工程方法_6sigma_10測量系統(tǒng)分析

1、MSA-Measurement System Analysis (GR&R)測量系統(tǒng)分析(重復性和再現(xiàn)性)主 要 培 訓 內(nèi) 容Learning Objectives學習目的Explain how measurement is a process解釋工序中如何進行測量的Effects of Measurement System variability on the process variability測量系統(tǒng)誤差對工序誤差的影響B(tài)asic terms and concepts in MSAMSA的基本術語和內(nèi)容Analysis of Variable GR&R計量型GRR 的分析Analys

2、is of Attribute GR&R計數(shù)型GRR的分析Analysis and Application of Nested GR&R 嵌套式GRR 的分析和應用如果從你座位前的電腦上看上面的圖片左邊的臉是生氣的臉而右邊的臉是平靜的臉但請你起立往后走35步突然間他們交換位置了!這個幻覺圖片是由Glasgow大學的PhillippeG.SchynsandAudeOliva所設計由此證明,我們可能從來沒看到過事情的真正面貌?？闯鰜砹藙e忘了回到座位上，呵呵What is a Measurement System?測量系統(tǒng)是什么? 測量: 以確定實體或系統(tǒng)的量值大小為目標的一整套作業(yè)測量系統(tǒng): 由人

3、,量具,測量方法和測量對象構成的過程的整體測量系統(tǒng)分析: 指用統(tǒng)計學的方法來了解測量系統(tǒng)中的各個波動源,以及它們對測量結果的影響,最后給出本測量系統(tǒng)是否合乎使用要求的明確判斷.觀測值真實值測量系統(tǒng)測量人員測量設備測量物料測量方法測量環(huán)境Verify product/ process conformity to specifications驗證產(chǎn)品/工序和規(guī)格的一直性Assist in continuous improvement activities為連續(xù)性的改善活動提供支持Why Worry About Measurement Variation? 為什么擔心測量系統(tǒng)誤差?Consider

4、the reasons why we analyze the measure system:想一下為何我們要分析測量系統(tǒng):How might measurementvariation affect these decisions?測量變異影響以上這些決定有多大程度?What if the amount of measurement variation is unknown如果測量誤差未知那又到何種程度?Product產(chǎn)品Measurement測量Product產(chǎn)品Measurement測量Measurement variation can make our processes LOOK wor

5、se than they are.測量誤差能使我們的工序看起來比實際更差MSA: Warm-up Exercise MSA: 熱身練習Line 2拉 2Line 1拉 1From ongoing line monitoring, we conclude that Line 1 and Line 2 are producing similar parts (same spread).從觀測結果看,我們認定拉1和拉2生產(chǎn)相同的產(chǎn)品(相同分布)Process variability study工序方差研究s2observed (Equal for both lines)兩條拉觀測值相同Enginee

6、ring decides to perform a MSA to understand measurement variability, before proceeding with improvement plans在進行改善計劃前,工程部決定進行測量系統(tǒng)分析來分析測量變異,Line 拉1Line拉 2Total Variability(observed)全部變異(觀測值)Measurement Variability測量變異S2observed觀測值s2 MS 1測量系統(tǒng)!s2 MS 2測量系統(tǒng)2MSA: Warm-up Exercise MSA: 熱身練習Process variabil

7、ity study工序方差研究Questions問題:1. Are the two lines equivalent ?兩條拉一樣嗎?2. Which measurement system is useful to detect process variability ?哪一個測量系統(tǒng)適用于檢測工序變異?3. What would you do next for process improvement for each line ?對于每一條拉的改善行動,你下一步打算做什么?Line拉 1Line拉 2Total Variability(observed)全部變異(觀測值)Measuremen

8、t Variability測量變異True Process Variability真實工序變異s2true process(真實狀況) + s2MS(測量系統(tǒng)) = s2observed(觀測的)MSA: Warm-up Exercise MSA: 熱身練習Measurement System Analysis Approach測量系統(tǒng)分析方法There are two types of measurements possible:兩種可能的測量Variable計量值Data can be described on a continuous scale數(shù)據(jù)可以用連續(xù)的標尺描述Attribute

