresSufficientWorkTimeMaintenanceStandardCalibrationFrequencyOperatorTrainingEaseofDataEntryTool工具Environment环境Work Methods工作方法Sources of Measurement Variation测量误差的来源WARNING敬告I

15、gnoring these variables can adversely affect the gage study.忽略这些变量会阻碍仪器研究Mechanical instability机械不稳定性 Electrical instability 电子不稳定性 Algorithm instability 运算不稳定性 Wear 磨损数据输入不仔细 员工培训 校正频率 维护标准 不足够的工作时间 标准程序 员工技术测量误差 湿度 清洁度 震动 电压变动温度波动Measurement System Variability - Determined through “R&R Study”测量系统误

16、差通过”重复性和再现性研究决定Accuracy准确性Precision精确性ssstotalproductmeasurement222=+totalproductmeasurementMeasurement System Bias -Determined through “Calibration Study”测量系统偏差通过”校正研究”决定Averages平均值Variability误差Effects of Measurement Error测量误差的影响Common Terms in Variable MSA计量值测量系统分析的一般术语“Accuracy” related terms:”准确

17、性”相关的术语Bias偏差Linearity线性Stability稳定性“Precision” related terms :”精确性”相关的术语Repeatability重复性Reproducibility再现性Discrimination (Resolution)分辨力(精度)Concerned with the Mean和均值有关Concerned with the Variance和方差有关准确度和精确度1)准确但不精确2) 精确但不准确3)既不精确也不准确4)既精确又准确Accuracy准确性Instrument accuracy (or bias) is the differenc

18、e between the observed average value of measurements and the master value.设备精确性(或偏差)是观测的平均值和基准值之间的差别The master value is an accepted, traceable reference standard (e.g., NIST).基准值(标准值)是可接受的,可追述的参考标准(Master Value基准值(Reference Standard)参考值Average Value平均值Accuracy or Bias精度或偏差Effects of Accuracy精确度的影响Ac

19、tual processAverage实际的工序均值Measurement Bias测量偏差Observed processAverage观测到的工序均值Effect on the process: 工序影响Shifts the mean of the distribution 分布均值的偏移Bias123全部产品测量系统Instrument 2Instrument 1Master Value(Reference Standard)AverageValueAccuracy精确度Accuracy may be affected by two different types of sources:

20、 精确度可能受两种来源的影响:Lack of good calibration to a true standard缺乏真实标准值的良好校正Average Bias: different operators or machines are centered differently, such that their average is offset from the true value平均偏差:不同的员工或不同的机器不同地集中,这样一来他们的均值和真实值有一定的偏移量.Average BiasBias标准值(参考标准)平均值偏差设备1设备2Accuracy or Bias精度或偏差An en

21、gineer chose five “golden units” that represented the expected range of measurements. Twelve random measurements were made on each part. Historical process variation was found to be 12 mm.一工程师选择五个”金标准样本”希望得出测量系统的偏差, 每一个样本随机测量12次, 历史工序误差是12mm.Data can be found in the 01-05.MTW file.数据在01-05文件Mean of

22、the sixty measurements 60次测量的均值 x= 5.9467 mmMean value of the five standards 5个标准值的均值 = 6 mmBias= x = 5.9467 6= 0.0533 mm= 0.444% of process variationExample 1例1A measure of the change in bias over the range of instrument capability.测量系统的线性是指在其量程范围内,偏倚是基准值的线性函数.Linearity is an issue here线性是这的一个结果Lin

23、earity线性BiasTrue Value真实值Accuracy changes over part range精度在整个范围的变化TrueValue1真实值1TrueValue 2真实值1TrueValue 3真实值3TrueValue 4真实值4偏倚定义Linearity线性BiasTrue Value真实值Accuracy changes over part range精度在整个范围的变化偏倚斜率b线性 = 斜率b X 过程变差Std Deviation标准偏差Linearity线性Using the data set from Example 1,用例1的数据(01-05文件)Mas

24、terMean Error 20.49167 40.12500 60.02500 8 - 0.29167 10 - 0.61667Best Fit Line最好的拟合线 : Mean Error 均值偏差 = 0.7367 - 0.1317 MasterLinearity线性 = 0.1317 12 = 1.58 mm(13.17% of process variation)Example 2例2= (Ave. of 12 measurements) - (Master Value)=(12个测量值的均值)-(标准值)Linearity线性Compute the accuracy and li

