TUV德國萊茵六西格碼黑帶培訓(xùn)資料MSAppt課件

1、Chapter 3.2Measurement Systems Analysis丈量系統(tǒng)分析1丈量是科學(xué)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丈量誤差平均值變差mmm總產(chǎn)品丈量系統(tǒng)=+丈量系統(tǒng)的偏向丈量系統(tǒng)的變差準(zhǔn)確度準(zhǔn)確度s2total = s2產(chǎn)品 + s2丈量系統(tǒng)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丈量誤差的緣由Measurement VariationHumidityCleanlinessVibrationLine Voltage VariationTemperatu

4、re FluctuationOperator TechniqueStandard ProceduresSufficient Work TimeMaintenance StandardCalibration FrequencyOperator TrainingEase of Data Entry 電性能不穩(wěn)定磨損 機(jī)械不穩(wěn)定性量具環(huán)境丈量方法計算不穩(wěn)定獲得數(shù)據(jù)的難易操作員培訓(xùn)校準(zhǔn)頻率量具維護(hù)規(guī)范足夠的任務(wù)時間規(guī)范操作規(guī)程操作員技術(shù)濕度清潔程度震動線電壓動搖溫度動搖6看到的不一定真實(shí)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過程變差分析長期過程變差短期抽樣產(chǎn)生的變差實(shí)踐過程變差穩(wěn)定性線性反復(fù)性 準(zhǔn)確度 量具變差操作員呵斥的變差丈量誤差過程變差觀測值“反復(fù)性 和 “再現(xiàn)性 是丈量誤差的主要來源再現(xiàn)性過程變差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準(zhǔn)確度(Accuracy)準(zhǔn)確度(Accuracy) 丈量的平均值能否與真值吻合?真值(True Value):實(shí)際上正確的值 國際度量衡規(guī)范偏倚Bias)丈量值的均值與真值的間隔丈量系統(tǒng)繼續(xù)地偏離目的系統(tǒng)錯誤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 丈量結(jié)果的平均值與參考值的差別. 參考值reference-v

9、alue是一個預(yù)先認(rèn)定的參考規(guī)范. 該規(guī)范可用更高一級丈量系統(tǒng)丈量的平均值來確定(例如：高一級計量室)觀測平均值參考值偏倚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同一操作者對同一工件丈量10次假設(shè)參考規(guī)范是 0.80mm. 過程變差為0.70mm = 0.75Bias = 0.75-0.8= -0.05% Bias=1000.05/0.70=7.1%闡明 7.1% 的過程變差是偏倚 BIAS偏倚BIAS 實(shí)例:15PrecisionTotal variation in the measurement systemMeasure of natural variation of repeated measurementsTerms: Random Error, Spread, Test/Retest errorRepeatabilit

12、y and ReproducibilitysssMSGO222=+16丈量系統(tǒng)總變差經(jīng)過反復(fù)丈量的方法丈量到的過程自然變差代表名詞：反復(fù)性 Repeatability和再現(xiàn)性ReproducibilitysssMSGO222=+準(zhǔn)確度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丈量系統(tǒng)內(nèi)在的變異性基于反復(fù)丈量的數(shù)據(jù)，用分組后組內(nèi)的規(guī)范偏向來估算 小于丈量系統(tǒng)的總變差 反復(fù)性指同一 人運(yùn)用同一丈量工具對同一對象產(chǎn)品的同一特性進(jìn)展多次丈量中產(chǎn)生的變差，用于估計短期的變差Master

14、Value準(zhǔn)確度：反復(fù)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準(zhǔn)確度：再現(xiàn)性丈量系統(tǒng)中操作員產(chǎn)生的變異基于不同操作者的丈量數(shù)據(jù)，按操作員分組，經(jīng)過組平均值的差來估。 應(yīng)扣除量具的要素組內(nèi)變差比丈量系統(tǒng)總變差小Inspector AMaster ValueInspector BInspector CInspector AInspector BInspector

16、 C再現(xiàn)性指不同的人在對同種特性進(jìn)展丈量時產(chǎn)生的變差21LinearityDifference in the accuracy values of a gage through the expected operating range of the gageGood LinearityBad Linearity22線性 Linearity 量具在不同丈量范圍的準(zhǔn)確度和準(zhǔn)確度的變化，當(dāng)丈量范圍較寬時尤為要關(guān)注好的線性差的線性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在一段時間內(nèi)，丈量結(jié)果的分布無論是均值還是規(guī)范偏向都堅(jiān)持不變和可預(yù)測的經(jīng)過較長時間內(nèi)，用被監(jiān)視的量具對一樣的規(guī)范或 規(guī)范件的同一特性進(jìn)展丈量的總變異來監(jiān)視可用時間走勢圖進(jìn)展分析穩(wěn)定性Stability時間-1時間-2時間穩(wěn)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丈量系統(tǒng)的分辨率 discrimination要求不低于過程變差或允許偏向 tolerance的非常之一零件之間的差別必需大于最小丈量刻度極差控制圖可顯示分辨率能否足夠看控制限內(nèi)有多少個數(shù)據(jù)階級不同數(shù)據(jù)等級的計算為 零件的規(guī)范偏向/ 總的量具偏向* 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計量型數(shù)據(jù)的GR&R研討均值-極差X-R法是確定丈量系統(tǒng)的反復(fù)性和再現(xiàn)性的數(shù)學(xué)方法，步驟如下：1 選擇三個丈量人A,

