TUV德国莱茵技术六西格码培训BasicStatisticsforSPC课件

1、TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC2022/9/27TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCTUV德国莱茵技术六西格码培训资料BasicStatistiWhat is statistics?什么是统计Definition of statistics:统计的定义* Statistics are facts and figures.统计是事实和数据* Statistics consist of a set of methods and rules for organizing and interpreting obser

2、vations from populations and samples统计通过一系列方法和规则来组织、解释来自总体和样本的观测值Populations and Samples总体和样本* Population is the entire group or set of all possible events of interest in the particular study. 总体是被关注、研究的对象的全部* Sample is a subset of the population样本是从总体中抽出的一部分ENTIRE POPULATION总体SAMPLE WITHIN(subset)样

3、本A Statistic:统计值A numerical value that describes a sample用来描述样本的数值TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCWhat is statistics?什么是统计DefiniTwo Types of Data统计获得的两种数据Attribute Data CategoriesYes, NoGo, No goMachine 1, Machine 2, Machine 3Pass/FailVariable Data Discrete (Count) DataMaintenance Equipment Fa

4、ilures, Number of ClogsNumber of customer returnsContinuous DataDecimal subdivisions are meaningfulTime, Pressure, Conveyor Speed 特性数据(定性)等级是非 通止 个体（如 1号机器, 2号机器, 3号机器)成败变量数据（定量)间断型数据（计数）如设备维修次数、阻塞次数等客户退货次数连续型数据 (计量)可有小数点如时间、压力、传送速度等 TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCTwo Types of Data统计获得的两种数据At

5、tDescription of Continuous Data-Graphical计量型数据的描述-图形HistogramHeight of 90 ladies# of ocurrenceHeight(inch) 数据分布图在实际统计中， 统计结果是分段表示的，因此作出的分布图为柱形图。 在分析数据时，通常将它拟合成连续的曲线。TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCDescription of Continuous DataExamples of distributions 不同的分布Negative Skew负斜Positive Skew正斜Symmet

6、ric Distribution对称分布Left-tailedRight-tailedTwo-tailedTUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCExamples of distributions 不同的分Mean: Arithmetic average of a set of values 均值：算数平均值Reflects the influence of all values反映全部数据的影响Strongly Influenced by extreme values受特殊值干扰大Median: Reflects the 50% rank - the ce

7、nter number after a set of numbers has been sorted from low to high.中位数：反映 系列的一半将一组数据按大小顺序排列，取中间的一个数据Does not include all values in calculation 计算中未包含全部数据Is “robust” to extreme outlier scores. 对特殊值的干扰有抵抗 The mean and median will be affected by the nature of the distribution of numbers. 均值和中值都受数据分布的影

8、响Mode: Most frequently occurring value in a data set. In a Pareto this is the largest bar on the chart. 众数：数据中重复次数最多的值， 在柏拉图上表现为最高的那条柱Description of Quantitative Data-Central Tendency计量型数据的描述-中心位置TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCMean: Arithmetic average of aRelationship: mean and median均值和中位数的比

9、较1101009080706050403020100500NormalFrequencyMean, Median807060504030201003002001000Neg SkewFrequencyMedianMean130120110100908070603002001000Pos SkewFrequencyMedianMeanTUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCRelationship: mean and medianSample mean of a distribution样本均值 Mean = Average= xi /Ni=1N = X1 +

10、 X2 +.XN NExamples:例Part weights零件重量: 8.47, 8.67, 9.34, 7.99 AVERAGE = 8.47 +8.67 + 9.34 + 7.99 = 8.62平均值4TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCSample mean of a distribution Dont Worry. That rope is one inch thick on the average.不要担心。 绳子是平均一英寸粗TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCDont Worry. That r

11、ope is oneRange = maximum value - minimum value范围=样本内最大值-最小值Variance= mean squared distance from the mean方差=数据与均值差距的平方之均值Standard deviation = is the square root of the variance and provides a measure of the standard distance from the mean.标准偏差=方差的开方Description of Quantitative Data-Dispersion or Spre

12、ad计量型数据的描述-离散度TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCRange = maximum value - minilDeviation（偏差） is the distance from the mean.是离开均值的距离lDeviation score（偏差值） = observation - true mean观测值-均值lVariance 方差= mean or average of squared deviation scores偏差值的平方均值. is the symbol for variance方差的符号.lStandard Devia

13、tion标准偏差 = square root of variance方差的开方.is the symbol for the standard deviation.标准偏差的符号The Standard Deviation is a Measure of Variability标准偏差是对变异的描述m= PopulationMean 总体的均值iDeviation (distance from mean)偏差s2sStandard Deviation标准偏差TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPClDeviation（偏差） is the distances

14、= Sample Standard Deviation样本标准偏差X= Sample Mean样本均值= Population Mean总体均值Statistics Estimate Parameters= Population Standard Deviation总体标准偏差SamplePopulationSAMPLE样本POPULATION总体Statistics or parameters?样本统计值与总体参数？统计活动的实质：用样本统计值来估计总体参数，从而了解总体TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCs = Sample StandardX= S