9、計數(shù)值Data cannot be adequately described on a continuous scale數(shù)據(jù)不能以連續(xù)的標尺描述Pass / Fail, very low counts通過/不通過,好/壞 Each must be approached differently.每一種方法必須用不同的處理方法Variable Measurement System Analysis計量值測量系統(tǒng)分析The ideal measurement system will produce “true” measurements every time it is used (Zero Bia

10、s, Zero Variance).理想的測量系統(tǒng)每次會得出”真”測量值(零偏差,零變異)Study of your measurement system will reveal the relative amount of variation in your data that results from measurement system error.研究你的測量系統(tǒng)可以揭示數(shù)據(jù)中包含的測量誤差的變異量It is also a great tool for comparing two or more measurement devices or two or more operators.

11、它可以是一個很好的工具比較兩或更多測量設備或兩或兩個以上測量員工.MSA should be used as part of the criteria for accepting a new piece of measurement equipment to manufacturing.MSA 應該是制造業(yè)的新測量系統(tǒng)的合格接受標準It should be the basis for evaluating a measurement system which is suspect of being deficient.應該為受懷疑的測量系統(tǒng)能力不足提供評估基礎It should be part

12、 of the periodic maintenance program.應該是定期維護程序的一部分.Possible Sources of Process Variation測量誤差的可能來源To address actual process variability, variation due to the measurement system must first be identified and separated from that of the process為了準確定義實際的工序變異,和測量系統(tǒng)變異,我們必須首先從工序變異中驗證和區(qū)分它們.Observed Process Va

13、riation觀測的工序誤差Actual Process Variation實際的工序誤差Measurement Variation測量誤差Long-term Process Variation長期的工序誤差Short-term Process Variation短期的工序誤差Variation With Sample樣本間誤差Variation dueTo instrument測量設備誤差Variation dueTo Operators員工操作誤差Repeatability重復性Bias偏差Stability穩(wěn)定性Linearity線性Reproducibility再現(xiàn)性Resolutio

14、n精度MeasurementVariationHumidityCleanlinessVibrationLineVoltageVariationTemperatureFluctuationOperatorTechniqueStandardProceduresSufficientWorkTimeMaintenanceStandardCalibrationFrequencyOperatorTrainingEaseofDataEntryTool工具Environment環(huán)境Work Methods工作方法Sources of Measurement Variation測量誤差的來源WARNING敬告I

15、gnoring these variables can adversely affect the gage study.忽略這些變量會阻礙儀器研究Mechanical instability機械不穩(wěn)定性 Electrical instability 電子不穩(wěn)定性 Algorithm instability 運算不穩(wěn)定性 Wear 磨損數(shù)據(jù)輸入不仔細 員工培訓 校正頻率 維護標準 不足夠的工作時間 標準程序 員工技術測量誤差 濕度 清潔度 震動 電壓變動溫度波動Measurement System Variability - Determined through “R&R Study”測量系統(tǒng)誤

16、差通過”重復性和再現(xiàn)性研究決定Accuracy準確性Precision精確性ssstotalproductmeasurement222=+totalproductmeasurementMeasurement System Bias -Determined through “Calibration Study”測量系統(tǒng)偏差通過”校正研究”決定Averages平均值Variability誤差Effects of Measurement Error測量誤差的影響Common Terms in Variable MSA計量值測量系統(tǒng)分析的一般術語“Accuracy” related terms:”準確

17、性”相關的術語Bias偏差Linearity線性Stability穩(wěn)定性“Precision” related terms :”精確性”相關的術語Repeatability重復性Reproducibility再現(xiàn)性Discrimination (Resolution)分辨力(精度)Concerned with the Mean和均值有關Concerned with the Variance和方差有關準確度和精確度1)準確但不精確2) 精確但不準確3)既不精確也不準確4)既精確又準確Accuracy準確性Instrument accuracy (or bias) is the differenc

