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1、1STATISTICAL PROCESS CONTROLSTATISTICAL PROCESS CONTROL (SPC) Part I Fundamentals(SPC) Part I Fundamentals R. S. Chen2方法方法物料物料机器机器人人环境环境测量测量输出输出3Precise, not AccuratePrecise, not Accurate精密，不准确精密，不准确1 15 51515Accuracy The closeness of the agreement between the results of measurement and the true val

2、uePrecision The degree of the agreement between repeated measurements of the same test material41515Accurate, Accurate, notnot PrecisePrecise准确，不精密准确，不精密51515Accurate andAccurate and PrecisePrecise准确精密准确精密6 w 151515151515Precise, not Accurate精密，不准确精密，不准确Accurate, not Precise准确，不精密准确，不精密Accurate and

3、Precise准确精密准确精密7 Precision And Accuracy Precise, not Accurate精密，不准确精密，不准确Accurate, not Precise准确，不精密准确，不精密Accurate and Precise准确精密准确精密8 e21222)(x(- x )f (x) =对于连续过程而言，若一随对于连续过程而言，若一随机变量由众多偶然因素机变量由众多偶然因素 (common causes)决定，且决定，且其中无主导因素，则该变量其中无主导因素，则该变量通常均服从正态分布规律通常均服从正态分布规律9A Consistent Process A Cons

4、istent Process Normal Distribution Normal DistributionA bell-shaped symmetrical curve对称分布曲线对称分布曲线Can be described by the process average and standard deviation过程性状可用过程均值过程性状可用过程均值和标准偏差表征和标准偏差表征Can predict where the data will fall under the curve可预测过程数据将落在可预测过程数据将落在曲线包含的范围内曲线包含的范围内标准偏差过程均值10Predict W

5、here Data Will Fall Under The CurvePredict Where Data Will Fall Under The Curve =过程均值过程均值 =过程标准偏差过程标准偏差(s =过程样本标准偏差）过程样本标准偏差）N=过程过程 个体的数量个体的数量(n = 过程样本个体的数量过程样本个体的数量)11Statistically Control A Process受控受控失控失控可预测可预测不可预测不可预测12The Purpose Conducting SPC统计过程控制的目的统计过程控制的目的To achieve quality excellenceTo a

6、chieve quality excellence实现质量卓越实现质量卓越 Operating on target with minimum Operating on target with minimum variabilityvariability按设定目标以最小的变异度运行按设定目标以最小的变异度运行SPC is a proactive approach to SPC is a proactive approach to manage qualitymanage qualitySPC SPC 是前瞻性的质量管理手段是前瞻性的质量管理手段13统计过程控制的工具统计过程控制的工具 控制图控制

7、图控制上限控制上限控制下限控制下限控制下限控制下限控制上限控制上限测测量量值值移移动动极极差差时间时间时间时间均值均值平均移动平均移动极差极差14Example: A Run Chart Of A Carbonation ProcessExample: A Run Chart Of A Carbonation Process例：一碳酸化过程例：一碳酸化过程 ( (含汽量含汽量) )的单值图的单值图含汽量含汽量样品序号样品序号15Where the process is targetedWhere the process is targeted： Average - The sum of the

8、 observations Average - The sum of the observations divided by the number of observationsdivided by the number of observations平均值平均值 Measures of variation or dispersion - How Measures of variation or dispersion - How variable the output of the process isvariable the output of the process isStandard

9、DeviationStandard Deviation A numerical value A numerical value that measures the spreading or variation that measures the spreading or variation of the dataof the data离散性标准差精密度离散性标准差精密度16Process Capability Study To Acquire The Two MeasuresThe process average and The process average and the dispersi

10、on of the the dispersion of the process are necessary process are necessary elements to make up elements to make up control charts. Process control charts. Process capability study is the way capability study is the way for acquiring the two for acquiring the two measures.measures. 过程均值及离散度是控制图过程均值及