22、 B,C和10個丈量樣品。 丈量人應(yīng)有代表性，代表經(jīng)常從事此項(xiàng)丈量任務(wù)的QC人員或消費(fèi)線人員 10個樣品應(yīng)在過程中隨機(jī)抽取，可代表整個過程的變差，否那么會嚴(yán)重影響研討結(jié)果。2 校準(zhǔn)量具3 丈量，讓三個丈量人對10個樣品的某項(xiàng)特性進(jìn)展測試，每個樣品每人丈量 三次，將數(shù)據(jù)填入表中。實(shí)驗(yàn)時遵照以下原那么： 盲測原那么1：對10個樣品編號，每個人測完第一輪后，由其他人對這10個樣品進(jìn)展隨機(jī)的重新編號后再測，防止客觀偏向。 盲測原那么2：三個人之間都相互不知道其他人的丈量結(jié)果。4 計算29計算A測的一切樣品的總平均值XA。同樣方法計算RB, XB, RC, Xc對每個樣品由三個人所測得的9個測試值求平均

23、值，計算這些均值的極差Rp計算A對每個樣品三次測試結(jié)果的極差，然后計算10 個樣品的極差的均值RA30丈量系統(tǒng)分析R=(RA+RB+RC)/3XDIFF=MaxXA,XB,XC-MinXA,XB,XC反復(fù)性-設(shè)備變差 EV=RK1 再現(xiàn)性-檢驗(yàn)人變差 AV= (XDIFF K2)2-(EV2/nr)過程變差 PV=RP K3R&R= (EV2+AV2)總變差 TV= (R&R2+PV2)%EV=EV/TV%AV=AV/TV%R&R=R&R/TV%PV=PV/TVP/T=R&R/Tolerancen=樣品個數(shù)r=每個人對每個樣品的實(shí)驗(yàn)次數(shù)rK1234.453.05K2233.652.70測試人數(shù)

24、nK3789101.821.741.671.62K1=5.15/d2*AV計算中，如根號下出現(xiàn)負(fù)值，AV取值031EV= Equipment Variation (Repeatability)儀器變差(反復(fù)性)AV= Appraiser Variation (Reproducibility)丈量人變差(再現(xiàn)性)R&R= Repeatability & Reproducibility反復(fù)性與再現(xiàn)性PV= Part Variation零件變差TV= Total Variation of R&R and PV總變差K1-Trial, K2-Operator, & K3-Part ConstantsG

25、R&R研討中的名詞32卡尺的R&R研討 Excel 運(yùn)算33R&R 對過程才干計算的影響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、丈量系統(tǒng)需求改良Gage R&R 判別原那么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 計算GR&RXbar-R 均值極差法注：運(yùn)用同組數(shù)據(jù)Discrim98.218.9=sspms=*.227.3MinitabStatQuality ToolsGage StudyGage R&R Study (Crossed)在Method of Analysis中選擇 Xbar and R37Minitab 計算GR&R圖解數(shù)據(jù)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 計算GR&R-ANOVA 法在Method of Analysis中選擇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 與 %R&R將丈量系統(tǒng)的變差與產(chǎn)品容差比較是最常用的方法:P/T 可以表達(dá)與產(chǎn)品規(guī)范比較時的好壞程度. 產(chǎn)品規(guī)范的制定有時會太緊，有時又太松。 普通來說，當(dāng)丈量系統(tǒng)只是用來檢驗(yàn)消費(fèi)線樣品能否合格時， P/T 是很有效的。由于這時候，即使過程才干(Cpk)缺乏， P/T 也可以給他足夠的自信心來判別產(chǎn)品的好壞丈量系統(tǒng)變差與過程變差的比較%R&R更適宜于研討過程的才干與過程改良。PT

34、Tolerance容差丈量系統(tǒng)/.*=515sTolerance = USL - LSL%&RR丈量系統(tǒng)總過程變差=ss10042%R&R = 20%R&R = 50%過程實(shí)踐的變差%R&R = 100%產(chǎn)品的容差LSLUSL丈量系統(tǒng)變差P/T = 20%P/T = 50%P/T = 100%43%R&R = 25%R&R = 50%過程實(shí)踐變差%R&R = 100%產(chǎn)品容差ToleranceLSLUSL丈量系統(tǒng)變差P/T = 50%P/T = 100%P/T = 200%44%R&R = 20%R&R = 40%R&R = 100%產(chǎn)品容差 ToleranceLSLUSL丈量系統(tǒng)變差P/T

