通用汽车SPC教材

1、MIT Consulting：http:/www.mit-1Statistical Process Control (SPC) WorkshopMIT Consulting：http:/www.mit-2Statistical Process Control (SPC) Workshop基本统计概念基本统计概念MIT Consulting：http:/www.mit-3Statistical Process Control (SPC) Workshop统计学(Statistics) n收集、 整理、展示 、分析 、解析统计资料Collect, collate, display, analysi

2、s, explain of datan由样本(sample)推论母体/群体(population)From sample to project the populationn能在不确定情况下作决策 Decision with uncertaintyn是一门科学方法、决策工具Scientific and decision tool基本统计概念基本统计概念 Basic SPC Concept抽样推论xMIT Consulting：http:/www.mit-4Statistical Process Control (SPC) Workshop统计量 Statistical ValuenR 全距(r

3、ange)n 算术平均数 (arithmetic mean)nMd 中位数(median)nMo众数(mode)n2 方差/变异(variance)n标准差(standard deviation)基本基本统计概统计概念念Basic SPC Concept)(xMIT Consulting：http:/www.mit-5Statistical Process Control (SPC) WorkshopnR 全距(range)R = Xmax - Xminn 算术平均数 (arithmetic mean)基本基本统计概统计概念念Basic SPC Conceptnxfxniii1)(xMIT C

4、onsulting：http:/www.mit-6Statistical Process Control (SPC) WorkshopnMd 中位数(median)顺序数列中的中心项的数值The medial number in the seriesnMo 众数(mode)资料中出现最多的数值The number with highest frequency基本基本统计概统计概念念Basic SPC ConceptMIT Consulting：http:/www.mit-7Statistical Process Control (SPC) Workshopn2 方差/变异(variance)基

5、本基本统计概统计概念念Basic SPC Concept)xx(.)xx()xx(1n11n)xx(f2n2221n1i2ii21n)xx(.)xx()xx(n1n)xx(f2n2221n1i2ii2nMIT Consulting：http:/www.mit-8Statistical Process Control (SPC) Workshopn标准差(standard deviation)基本基本统计概统计概念念Basic SPC Concept2n2221n1i2iin)xx(.)xx()xx(n1n)xx(f2n2221n1i2ii1n)xx(.)xx()xx(1n11n)xx(fMIT

6、 Consulting：http:/www.mit-9Statistical Process Control (SPC) Workshop例：Case1, 1, 2, 3, 4, 6, 11nR = 10n = 4nMd = 3nMo = 1nn 2 = 10.86 n-12 = 12.67nn= 3.29 n-1= 3.56 基本基本统计概统计概念念Basic SPC ConceptxMIT Consulting：http:/www.mit-10Statistical Process Control (SPC) Workshop数列 Series： 12, 11, 12, 13, 18, 3

7、0, 24, 9请计算下列统计量 Calculate the following:nR n nMd nMo nn 2 = n-12 =nn= n-1=练习练习ExercisexMIT Consulting：http:/www.mit-11Statistical Process Control (SPC) Workshop数数据的收集据的收集与与整理整理Data Collection and Collation群体群体Population样样本本Sample数数据据Data结结论论C Conclusion抽抽样样Sampling分析分析测测试试行行动动ActionTestAnalysisMIT

8、Consulting：http:/www.mit-12Statistical Process Control (SPC) Workshop数数据收集据收集 Data Collection333330313131282929342733273029333128273433263235322632283428282930282934323031283027322930263028313031322925272930273033292929263132MIT Consulting：http:/www.mit-13Statistical Process Control (SPC) Workshop数数

9、据整理据整理 Data CollateData Collate - - 次次数数分分布布 Frequency DistributionFrequency Distribution数值 Value 次数划记 Freq Marks 次数 Freq 25 X 1 26 XX 4 27 XXXXXX 6 28 XXXXXXXX 8 29 XXXXXXXXXX 10 30 XXXXXXXXXX 10 31 XXXXXXXX 8 32 XXXXXX 6 33 XXXXXX 6 34 XXXX 4 35 X 1 MIT Consulting：http:/www.mit-14Statistical Proce