25、nearity for the data in Example 1, using MiniTabs Gage Linearity Study.计算在例1中数据的精度和线性,用MiniTab: Gage Linearity StudyExample 3例3Stat Quality Tools Gage Linearity StudyExample 3此为MiniTab13版本Gage Linearity & Accuracy Study计量仪线性和精度研究Gage Linearity & Accuracy Study计量仪线性和精度研究Stability稳定性The distribution o

26、f measurements remains constant and predictable over time for both mean and standard deviation对于均值和标准偏差测量的分布随时间保留恒定的可预测的No drifts, sudden shifts, cycles, etc无漂移,突然偏移,循环,等等.Evaluated using a trend chart用一个趋势图评估Ensured through a regular calibration and R&R program通过定期的校正和重复性和再现性程序Master Value真实值(Refer

27、ence Standard)参考标准Time 2时间2Time 1时间1A measure of the change in bias over time.在一定时间内偏差变化的测量Effects of Stability稳定性的影响Long term observedvariabilityActual processdistributionMeas. Systemday 1Meas. Systemday 2Meas. Systemday 3Effect on the process:工序的影响Increases process variability over time.随时间增加工序变异T

28、ime实际的工序分布测量系统第一天测量系统第二天测量系统第三天长期观测到的变异Precision精确度Actual processvariabilityMeasurement variabilityTotal observedvariabilityEffect on the process:工序的影响Increases process variability.增加工序变异实际的工序变异测量变异全部观测到的变异Precision精确度Total variation in the measurement system测量系统的全部变异Measure of the total variation o

29、f repeated measurements重复测量的全部变异Precision equals the sum of Repeatability and Reproducibility精确度相当于重复性和再现性的总和 s reproducibilityrepeatabilityproducttotal 2 2 2 2 sss + +=Precision: Repeatability精确度:重复性Repeatability重复性The inherent variability of the measurement device测量设备本身的变异Variation that occurs whe

30、n repeated measurements are made of the same variable under similar conditions:在相同的状态下测量重复的数据时产生的变异: Same part 相同的产品 Same operator 相同的员工 Same set-up 相同的设置 Same environmental conditions 相同的环境状况 Short-term 短期Estimated by the pooled (average) standard deviation of the distribution of repeated measureme

31、nts利用pooled (average) standard deviation 计算重复测量sss s 2 2 2 2totalproductrepeatabilityreproducibility=+ +Precision: Repeatability精确度:重复性Repeatability: the variation between successive measurements of the same part, same characteristic, by the same person using the same instrument. Also known as test

32、- retest error; used as an estimate of short-term measurement variation.重复性: 同一个操作者利用相同的设备,连续测量相同部分,相同特性,所获得的测量值的变差.Master ValueGood RepeatabilityPoor Repeatability标准值良好的重复性差的重复性sss s 2 2 2 2totalproductrepeatabilityreproducibility=+ +Precision: Reproducibility精确度: 再现性Reproducibility:再现性 The variati

33、on that results when different conditions are used to make the same measurements 在不同状况下做相同测量而导致的变异:Different operators 不同的操作者Different set-ups 不同的设置Different test units 不同的测量对象Different environmental conditions 不同的环境状况Long-term measurement variation 长期的测量变异 Estimated by the standard deviation of the

34、 averages of measurements from different measurement conditions用不同的测量状况下的测量均值的标准差计算Inspector AMaster ValueInspector BInspector CMachine AMachine BMachine CReproducibility: The standard deviation of the averages of the measurements made by different persons, machines, tools, etc. when measuring the i

35、dentical characteristic on the same part再现性: 当测量相同元件的指定特性时,不同操作者,机器,工具等的测量均值的标准偏差.Precision: Reproducibility精确度: 再现性标准值操作者A操作者B机器A操作者C机器B机器CExample: Accuracy vs Precision练习:准确性和精确性Suppose we have a reference material with a true hardness of 5.0:假设我们有一个”真”强度值5.0的参考材料Method 1 gives the following readi

36、ngs:方法1.给出下列读值3.8, 4.4, 4.2, 4.0Method 2 gives the following readings:方法2.给出下列读值6.5, 4.0, 3.2, 6.3Which method is more accurate?哪种方法更准确?Which method is more precise?哪种方法更精确Which method do you prefer? Why?你更愿意用哪种方法? 为何?Discrimination (Resolution)分辨力(精度)The number of decimal places that can be measure

37、d by the system. Increments of measure should be at least one-tenth of the width of the product specification or process variation.测量系统测量的小数点的位数, 测量的增量至少是产品规格或工序总波动的1/10.12Which ruler should be used to measure parts for the process represented by the distribution above ?哪一个尺子应该用于测量上述工序分布?Measurement