18、e between the observed average value of measurements and the master value.設備精確性(或偏差)是觀測的平均值和基準值之間的差別The master value is an accepted, traceable reference standard (e.g., NIST).基準值(標準值)是可接受的,可追述的參考標準(Master Value基準值(Reference Standard)參考值Average Value平均值Accuracy or Bias精度或偏差Effects of Accuracy精確度的影響Ac

19、tual processAverage實際的工序均值Measurement Bias測量偏差Observed processAverage觀測到的工序均值Effect on the process: 工序影響Shifts the mean of the distribution 分布均值的偏移Bias123全部產(chǎn)品測量系統(tǒng)Instrument 2Instrument 1Master Value(Reference Standard)AverageValueAccuracy精確度Accuracy may be affected by two different types of sources:

20、 精確度可能受兩種來源的影響:Lack of good calibration to a true standard缺乏真實標準值的良好校正Average Bias: different operators or machines are centered differently, such that their average is offset from the true value平均偏差:不同的員工或不同的機器不同地集中,這樣一來他們的均值和真實值有一定的偏移量.Average BiasBias標準值(參考標準)平均值偏差設備1設備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.一工程師選擇五個”金標準樣本”希望得出測量系統(tǒng)的偏差, 每一個樣本隨機測量12次, 歷史工序誤差是12mm.Data can be found in the 01-05.MTW file.數(shù)據(jù)在01-05文件Mean of

22、the sixty measurements 60次測量的均值 x= 5.9467 mmMean value of the five standards 5個標準值的均值 = 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.測量系統(tǒng)的線性是指在其量程范圍內(nèi),偏倚是基準值的線性函數(shù).Linearity is an issue here線性是這的一個結果Lin

23、earity線性BiasTrue Value真實值Accuracy changes over part range精度在整個范圍的變化TrueValue1真實值1TrueValue 2真實值1TrueValue 3真實值3TrueValue 4真實值4偏倚定義Linearity線性BiasTrue Value真實值Accuracy changes over part range精度在整個范圍的變化偏倚斜率b線性 = 斜率b X 過程變差Std Deviation標準偏差Linearity線性Using the data set from Example 1,用例1的數(shù)據(jù)(01-05文件)Mas

24、terMean Error 20.49167 40.12500 60.02500 8 - 0.29167 10 - 0.61667Best Fit Line最好的擬合線 : Mean Error 均值偏差 = 0.7367 - 0.1317 MasterLinearity線性 = 0.1317 12 = 1.58 mm(13.17% of process variation)Example 2例2= (Ave. of 12 measurements) - (Master Value)=(12個測量值的均值)-(標準值)Linearity線性Compute the accuracy and li

25、nearity for the data in Example 1, using MiniTabs Gage Linearity Study.計算在例1中數(shù)據(jù)的精度和線性,用MiniTab: Gage Linearity StudyExample 3例3Stat Quality Tools Gage Linearity StudyExample 3此為MiniTab13版本Gage Linearity & Accuracy Study計量儀線性和精度研究Gage Linearity & Accuracy Study計量儀線性和精度研究Stability穩(wěn)定性The distribution o

26、f measurements remains constant and predictable over time for both mean and standard deviation對于均值和標準偏差測量的分布隨時間保留恒定的可預測的No drifts, sudden shifts, cycles, etc無漂移,突然偏移,循環(huán),等等.Evaluated using a trend chart用一個趨勢圖評估Ensured through a regular calibration and R&R program通過定期的校正和重復性和再現(xiàn)性程序Master Value真實值(Refer

27、ence Standard)參考標準Time 2時間2Time 1時間1A measure of the change in bias over time.在一定時間內(nèi)偏差變化的測量Effects of Stability穩(wěn)定性的影響Long term observedvariabilityActual processdistributionMeas. Systemday 1Meas. Systemday 2Meas. Systemday 3Effect on the process:工序的影響Increases process variability over time.隨時間增加工序變異T