10、ss Control (SPC) Workshop直方直方图图 (Histogram) (Histogram)MIT Consulting：http:/www.mit-15Statistical Process Control (SPC) Workshop分布曲分布曲线线 Distribution CurveMIT Consulting：http:/www.mit-16Statistical Process Control (SPC) Workshop正正态态( (常常态态) )分布的曲分布的曲线图线图Normal Distribution CurveNormal Distribution C

11、urve0.4)(zf-2.5-2.0-1.5-1.0-0.500.51.01.52.02.522121)(zezf11MIT Consulting：http:/www.mit-17Statistical Process Control (SPC) Workshop正正态态分布的性分布的性质质Nature of Normal DistributionNature of Normal Distribution- 3 - 2 -1 1 2 3 机会率机会率 Probaility 0.67 50.00 % 1 68.26 % 1.96 95.00 % 2 95.45 % 2.58

12、99.00 % 3 99.73 % MIT Consulting：http:/www.mit-18Statistical Process Control (SPC) Workshop数数据据 DataData 直方直方图图Histogram Histogram 分布曲分布曲线线 DistributionDistributionxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

13、xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx333330313131282929342733273029333128273433263235322632283428282930282934323031283027322930263028313031322925272930273033292929263132MIT Consulting：http:/www.mit-19Statistical Process Control (SPC) Workshop

14、两套三颗色子 (骰子)，以下列条件，每组各掷120120次次，然后把点数出现频次记录在直方图上。Two set of 3 dices, each set was thrown 120 times, and add up the sum in the histogram.nGroup A 组：如常 NormalnGroup B & C 组：色子出现2点，则当5点计算uIf 2 points, counts it as 5nD & E 组： 色子出现5点，则当1点计算 if 5 count as 1每 组：若总数是单数则加1。If sum is single, add 1练习练习

15、ExerciseMIT Consulting：http:/www.mit-20Statistical Process Control (SPC) Workshop直方直方图图 Histogram Histogram 分布分布 DistributionDistribution01020304050525 530 535540 545 550555 560 565570 575 58001020304050-0.75-0.7-0.65-0.6-0.55-0.5-0.45-0.4正常型正常型 NormalMIT Consulting：http:/www.mit-21Statistical Proce

16、ss Control (SPC) Workshop直方直方图图 Histogram Histogram 分布分布 DistributionDistribution02468101211811912012112212312412512612712812901020304016171819202122232425偏向型偏向型 BiasMIT Consulting：http:/www.mit-22Statistical Process Control (SPC) Workshop直方直方图图 分布分布02468100.640.660.680.70.720.740.76051015200.530.55

17、0.570.590.610.630.650.670.690.710.730.750.770.790.810.83孤岛型孤岛型 IslandMIT Consulting：http:/www.mit-23Statistical Process Control (SPC) Workshop过过程程变变差差Process VariationMIT Consulting：http:/www.mit-24Statistical Process Control (SPC) Workshop输入 (材料)机器人方法过程 (生产/装配)输出 (产品)反馈 (测量/检验)测量系统材料过过程程变变差差 Proces

18、s VariationProcess VariationMIT Consulting：http:/www.mit-25Statistical Process Control (SPC) WorkshopInput (Matl)MachineManMethodProcessOutput ProductFeedbackTest/ InspMSAMaterial过过程程变变差差 Process VariationProcess VariationMIT Consulting：http:/www.mit-26Statistical Process Control (SPC) Workshop过过程程变

19、变差差 Process Variationn输入材料 Material Inputu不同批次之间的差异 Lot to Lot Variationu批次内的差异 Within Lot Variationu随时间产生的差异 Variation in Time Seriesu随环境而产生的差异 Variation due to EnvironmentMIT Consulting：http:/www.mit-27Statistical Process Control (SPC) Workshop过过程程变变差差 Process Variationn生产/装配 Production/ Assemblyu

20、设备及工装夹具的差异 Equipment and Tooling Variationu随时间而产生的磨损，漂移等 Aging and Shift by timeu操作工之间的差异(如手工操作的过程)uVariation between Operators ( Manual Work)u设置的差异 Different Setupu环境的差异 Different EnvironmentsMIT Consulting：http:/www.mit-28Statistical Process Control (SPC) Workshop过过程程变变差差 Process Variationn输出产品 Ou