38、 System Variance: s2meas = s2repeat + s2reprod 测量系统方差 Primary output of analytical Gage R&R 分析GRR的主要输出To determine whether the measurement system is “good” or “bad” for a certain application, you need to compare the measurement variation to the product spec or the process variation决定测量系统是否是”好的” 或”怀的

39、”对于一定的应用. Comparing s2meas with Tolerance:同公差比较s2meas Precision-to-Tolerance Ratio (P/T)精确度对于公差比 Comparing s2meas with Process Variation (P/TV):同工序变异比较s2meas % Repeatability and Reproducibility (%R&R) 重复性和再现性的百分比Discrimination Index 分辨指数Measurement System Metrics测量系统组成Precision to Tolerance Ratio精确度

40、对于公差比Addresses what percent of the Tolerance is taken up by measurement error.表明测量误差占了公差的百分比5.15 smeas represents 99% of all measurements5.15 smeas 代表 99% 的测量Best case: 10% Marginally Acceptable: 30%最好: 10% 最低可接受: 30% Includes both repeatability and reproducibility包括重复性和再现性Usually expressed as perce

41、nt通常用百分比表达Tolerance = USL - LSLP/T Ratio精确度对于公差比P/TV%R&R(or % Contribution)Addresses what percent of the Total Variation is due to measurement error表明测量误差占了全部方差的百分比P/TV: Best case: 10% Acceptable: 30%P/TV: 最好: 10% 可接受: Make Patterned Data Simple Set of Numbers (for each input)Step 4: Ask the first o

42、perator to measure all the samples once in random order. Blind sampling, in which the operator does not know the identity of each part should be used to reduce human bias.步骤4: 让第一个员工随机测量所有的样本一次, 模糊样本,让操作者不知道哪一个样本以减少人为误差.Step 5: Have the second operator measure all the samples once in random order an

43、d continue until all operators have measured the samples once (this is trial 1)步骤5.: 让第二个操作者随机测量所有的样本,一直到所有的操作者测量完所有的样本一次.(这是第一次)Step 6: Repeat steps 4 & 5 for the required number of trials. It is best if these measurements can be done over several days.步骤6.重复步骤4.和5完成需要的次数.最好是这些测量能在这几天内完成.Step 7: En

44、ter the data and tolerance information into Minitab 步骤7: 输入数据和公差在MiniTab中.Stat Quality Tools Gage R&R StudyStat Quality Tools Gage Run ChartStep 8: Analyze the results by assessing the quality of the measurement system based on the guidelines on the following page. Determine follow-up actions.步骤8: 根

45、据下面的指引通过评估测量的质量来分析结果.决定下列步骤: The Method - Calculating Gage Capability方法计算测量仪器能力MSA Sample Guidelines测量系统分析 样本指引Usually 10 samples, 2-4 operators (if several operators use the gauge), 2-3 trials用10个样本2-4个操作者(如果有几个操作者使用这个仪器),2-3次重复Depending on the purpose of the study 1 or more gages will be included由

46、研究1或更多的仪器所决定.In general select enough samples so that number of samples x number of operators/gages 15一般来说选择足够的样本,样本数量和操作者成绩和仪器比大于15SAMPLE SELECTION 样本选择Option 1: if process variability is unknown, the samples selected should be representative of the normal process/product variation (to get TV)选择1:

47、如工序变异不知,样本选择应该代表正常的工序/产品变异(取得全部变异)Option 2: if process variability is known, the samples selected should uniformly span beyond the width of the specs选择2: 如工序变异已知,则样本选择应均匀分布在规格范围内外(不应超过规格过多).*Example: Minitab例: MiniTabStep 1: Randomly select 10 samples. In addition, identify the operators who use thi

48、s instrument daily步骤1.随机选取10个样本,并且确认每日操作此设备的员工(Parts 1 through 10 were collected and three operators were identified).部分1到10被选取并三个确认的操作者Step 2: Calibrate the gage or verify the last calibration date is valid步骤2.校正测量仪器或确认最近的一次校正是否有效Use Calc Make Patterned Data Simple Set of NumbersStep 3: Setup the M

49、initab data collection sheet for the R&R study. Create the R&R data collection sheet for 10 parts each measured 2 times by 3 operators步骤3.准备好MiniTab数据收集sheet做GR&R研究,每10单位测量2次被3个操作者, Column headings: 列题头Column 1: Part ID (1-10)Column 2: Operator (1-3)Column 3: Trial (1-2)Column 4: Measurement(s)Step