28、ime實際的工序分布測量系統(tǒng)第一天測量系統(tǒng)第二天測量系統(tǒng)第三天長期觀測到的變異Precision精確度Actual processvariabilityMeasurement variabilityTotal observedvariabilityEffect on the process:工序的影響Increases process variability.增加工序變異實際的工序變異測量變異全部觀測到的變異Precision精確度Total variation in the measurement system測量系統(tǒng)的全部變異Measure of the total variation o

29、f repeated measurements重復測量的全部變異Precision equals the sum of Repeatability and Reproducibility精確度相當于重復性和再現(xiàn)性的總和 s reproducibilityrepeatabilityproducttotal 2 2 2 2 sss + +=Precision: Repeatability精確度:重復性Repeatability重復性The inherent variability of the measurement device測量設備本身的變異Variation that occurs whe

30、n repeated measurements are made of the same variable under similar conditions:在相同的狀態(tài)下測量重復的數(shù)據(jù)時產(chǎn)生的變異: Same part 相同的產(chǎn)品 Same operator 相同的員工 Same set-up 相同的設置 Same environmental conditions 相同的環(huán)境狀況 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 計算重復測量sss s 2 2 2 2totalproductrepeatabilityreproducibility=+ +Precision: Repeatability精確度:重復性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.重復性: 同一個操作者利用相同的設備,連續(xù)測量相同部分,相同特性,所獲得的測量值的變差.Master ValueGood RepeatabilityPoor Repeatability標準值良好的重復性差的重復性sss s 2 2 2 2totalproductrepeatabilityreproducibility=+ +Precision: Reproducibility精確度: 再現(xiàn)性Reproducibility:再現(xiàn)性 The variati

33、on that results when different conditions are used to make the same measurements 在不同狀況下做相同測量而導致的變異:Different operators 不同的操作者Different set-ups 不同的設置Different test units 不同的測量對象Different environmental conditions 不同的環(huán)境狀況Long-term measurement variation 長期的測量變異 Estimated by the standard deviation of the

34、 averages of measurements from different measurement conditions用不同的測量狀況下的測量均值的標準差計算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再現(xiàn)性: 當測量相同元件的指定特性時,不同操作者,機器,工具等的測量均值的標準偏差.Precision: Reproducibility精確度: 再現(xiàn)性標準值操作者A操作者B機器A操作者C機器B機器CExample: Accuracy vs Precision練習:準確性和精確性Suppose we have a reference material with a true hardness of 5.0:假設我們有一個”真”強度值5.0的參考材料Method 1 gives the following readi

36、ngs:方法1.給出下列讀值3.8, 4.4, 4.2, 4.0Method 2 gives the following readings:方法2.給出下列讀值6.5, 4.0, 3.2, 6.3Which method is more accurate?哪種方法更準確?Which method is more precise?哪種方法更精確Which method do you prefer? Why?你更愿意用哪種方法? 為何?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.測量系統(tǒng)測量的小數(shù)點的位數(shù), 測量的增量至少是產(chǎn)品規(guī)格或工序總波動的1/10.12Which ruler should be used to measure parts for the process represented by the distribution above ?哪一個尺子應該用于測量上述工序分布?Measurement

38、 System Variance: s2meas = s2repeat + s2reprod 測量系統(tǒng)方差 Primary output of analytical Gage R&R 分析GRR的主要輸出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決定測量系統(tǒng)是否是”好的” 或”懷的

39、”對于一定的應用. Comparing s2meas with Tolerance:同公差比較s2meas Precision-to-Tolerance Ratio (P/T)精確度對于公差比 Comparing s2meas with Process Variation (P/TV):同工序變異比較s2meas % Repeatability and Reproducibility (%R&R) 重復性和再現(xiàn)性的百分比Discrimination Index 分辨指數(shù)Measurement System Metrics測量系統(tǒng)組成Precision to Tolerance Ratio精確度

40、對于公差比Addresses what percent of the Tolerance is taken up by measurement error.表明測量誤差占了公差的百分比5.15 smeas represents 99% of all measurements5.15 smeas 代表 99% 的測量Best case: 10% Marginally Acceptable: 30%最好: 10% 最低可接受: 30% Includes both repeatability and reproducibility包括重復性和再現(xiàn)性Usually expressed as perce