21、tput Productu输出的产品随时间而产生的变化uProduct Variation by time seriesu输出的产品随环境而产生的变化uProduct Variation due to environmentMIT Consulting：http:/www.mit-29Statistical Process Control (SPC) Workshop过过程程变变差差 Process Variationn反馈 - 测量 Feedback- Measurementu由于测量用于过程中的所有组成部分，测量的变差会对过程的各个阶段产生影响uMeasurements are part

22、of the process, variation in the measurement can affect the process in various stages偏倚 Bias稳定性 Stability重复性 Repeatability再现性 Reproducibility分辨率 ResoultionMIT Consulting：http:/www.mit-30Statistical Process Control (SPC) Workshop量具精确度量具精确度( (偏差偏差) Equipment Accuracy (Bias) Equipment Accuracy (Bias)量具

23、精确度指测量观察平均值与真实值(基准值)的差异。真实值由更精确的测量设备所确定。Observed mean compare with Standard. The standard is measured with higher grade equipment.测测量系量系统变统变差差 Measurement System VariationMeasurement System Variation观察平均值 Observed Mean真实值(基准值) STD精确度(偏差)BiasMIT Consulting：http:/www.mit-31Statistical Process Control

24、(SPC) Workshop量具重量具重复复性性 RepeatabilityRepeatability量具重复性是由一个操作者，采用一种测量仪器，多次测量同一零件的同一特性时获得的测量值变差。Variation from: Same operator uses the same equipment to take multiple measurements on the same characteristic.测测量系量系统变统变差差 Measurement System VariationMeasurement System Variation重复性RepeatabilityRepeatab

25、ilityMIT Consulting：http:/www.mit-32Statistical Process Control (SPC) Workshop量具再量具再现现性性 ReproducibilityReproducibility量具再现性是由不同的操作者，采用相同的测量仪器，测量同一零件的同一特性时测量平均值的变差。Variation from the mean of: Various operators use the same equipment to take multiple measurements on the same characteristic.测测量系量系统变统变

26、差差 Measurement System VariationMeasurement System Variation再现性 ReproducibilityReproducibility操作者 A操作者 B操作者 CMIT Consulting：http:/www.mit-33Statistical Process Control (SPC) Workshop量具量具稳稳定性定性 StabilityStability量具稳定性是同一测量系统在不同时间测量同一零件时至少两组测量值的总变差。Total Variation of the means in different time periods

27、.测测量系量系统变统变差差Measurement System VariationMeasurement System Variation稳定性StabilityStabilityTime时间 1Time时间 2MIT Consulting：http:/www.mit-34Statistical Process Control (SPC) Workshop量具量具线线性性 LinearityLinearity量具线性是在量具预期的工作范围内，偏倚值的差值。Within the measurement range, the bias to bias variation观察平均值 (Obs) St

28、d 真实值(基准值)精确度较好(偏差较小)Less Bias观察平均值 Obs Std真实值(基准值)精确度较差(偏差较大)High BiasMIT Consulting：http:/www.mit-35Statistical Process Control (SPC) Workshop过过程程变变差差 Process VariationProcess Variationn对于所有的过程输出，都有两个主要的统计：For all process output, there are two major statistical pointsu对中性 Centering指由过程的平均值至最近的规格限的

29、距离Mean to nominal specu变差(波动)Variationu指过程的分布宽度Process Spread对中性CenteringLSLUSL变差(波动) SpreadMIT Consulting：http:/www.mit-36Statistical Process Control (SPC) Workshop过过程程变变差差 Process Variationn过程的变差分两个类型 Two Categoriesu特殊原因造成的变差 Special Causesu普通原因造成的变差 Normal CausesMIT Consulting：http:/www.mit-37Sta