11、离散度是控制图 的必要参数，过程能力分析的必要参数，过程能力分析 是获取这二个数据的方法。是获取这二个数据的方法。理想理想理理想想实实际际（假设目标是（假设目标是100）频率频率频率频率17 Precision () is the key to process capability. In order to separate process variability from all others, it is necessary to stabilize the process and keep all the process elements in the “standardized” op

12、erational status. keeping one analyst with one set of data analysis; sufficiently accurate and precise testing equipment that is in calibration status; same shift and same container of materials; all machines in good maintenance status, . 由一位分析员对一套数由一位分析员对一套数据进行测试据进行测试; ; 测试仪器符合准确度和测试仪器符合准确度和精密度的要求，

13、且处于校精密度的要求，且处于校正状态；正状态； 所有设备均处于良好的所有设备均处于良好的维护保养状态，维护保养状态， 18Step-By-Step ApproachStep-By-Step Approach To Performing A Process To Performing A Process Capability StudyCapability Study 1.1. Identify a production run of sufficient length to represent the process studied.确定一个代表被分析过程的生产时间足够长的批次确定一个代表被分

14、析过程的生产时间足够长的批次2.2. Divide the run time by 30 for randomly capturing at least 30 samples by using a random number table.The actual sampling interval will be sometimes more and sometimes less than the average according to the random number table.以该批次的生产时间除以至少以该批次的生产时间除以至少3030个样品，得采样的平均个样品，得采样的平均时间间隔实际

15、采样间隔按随机数表决定，有些会大于时间间隔实际采样间隔按随机数表决定，有些会大于平均间隔有些则会小于平均间隔平均间隔有些则会小于平均间隔19A Random Number Table20Step-By-Step ApproachStep-By-Step Approach To Performing A To Performing A Process Capability StudyProcess Capability Study过程能力分析的步骤过程能力分析的步骤 ( (例：制造例：制造) )3.Assign a single technician to confirm and monitor

16、 to ensure that proper start-up and run procedures have been used.指指4.Design a data collecting sheet that is also the record to be maintained together with the dotted control charts.设计一份数据表记录测试结果及采样相关信息。设计一份数据表记录测试结果及采样相关信息。5. 5. Begin sampling when the technician and operators are through with the

17、start-up of the production and the process is running smoothly.当当且过程运行平稳后开始采样。且过程运行平稳后开始采样。6.Test and record the test results in the order that sample was collected.按采样顺序测试样品和记录测试结果按采样顺序测试样品和记录测试结果21(Brix)日期日期时间时间数据数据目标目标记录记录22Step-By-Step ApproachStep-By-Step Approach To Performing A To Performing

18、A Process Capability StudyProcess Capability Study过程能力分析的步骤过程能力分析的步骤 ( (例：制造例：制造) )7. 7. Analyze and calculate the data 7 7. 1. 1 Histogram Construct a histogram to determine the type and shape Construct a histogram to determine the type and shape of the distributionof the distributionThe frequency

19、histogram reveals the statistical The frequency histogram reveals the statistical pattern of the data set, it graphically shows the pattern of the data set, it graphically shows the central location and spread of the individual values.central location and spread of the individual values.23Histogram

20、Histogram A histogram can graphically show three things:A histogram can graphically show three things:位置：位置：A visual indication of the central tendency or location of the A visual indication of the central tendency or location of the datadata分布形状：分布形状：A visual indication of the shape or distribution

21、 of the dataA visual indication of the shape or distribution of the data离散性：离散性：A visual indication of the spread or variation of the dataA visual indication of the spread or variation of the dataFrequency (# of observations)Class Interval Width (w)Start Value (CS)Class Interval# n 分组上限值分组上限值Upper B