35、= 10%P/T = 20%P/T = 50%過程實(shí)踐變差45平均范圍 = = (2+1+1+2+1)/5 = 7/5 = 1.4量具誤差 = 5.15 * /d =5.15 / 1.19 * = 4.33 * = 4.33 * 1.4 = 6.1% Gage R&R = 量具誤差Gage Error / 允差Tolerance = 6.1 / 20 * 100 % = 30.5%快速GR&R短期方式d常數(shù)表允差Tolerance = 20= 最大值-最小值RRRRR46短期方式練習(xí)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短期與長期方法的比較短期方式用消費(fèi)設(shè)備 用消費(fèi)操作員快速 - 只需幾個樣品(5)無反復(fù)replicates估計總的變差(Total Gage R&R)不能區(qū)分 AV 和EV不能指點(diǎn)改良的方向可用于破壞性測試長期方式用消費(fèi)設(shè)備 用消費(fèi)操作員較多樣品 (5)要求反復(fù) Replicates (3)估計總的變差 (Total Gage R&R)可以區(qū)分 A

37、V 和EV為丈量系統(tǒng)的改良提供指點(diǎn)48正常規(guī)范方法Part ABTest 1Test 2Operator對同樣的樣品進(jìn)展反復(fù)丈量(稱之為交叉設(shè)計 Crossed Designed)巢式設(shè)計 Nested DesignCTest 1Test 2Test 1Test 2OperatorIOperatorIIOperatorIII樣品來自同一總體PartTestABC121212DEF121212GHI121212IIIIII破壞性丈量和不可反復(fù)的丈量49破壞性丈量和不可反復(fù)的丈量與可反復(fù)丈量的丈量系統(tǒng)比較 樣品的個數(shù)不是幾個(例如10個), 而是幾組(例如10組), 每組內(nèi)樣品的個數(shù)等于對該組要進(jìn)

38、展的破壞性測試的次數(shù) 每組樣品來自過程中延續(xù)的產(chǎn)出, 默許該組內(nèi)各樣品之間是沒有差別的 MinitabStatQuality ToolsGage StudyGage R&R Study (Nested) 結(jié)果中只能看到丈量系統(tǒng)的反復(fù)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運(yùn)用前面

40、一樣的數(shù)據(jù)51NO-GOGOErrorOperator 2Operator 1定性數(shù)據(jù)(Attribute Data)的丈量系統(tǒng)52定性數(shù)據(jù)(Attribute Data)的丈量系統(tǒng)的可靠性 Go-No Go 數(shù)據(jù)方式人為要素主導(dǎo)，情況復(fù)雜 統(tǒng)計模型多種多樣 統(tǒng)計學(xué)上各家爭鳴，尚無定論 實(shí)際中采用何種方式，取決于實(shí)例與統(tǒng)計模型的接近程度53對于以“是和“不是為計數(shù)根底的定性數(shù)據(jù)，其 GR&R調(diào)查的概念是與定量數(shù)據(jù)一樣的。但方法上完全不同.定性數(shù)據(jù)丈量系統(tǒng)的才干取決于操作員判別的有效性，即將“合格判別成合格，將“不合格判別成不合格的程度.計數(shù)型丈量系統(tǒng)才干分析方法例如54以下為判別所用的目的 有

41、效性 Effectiveness(E) - 即判別“合格與“不合格的準(zhǔn)確性 E= 實(shí)踐判別正確的次數(shù)/能夠判別正確的時機(jī)次數(shù). 漏判的幾率 Probability of miss(P-miss) - 將“不合格判為合格的時機(jī) P(miss)=實(shí)踐漏判的次數(shù) / 漏判的總時機(jī)數(shù).誤判的幾率 Probability of false alarm(P-FA) - 將“合格判為不合格的時機(jī). P(false alarm)=實(shí)踐誤判次數(shù) / 誤判的總時機(jī)數(shù).偏倚 Bias(B) - 指漏判或誤判的偏向. B=P(false alarm) / P(miss) B=1, 無偏倚 B1, 偏向誤判 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等級關(guān)聯(lián)絡(luò)數(shù)Intraclass Correlation Coefficient當(dāng)產(chǎn)品的質(zhì)量斷定不僅僅是合格與不合格兩種性質(zhì)，而是進(jìn)展多個等級的區(qū)分時ICC針對不同情行下的丈量系統(tǒng)進(jìn)展評價ICC運(yùn)用平方和 Sums of Square來進(jìn)展評價任務(wù)實(shí)例：某公司建立評價系統(tǒng)來丈量采購訂單(PO)完成的質(zhì)量程度，選了三個高級采購員對個訂單的完成好壞進(jìn)展打分評價，分代表很差，分代表很好，結(jié)果如下63PO#Buyer ABuyer BBuyer C15762654344344545765667778988988955610678定義如下平方和項(xiàng)BMS=Between mean square EMS=Error mean squareJMS=Judge mean squareWMS=Within mean squareTMS=Total mean square64PO#Buyer ABuyer BBuye