30、tistical Process Control (SPC) Workshop过过程程变变差差 Process Variationn普通原因变差 Normal Causes in Variationu影响过程中每个单位 affect each unit in the processu在控制图上表现为随机性 random point in the chartu没有明确的图案 No obvious patternu但遵循一个分布 follow a particular distributionu是由所有不可分派的小变差源组成 Formed by various variation sourcesu

31、通常需要采取系统措施来减小Use system corrective actions to reduceMIT Consulting：http:/www.mit-38Statistical Process Control (SPC) Workshop过过程程变变差差 Process Variationn特殊原因变差 Special Causes in Variationu间断的，偶然的，通常是不可预测的和不稳定的变差Discontinued, occidental, unpredictable and unstableu在控制图上表现为超出控制限的点或链或趋势As the points out

32、 of control lines or chains or trendu非随机的图案 Non random patternu是由可分派的变差源造成该变差源可以被纠正Can be corrected, the cause is from the particular sourceMIT Consulting：http:/www.mit-39Statistical Process Control (SPC) Workshop过过程程变变差差 Process Variationn工业经验建议为：Industrial Experienceu只有过程变差的15%是特殊的可以通过与操作直接有关的人员纠正

33、Only 15% are special causes, can be corrected by those operation staff directlyu大部分 (其余的85%) 是管理人员通过对系统采取措施可纠正的Other 85% must go through the system corrective actions by the management staffMIT Consulting：http:/www.mit-40Statistical Process Control (SPC) Workshop过过程程变变差差 Process Variation范围范围范围范围每件产

34、品的尺寸与别的不同Each product dimension has differencesSPECMIT Consulting：http:/www.mit-41Statistical Process Control (SPC) Workshop过过程程变变差差 Process Variation范围范围范围但它们形成一个模型，若稳定，可以描述为一个分布The data are grouped to form the model. If stable, it can be descried as the distribution.MIT Consulting：http:/www.mit-42

35、Statistical Process Control (SPC) Workshop过过程程变变差差 Process Variation分布可以通用过以下因素来加以区分Distribution can be descried with various elements或这些因数的组合 Or the combination of these elements范围范围范围位置位置 Posotion分布分布宽宽度置度置Spread形形状状 Form/ ShapeMIT Consulting：http:/www.mit-43Statistical Process Control (SPC) Works

36、hop过过程程变变差差Process Variation目标直线Target Line预测Forecast范围 SPEC时间 Time如果只存在如果只存在变变差的普通原因，差的普通原因，随随著著时间时间的推移，的推移，过过程的程的输输出出形成一形成一个稳个稳定的分布定的分布并并可可预测预测If there are only the normal causes, and move in time series, the process outputs are predictable with stable distribution MIT Consulting：http:/www.mit-44S

37、tatistical Process Control (SPC) Workshop过过程程变变差差 Process Variation目标直线 Target Line预测 Forecast范围 Spec时间 Time如果存在如果存在变变差的特殊差的特殊原因，原因，随随著著时间时间的推移，的推移，过过程的程的输输出不出不稳稳定定If the special cause is in the variation, in time series, the process become unstable？MIT Consulting：http:/www.mit-45Statistical Process

38、 Control (SPC) Workshop过过程控制程控制 Process Process ControlControl受控 In Control(消除了特殊原因)Eliminate the Special Cause时间 Time范围 Spec不受制 Out Of Control(存在特殊原因) with Special Cause过过程控制和程控制和过过程能力程能力Process Control and Process CapabilityProcess Control and Process CapabilityMIT Consulting：http:/www.mit-46Stati

39、stical Process Control (SPC) Workshop过程能力 Process Capability规范上限受控且有能力符合规范(普通原因造成特变差)Control and capable to fit the spec (variation due to Normal Cause)时间受控但没有能力符合规范 Control but without capability to fit the spec(普通原因造成变差太大) Large variation due to Normal Cause TimeSpec过过程控制和程控制和过过程能力程能力Process Contr

40、ol and Process CapabilityProcess Control and Process CapabilityMIT Consulting：http:/www.mit-47Statistical Process Control (SPC) Workshopn每个过程可以分类如下：Each process can be categorized as:u受控或不受控 Control or out of controlu是否满足客户要求 Fit the customer requirementsn Fit the Spec control out of control满足要求 受控