22、oundary (CB#n)Histogram Class Interval Width and Boundaries组距组距起始值起始值24A Guide for preparing frequency histogramA Guide for preparing frequency histogram 1. Number of interval (nc): Square root of sample 1. Number of interval (nc): Square root of sample size (n) A “rule of thumb” size (n) A “rule of

23、 thumb” 2. Calculate sample range (R): R = High value - Low 2. Calculate sample range (R): R = High value - Low value value 3. Calculate class interval width (w): w = R 3. Calculate class interval width (w): w = R nc nc 4. Determine measurement accuracy: 4. Determine measurement accuracy: = = Measur

24、ing Measuring resolution resolution w1.1.Step-By-Step ApproachStep-By-Step Approach To Performing A To Performing A Process Capability StudyProcess Capability Study过程能力分析的步骤过程能力分析的步骤 ( (例：制造例：制造) )25Step-By-Step ApproachStep-By-Step Approach To Performing A To Performing A Process Capability StudyPr

25、ocess Capability Study过程能力分析的步骤过程能力分析的步骤 ( (例：制造例：制造) )怎样绘制怎样绘制频率直方图频率直方图w5. 5. Start value for the first Class interval: Start ValueStart value for the first Class interval: Start Value (CS) = Lowest (CS) = Lowest value value ( ( 2) 2)w6. Calculate upper boundary for each class interval:Interval #1

26、 upper boundary (CB #1) = CS + wInterval #2 upper boundary (CB #2) = CS + 2w Interval #n upper boundary (CB #3) = CS + nww5, 区间区间1 1的起始值的起始值( (cs): cs=cs): cs=最低值最低值- (- (/2)/2)w6.6.每个区间的上限值每个区间的上限值: :l区间区间1 1 cs+wcs+wl区间区间2 2cs+2wcs+2wll区间区间n ncs+nwcs+nw26Whats More Histograms May Tell You?27Step-B

27、y-Step ApproachStep-By-Step Approach To Performing A To Performing A Process Capability StudyProcess Capability Study过程能力分析的步骤过程能力分析的步骤 ( (例：制造例：制造) )7. 2 Calculate the data7. 2 Calculate the data 计算数计算数据据 7 7.2.1 Sample Average.2.1 Sample Average 样品均值样品均值7.2.2 Accuracy7.2.2 Accuracy准确度准确度样品均值样品均值 x

28、= = 总和总和 i 值值 n = 样样品数品数 x 样品均值样品均值 目标值目标值 真值或确定值真值或确定值28Step-By-Step ApproachStep-By-Step Approach To Performing A To Performing A Process Capability StudyProcess Capability Study过程能力分析的步骤过程能力分析的步骤 ( (例：制造例：制造) ) wS = S = sample standard deviationsample standard deviation样品标准样品标准偏差偏差w = = sample av

29、eragesample average样品均值样品均值wX = individual sample valueX = individual sample value单个样品值单个样品值wn = number of samplesn = number of samples样品数样品数w = = summationsummation总和总和7. 2.3 Sample Standard Deviation 29Step-By-Step ApproachStep-By-Step Approach To Performing A To Performing A Process Capability St

30、udyProcess Capability Study过程能力分析的步骤过程能力分析的步骤 ( (例：制造例：制造) ) The CP index does not account for process centering. If the process average is not exactly centered between the specification limits, the CP index will give misleading results.CpCp不反映过程的不反映过程的趋趋中性中性 ( (与目标的偏离与目标的偏离) )USL Upper specificatio

31、n limitUSL Upper specification limit 规格范围上限规格范围上限LSL LSL Lower specification limitLower specification limit规格范围下限规格范围下限 Standard deviationStandard deviation标准偏差标准偏差Cp is calculated as:Cp = USL - LSL 6 Cp = Referred to as capability index Cp = Referred to as capability index 7 7. 2. 4 Capability Indi