50、4: Ask the first operator to measure all the samples once in random order. Blind sampling, in which the operator does not know the identity of each part should be used to reduce human bias.步骤4: 让第一个员工随机测量所有的样本一次, 模糊样本,让操作者不知道哪一个样本以减少人为误差.Step 5: Have the second operator measure all the samples once

51、in random order and continue until all operators have measured the samples once (this is trial 1).步骤5.: 让第二个操作者随机测量所有的样本,一直到所有的操作者测量完所有的样本一次.(这是第一次)Step 6: Repeat steps 4 & 5 for the required number of trials.(We assume the above steps were executed. See GageR&R.mtw.) 步骤6.重复步骤4.和5完成需要的次数(我们假设上述步骤已完成

52、,看文件01-06)Example - Gage R&R using Minitab例子: 仪器重复性和再现性研究用MiniTabANOVA method is preferred.选择ANOVA方法.Step 7: Enter the data and tolerance information into Minitab.步骤7: 输入数据和公差在MintTab Stat Quality Tools Gage R&R StudyFN: GageR&R.mtwEnter Gage Info and Options (see next page)Example - Gage R&R using

53、Minitab例子: 仪器重复性和再现性研究用MiniTabtotalmeastotalmeasTVPssss=22/Step 7: Enter the data and tolerance information into Minitab. 步骤7: 输入数据和公差在MintTabStat Quality Tools Gage R&R StudyGage Info (see below) & OptionsLSLUSLLSLUSLTPMSMS-=-=ss*15.5*15.5/2Note: The denominator of the P/TV calculation can be estim

54、ated from the samples used in the study or from a historical estimate.注意:P/TV 计算的分母是由所研究的样本得来的,或从历史数据而来.Example - Gage R&R using Minitab例子: 仪器重复性和再现性研究用MiniTabGage R&R Study - ANOVA MethodANOVA Table With Operator*Part InteractionSource DF SS MS F P Parts 9 2.05871 0.228745 39.7178 0.00000Operators

55、2 0.04800 0.024000 4.1672 0.03256Oper*Part 18 0.10367 0.005759 4.4588 0.00016Repeatability 30 0.03875 0.001292 Total 59 2.24912 Gage R&RSource VarComp StdDev 5.15*SigmaTotal Gage R&R 0.004437 0.066615 0.34306 Repeatability 0.001292 0.035940 0.18509 Reproducibility 0.003146 0.056088 0.28885 Operator

56、0.000912 0.030200 0.15553 Oper*Part 0.002234 0.047263 0.24340 Part-To-Part 0.037164 0.192781 0.99282 Total Variation 0.041602 0.203965 1.05042 Source %Contribution %Study Var %ToleranceTotal Gage R&R 10.67 32.66 22.87 Repeatability 3.10 17.62 12.34 Reproducibility 7.56 27.50 19.26 Operator 2.19 14.8

57、1 10.37 Oper*Part 5.37 23.17 16.23 Part-To-Part 89.33 94.52 66.19 Total Variation 100.00 100.00 70.03 Number of Distinct Categories = 4 Session Window Output:Graphical Output:Answers! But what do they mean?Lets investigate each section one at a time.Gage R&R Output重复性和再现性输出Gage R&R Study - ANOVA Met

58、hodANOVA Table With Operator*Part InteractionSource DF SS MS F p-valueParts 9 2.05871 0.228745 39.7179 0.00000Operators 2 0.04800 0.024000 4.1672 0.03256Oper*Part 18 0.10367 0.005759 4.4588 0.00016Repeatability 30 0.03875 0.001292 Total 59 2.24913 The ANOVA table provides insight into the significan

59、ce of the various possible sources of errorANOVA方法揭示了不同可能原因错误的重要度However, ANOVA will be covered in the Module 3.Gage R&R, ANOVA TableGauge R&R Study - ANOVA MethodSource Var Comp Std Dev 95% Conf Int 5.15*Sigma Total Gauge R&R 0.004437 0.066615 (0.0597,0.2250) 0.34306 Repeatability 0.001292 0.035940

60、 (0.0287,0.0480) 0.18509 Reproducibility 0.003146 0.056088 ( *, *) 0.28885 Operator 0.000912 0.030200 (0.0000,0.2169) 0.15553 Oper*Part 0.002234 0.047263 (0.0254,0.0800) 0.24340 Part-To-Part 0.037164 0.192781 (0.1098,0.3345) 0.99282 Total Variation 0.041602 0.203965 1.05042 Variance due to the measu