41、不受控Pass符合(合格) 1类 3类Fail不符合(不合格) 2类 4类过过程控制和程控制和过过程能力程能力Process Control and Process CapabilityProcess Control and Process CapabilityMIT Consulting：http:/www.mit-48Statistical Process Control (SPC) Workshop过过程控制和程控制和过过程能力程能力Process Control and Process CapabilityProcess Control and Process Capability1

42、1类类 ( (符合要求符合要求，受控，受控) Cat 1 (Pass, In control) Cat 1 (Pass, In control)n是理想状况。为持续改进可能需要进一步减小变差Ideal Status, to reduce variation for continuous improvement.2 2类类 ( (不符合要求，受控不符合要求，受控) Cat.2 (Fail, in control) Cat.2 (Fail, in control)n存在过大的普通原因变差 with large variation from normal causen短期内，进行100%检测以保护客

43、户不受影响In short term, go for 100% inspection to reduce the effect for customern必须进行持续改进找出并消除普通原因的影响Must go for continuous improvement to eliminate the effect from special causeMIT Consulting：http:/www.mit-49Statistical Process Control (SPC) Workshop过过程控制和程控制和过过程能力程能力Process Control and Process Capabil

44、ityProcess Control and Process Capability3 3类类 ( (符合要求符合要求，不受控，不受控) Cat 3. Pass but out of control) Cat 3. Pass but out of control n有相对较小的普通原因及特殊原因变差With less normal and special causesn如果存在的特殊原因已经明确但消除具影响可能不大经济，客户可能接受这种过程状况If the special causes are known but the cost may be high to eliminate them, c

45、ustomer may accept this process status.4 4类类 ( (不符合要求，不受控不符合要求，不受控) Cat 4 ( Fail, Out of Control) Cat 4 ( Fail, Out of Control)n存在过大的普通原因及特殊原因的变差Larger Normal and special causes in the variationn需要进行100%检测以保护客户利益 100% inspection to protect customern必须采取紧急措施使过程稳定，并减小变差Must go for contingency/ contain

46、ment actions to stable the process and reduce variationsMIT Consulting：http:/www.mit-50Statistical Process Control (SPC) Workshop过过程控制和程控制和过过程能力程能力Process Control and Process CapabilityProcess Control and Process Capabilityn判断一个过程是否满足规格要求： Judge the process can fit the spec requirementsCapability In

47、dex 能力指数 - CpkPerformance Index 性能指数 - Ppkn判断一个 过程是受控还是不受控用：Judge the process is in control or out of control控制图 Control ChartsMIT Consulting：http:/www.mit-51Statistical Process Control (SPC) Workshop控制控制图图Control ChartsMIT Consulting：http:/www.mit-52Statistical Process Control (SPC) Workshop控制控制图图

48、Control ChartsControl ChartsY Y是是N N否否 正正 常常独独立立处处理理Treat it Treat it independentlyindependently过过程程 ProcessProcess控制控制图图 Control ChartsControl Charts调调整整 AdjustAdjust过过程的程的声声音音( (测测量量) )Feedback Voice Feedback Voice ( Measurement)( Measurement)交付交付客客户户控制控制图图的的应应用用 ApplicationApplicationcustomerDeli

49、veryNormalMIT Consulting：http:/www.mit-53Statistical Process Control (SPC) Workshop基本基本概概念念 Basic ConceptBasic Conceptn1920年由 W.A. Shewhart 提出 ( in 1920, Bell Lab)n一般称为Shewhart控制图或3控制图 Shewhart Control Chart or 3 Sigma Control Chartn广泛在工业界应用 (Frequently used in industries)n为判断制程变差的普通原因或特殊原因的主要统计分析工具

50、。To judge the process variation with normal or special cause as the major statistical analysis toolMIT Consulting：http:/www.mit-54Statistical Process Control (SPC) Workshop基本基本概概念念 Basic ConceptBasic Conceptn控制图中包括三条线 3 lines in Control Chartu控制上限 (Upper Control Limit; UCL)u中心线 (Center Line; CL)u控制下