32、ces 过程能力指数过程能力指数30Step-By-Step ApproachStep-By-Step Approach To Performing A To Performing A Process Capability StudyProcess Capability Study过程能力分析的步骤过程能力分析的步骤 ( (例：制造例：制造) ) Z (minimum) is equal to the smaller of the two valuesZ (minimum) is equal to the smaller of the two valuesZ (upper) = Z (uppe

33、r) = USL Process AverageUSL Process Average 3 3 Z (lower) = Z (lower) = Process Average LSLProcess Average LSL 3 3 Cpk Cpk Calculated as:CPK = Z (Smaller) 3 Cpk = Referred to as capability index Cpk = Referred to as capability index 7. 2. 4Capability Indices Capability Indices 过程能力指数过程能力指数31Cp = Cpk

34、 Cp = Cpk Process is well Process is well centeredcenteredCpk CpCpk CpProcess is not Process is not properly centeredproperly centered 过程设定准确，均过程设定准确，均值与目标值重合值与目标值重合过程未能准确设定过程未能准确设定32 Example: Filling Process Capability Study Example: Filling Process Capability Study Specification:Specification: Tar

35、get Target = 20.00 Kg= 20.00 KgLower Specification Limit(LSL) = 19.90 KgLower Specification Limit(LSL) = 19.90 KgUpper Specification Limit(USL) = 20.10 KgUpper Specification Limit(USL) = 20.10 KgSample Data:Sample Data:1.1. 20.020 20.020 9.9. 19.995 19.995 17.17. 20.025 20.025 25.25. 20.010 20.0102.

36、2. 20.005 20.005 10.10. 20.010 20.010 18.18. 20.005 20.005 26.26. 19.995 19.9953.3. 20.010 20.010 11.11. 20.000 20.000 19.19. 19.990 19.990 27.27. 20.025 20.0254.4. 20.000 20.000 12.12. 20.020 20.020 20.20. 20.010 20.010 28.28. 19.975 19.9755.5. 19.990 19.990 13.13. 20.005 20.005 21.21. 20.010 20.01

37、0 29.29. 20.015 20.0156.6. 19.985 19.985 14.14. 19.995 19.995 22.22. 19.980 19.980 30.30. 20.000 20.0007.7. 20.010 20.010 15.15. 19.990 19.990 23.23. 20.005 20.005 31.31. 19.990 19.9908.8. 19.975 19.975 16.16. 20.010 20.010 24.24. 19.980 19.980 32.32. 19.980 19.980 Sample number = 32 Sample number =

38、 32 Sample average = 20.000Kg Sample average = 20.000Kg Standard deviation = 0.0142 KgStandard deviation = 0.0142 Kg Accuracy = 0.00 kg Accuracy = 0.00 kg ( (与目标值一致）与目标值一致）Example: Capability Study Of Syrup Example: Capability Study Of Syrup Filling Process (Hypothetical)Filling Process (Hypothetica

39、l)例：糖浆灌注过程能力分析例：糖浆灌注过程能力分析 (假设）假设）33Example: Capability Study Of Syrup Example: Capability Study Of Syrup Filling Process Filling Process (Hypothetical)(Hypothetical)例：糖浆灌注过程能力分析例：糖浆灌注过程能力分析 ( (假设假设) )产品规格产品规格USL产品规产品规格格LSL规格范围规格范围 0.2kg19.90kg19.95 kg 20 kg(目目标标 ) 20.05 kg20.10 kg34Example: Capabil

40、ity Study Of Syrup Example: Capability Study Of Syrup Filling Process Filling Process (Hypothetical)(Hypothetical)例：糖浆灌注过程能力分析例：糖浆灌注过程能力分析 ( (假设假设) )Histogram Histogram 直方图直方图R (样品范围) =最高值最低值= 20.025 kg19.975 kg=0.050 kgW (区间宽度）= R/ ( (分辨率分辨率) = 0.005 kg) = 0.005 kgCS (CS (起始值起始值) = 19.975 (0.005/2)