41、nt通常用百分比表達Tolerance = USL - LSLP/T Ratio精確度對于公差比P/TV%R&R(or % Contribution)Addresses what percent of the Total Variation is due to measurement error表明測量誤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.步驟4: 讓第一個員工隨機測量所有的樣本一次, 模糊樣本,讓操作者不知道哪一個樣本以減少人為誤差.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)步驟5.: 讓第二個操作者隨機測量所有的樣本,一直到所有的操作者測量完所有的樣本一次.(這是第一次)Step 6: Repeat steps 4 & 5 for the required number of trials. It is best if these measurements can be done over several days.步驟6.重復步驟4.和5完成需要的次數(shù).最好是這些測量能在這幾天內(nèi)完成.Step 7: En

44、ter the data and tolerance information into Minitab 步驟7: 輸入數(shù)據(jù)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.步驟8: 根

45、據(jù)下面的指引通過評估測量的質(zhì)量來分析結果.決定下列步驟: The Method - Calculating Gage Capability方法計算測量儀器能力MSA Sample Guidelines測量系統(tǒng)分析 樣本指引Usually 10 samples, 2-4 operators (if several operators use the gauge), 2-3 trials用10個樣本2-4個操作者(如果有幾個操作者使用這個儀器),2-3次重復Depending on the purpose of the study 1 or more gages will be included由

46、研究1或更多的儀器所決定.In general select enough samples so that number of samples x number of operators/gages 15一般來說選擇足夠的樣本,樣本數(shù)量和操作者成績和儀器比大于15SAMPLE SELECTION 樣本選擇Option 1: if process variability is unknown, the samples selected should be representative of the normal process/product variation (to get TV)選擇1:

47、如工序變異不知,樣本選擇應該代表正常的工序/產(chǎn)品變異(取得全部變異)Option 2: if process variability is known, the samples selected should uniformly span beyond the width of the specs選擇2: 如工序變異已知,則樣本選擇應均勻分布在規(guī)格范圍內(nèi)外(不應超過規(guī)格過多).*Example: Minitab例: MiniTabStep 1: Randomly select 10 samples. In addition, identify the operators who use thi

48、s instrument daily步驟1.隨機選取10個樣本,并且確認每日操作此設備的員工(Parts 1 through 10 were collected and three operators were identified).部分1到10被選取并三個確認的操作者Step 2: Calibrate the gage or verify the last calibration date is valid步驟2.校正測量儀器或確認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步驟3.準備好MiniTab數(shù)據(jù)收集sheet做GR&R研究,每10單位測量2次被3個操作者, Column headings: 列題頭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.步驟4: 讓第一個員工隨機測量所有的樣本一次, 模糊樣本,讓操作者不知道哪一個樣本以減少人為誤差.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).步驟5.: 讓第二個操作者隨機測量所有的樣本,一直到所有的操作者測量完所有的樣本一次.(這是第一次)Step 6: Repeat steps 4 & 5 for the required number of trials.(We assume the above steps were executed. See GageR&R.mtw.) 步驟6.重復步驟4.和5完成需要的次數(shù)(我們假設上述步驟已完成

52、,看文件01-06)Example - Gage R&R using Minitab例子: 儀器重復性和再現(xiàn)性研究用MiniTabANOVA method is preferred.選擇ANOVA方法.Step 7: Enter the data and tolerance information into Minitab.步驟7: 輸入數(shù)據(jù)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: 儀器重復性和再現(xiàn)性研究用MiniTabtotalmeastotalmeasTVPssss=22/Step 7: Enter the data and tolerance information into Minitab. 步驟7: 輸入數(shù)據(jù)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 計算的分母是由所研究的樣本得來的,或從歷史數(shù)據(jù)而來.Example - Gage R&R using Minitab例子: 儀器重復性和再現(xiàn)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重復性和再現(xiàn)性輸出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錯誤的重要度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