51、限 (Lower Control Limit; LCL)UCLCLLCLMIT Consulting：http:/www.mit-55Statistical Process Control (SPC) Workshop控制控制图图的的种类种类Types of Control ChartsTypes of Control Chartsn数据：是能够客观地反映事实的资料和数字nData: Can get the fact from the information and datan数据的质量特性值分为：Quality Characteristics in datau计量值 Variableu可以用

52、量具，仪表等进行测量而得出的连续性数值，可以出现小数Use measurement equipment to take measurements in seriesu计数值 Attributeu不能用量具，仪表来度量的非连续性的正整数值。Without Equipments to measure the non continuous countsMIT Consulting：http:/www.mit-56Statistical Process Control (SPC) Workshop控制控制图图的的种类种类Type of Control ChartsType of Control Cha

53、rtsn计量型数据的控制图 Variable Control ChartsuXbar-R图uXbar-S图uX-MR图n计数型数据的控制图 Attribute Control Chartsup图unp图uc图uu图MIT Consulting：http:/www.mit-57Statistical Process Control (SPC) Workshop控制控制图图的使用策的使用策划划Planning for the Control Charts作控制图需要按以下步骤：Follow the necessary stepsn计划 Planningn资源 Resourcesn评估和改进 Eva

54、luation and ImprovementMIT Consulting：http:/www.mit-58Statistical Process Control (SPC) Workshop控制控制图图的使用策的使用策划划Planning for the Control Chartsn要点 Main Pointsu建立适于采取措施的环境 Set the right environment to take actionsu确定过程 Verify the processu确定待管理的特性 Focus on the characteristics that need to be managedu

55、考虑：Consider客户的要求 Customer Requirements当前及潜在的问题区 Existing and potential problem area特性间的相互关系 Interrelation between characteristicsu确定测量系统 Establish the MSAu使不必要的变差最小化 Reduce the variations in those avoidable areaMIT Consulting：http:/www.mit-59Statistical Process Control (SPC) WorkshopXbar - R 图图Chart

56、n平均数 - 全距控制图 Average and Range Chartu数据可以合理分组时分析或控制u Data can be grouped for analysis and control制程平均使用 Xbar 图 X Bar for process average制程变差使用R图 Variation by R chartu工业界最常使用的计量值控制图uThe most common chart for the industryMIT Consulting：http:/www.mit-60Statistical Process Control (SPC) WorkshopXbar - R

57、 图图 ChartRAXLCLRAXUCLRDLCLRDUCLKR.RRRKX.XXX2X2X3R4Rk21k21n2345A21.881.020.730.58D43.272.572.282.11D3*MIT Consulting：http:/www.mit-61Statistical Process Control (SPC) Workshop建立建立XbarXbar-R-R控制控制图图的步的步骤骤Set up the steps for X-R ChartsSet up the steps for X-R Charts1.收集数据 Collect Data选择子组大小，频率和子组数量Sel

58、ect the subgroup size, frequency and group numbersn建立控制图及记录原始数据Set up control chart and raw data gatheringn计算每个子组的X平均值和极差RCalculate each subgroup X avg and Range Rn选择控制图的刻度 Select the scale on the chartsn将平均值和极差画到控制图上Draw the X avg and Range R on the chartMIT Consulting：http:/www.mit-62Statistical P

59、rocess Control (SPC) Workshop建立建立XbarXbar-R-R控制控制图图的步的步骤骤Set up the steps for X-R ChartsSet up the steps for X-R Charts2.计算控制限 Calculate Control Limitn计算极差的平均值和过程平均值Calculate the average of X avg and Rn计算控制限 Calculate Control Limitsn在控制图上画出中心线及控制线Draw the center lines and control limitsMIT Consultin

60、g：http:/www.mit-63Statistical Process Control (SPC) Workshop建立建立XbarXbar-R-R控制控制图图的步的步骤骤Set up the steps for X-R ChartsSet up the steps for X-R Charts3.过程控制解释 Explain the Process Controln分析极差图(R图)上的数据点 Analyse the R points in R curven识别并标注特殊原因(R图) Identify and mark the special causesn重新计算控制极限(R图) Recalculat