41、 ) = 19.975 (0.005/2) =179725 kg =179725 kg nc(分组数）分组数）=32nc= 0.050/6 = 0.050/6 = 0.0083 kg = 0.0083 kg 0.010 kg 0.010 kg各分组的上限值各分组的上限值35Example: Capability Study Of Syrup Example: Capability Study Of Syrup Filling Process Filling Process (Hypothetical)(Hypothetical)例：糖浆灌注过程能力分析例：糖浆灌注过程能力分析 ( (假设假设)

42、 )36Example: Capability Study Of Syrup Example: Capability Study Of Syrup Filling Process (Hypothetical)Filling Process (Hypothetical)例：糖浆灌注过程能力分析例：糖浆灌注过程能力分析 ( (假设假设) )Capability IndicesCapability Indices能力指数能力指数Potential Capability Index (Cp)Potential Capability Index (Cp)潜在能力指数潜在能力指数Cp = (20.10 1

43、9.90) (6 x 0.0142) = 2.35 Actual Capability Index (Cpk)实际能力指数实际能力指数Cpk = Z (Smaller) Z Z (Upper) = (20.10 20.00) (0.0142 x 3) = 2.35 Z (Lower) = (20.00 19.90) (0.0142 x 3) = 2.35 37Example: Capability Study Of Syrup Example: Capability Study Of Syrup Filling Process Filling Process (Hypothetical)(Hy

44、pothetical)例：糖浆灌注过程能力分析例：糖浆灌注过程能力分析 ( (假设假设) )The process is approximately normally distributed. It is both precise and perfectly centered.目标目标规格下限规格下限规格下限规格下限38 Controls charts monitoring changes in Controls charts monitoring changes in process process accuracyaccuracy 监控过程准确度的变化监控过程准确度的变化X-charts

45、(Individual Observation Chart) X-charts (Individual Observation Chart) 单值图单值图X-bar-charts X-bar-charts 均值图均值图P-charts P-charts 百分率图百分率图 Control charts monitoring changes in processControl charts monitoring changes in process precision precision 监控控过程精密度的变化监控控过程精密度的变化R-bar-charts (Moving Range Charts

46、) R-bar-charts (Moving Range Charts) 移动极差图移动极差图S-charts S-charts 标准差图标准差图39Example: Capability Study Of Syrup Filling ProcessExample: Capability Study Of Syrup Filling Process 单值图单值图13579111315171921232527293119.9419.9619.9820.0020.0220.0420.06Container Weight ( Kg )UCLx=20.049KgXbar=20.000KgLCLx=19

47、.951KgTest OrderIndividual ValuesSample MeanUCLx and LCLxX-chart for Process Capability Study 能力分析单值图能力分析单值图UCL 控制范围上限控制范围上限LCL 控制范围下限控制范围下限 40Example: Capability Study Of Syrup Filling Process Example: Capability Study Of Syrup Filling Process 0.0000.0100.0200.0300.0400.0500.060Moving Range Chart f

48、or Process Capability Study 能力分析移动极差图能力分析移动极差图2468101214161820222426283032Test OrderRmRm barUCLm and LCLmRmi0.070UCLm=0.060KgRm-bar=0.018KgLCLm=0.000KgUCL 控制范围上限控制范围上限LCL 控制范围下限控制范围下限41 Control Charts Should Be Used in PairsControl Charts Should Be Used in Pairs 控制图的应用组合控制图的应用组合An appropriate combin

49、ation of control charts An appropriate combination of control charts for continuously monitoring the process for continuously monitoring the process average and process variabilityaverage and process variability Acceptable choice would be X & MR, Acceptable choice would be X & MR, X-bar & R, or Xbar

50、 & S charts.X-bar & R, or Xbar & S charts.Control charts should always be prepared and analyzed Control charts should always be prepared and analyzed in pairs one chart for location and another for spreadin pairs one chart for location and another for spread42Individuals charts are not as sensitive