15、amplPopulation vs. sample总体和样本计算公式Population Mean总体均值Sample Mean样本均值Population Standard Deviation总体标准偏差Sample Standard Deviation样本标准偏差=x=xnii=1n =s=(X )n-1i2i=1nX TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCPopulation vs. sample总体和样本计算公Example: Calculating “sigma”计算练习Using the form above, calculate the st

16、andard deviation for the numbers用上列的表计算以下5个数据的标准偏差：2， 1， 3， 5 ，4 X X-X (X-)2XTUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCExample: Calculating “sigma”计算Exercise Solution计算结果: X X-X (X-)2XTUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCExercise Solution计算结果: 数据的描述总览分布的位置 LocationMean 均值Median 中值Mode 代表值Quantiles 分位数Q

17、1 四分之一处Q2 二分之一处Q3 四分之三处 P 机率位置离散度 SpreadRange 范围Standard Deviation 标准偏差Variance 变差Stability Factor 稳定因子Span 跨度Interquartile Range 内分位宽度Sum of Squares 平方和Shape 形状Histograms 直方图Run Charts 运行图Time Plots 时序图Scatter Plots 散点图Box Plots 盒状图Block Chart 块图Normality Plot 正态性图NumercialGraphicalTUV德国莱茵技术六西格码培训资

18、料BasicStatisticsforSPC数据的描述总览分布的位置 Location离散度 SpreaNormal Distribution正态分布Mean均值Bell-shape Symmetric Distribution倒钟状对称分布fx(x)=12ps2e-(x-m)2/2s2TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCNormal Distribution正态分布Measured by Standard Deviation用标准偏差为尺度mean68.27 %15.865%15.865%TUV德国莱茵技术六西格码培训资料BasicStatistics

19、forSPCMeasured by Standard DeviationMeasured by Standard Deviation用标准偏差为尺度mean95.45 %TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCMeasured by Standard Deviation68.2% 的数据落在1s 以内95.4% 的数据落在2s 以内99.7% 的数据落在3s 以内99.99999975% 的数据落在6s 以内Measured by Standard Deviation用标准偏差为尺度+4+5+6+1+2+3-2-1-4-3-6-5068.27%95.45%9

20、9.73%99.9937%99.999943%99.9999998%TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC68.2% 的数据落在1s 以内Measured by S总体任意抽取4组样品，每组3个样品总体的参数样品的统计值总体与样品在统计上的关系 TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC总体任意抽取4组样品，每组3个样品总体的参数样品的统计值总体样品之间的统计分布TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC样品之间的统计分布TUV德国莱茵技术六西格码培训资料Basi中心极限定理（Centra

21、l Limit Theorem）*条件:X1, X2, , Xn 是从总体中随机抽取样品的某特性的测量值，总体关于该特性的均值为 , 总体的标准偏差为 ,结论:该组样品的均值 所属分布（假定有多组这样的样品，多组的均值形成一个分布）的均值和标准偏差为:另外样品大小 n 越大，组均值的分布越接近正态分布. nXXXnX+=.21使用正态分布来讨论大多数问题的基础TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC中心极限定理（Central Limit Theorem）*(a)正态型l(b)规则型(c)指数型(d)偶次方型总体分布形状样品大小 n = 2的均值分布 n =

22、 5n = 30不论其总体的分布如何，其样品的均值的分布趋向正态分布实践经验如果总体是正态分布, 样品均值一定为正态分布，无论样品大小如何如果总体的分布不够对称， 520的样品大小即可最差的情形: 30的样品大小可以应付一切形状的总体分布，无论总体的分布离正态分布相差多远TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC(a)正态型l(b)规则型(c)指数型(d)偶次方型总体分布二项分布与泊松分布计数型数据（合格与不合格）的分布遵从二项分布或泊松分布的规律：假定一批产品的不合格的几率为p，从中随机抽出一个容量为n的样本，那么n件产品中不合格品数X是一个离散型的随机变量

23、, 它服从二项分布（Binomial or Bernoulli)的规律。PX=r=Crnpr(1-p)n-r r=1, 2, ., n当n 很大，不合格数nu很小时，不合格数Cnu的分布趋向于泊松分布(Poisson)： lc Pc= C-l C!当n充分大（n50），nu不小于5时，二项分布和泊松分布都趋于正态分布。TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC二项分布与泊松分布TUV德国莱茵技术六西格码培训资料BasiVariation&Capability变差与过程能力TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCVariati

24、on变差与过程能力TUV德国莱茵技术六西格码培Introduction to Variation什么是变差TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCIntroduction to VariationTUV德国160155150145165170175Will the ball always go the same distance? 球会总是落在同一点吗？TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC160155150145165170175Will the There will always be variability pre

25、sent in any process变差存在于任何过程We can tolerate variability if 我们在下列条件下可以容忍变差The total variability of the Output is relatively small compared to the process specifications and the process is on target 与过程的工程规范相比较而言过程的变差很小,并且过程对中于目标值The process is stable over time过程长时间稳定LSLUSLNomUSLCost成本Traditional传统观念A

26、cceptable可接受LSLUSLNomCost成本New新观念Can We Tolerate Variability?我们能容忍变差吗?TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCThere will always be variabiliAs the standard deviation increases probability of defect increase标准偏差越大, 缺陷几率越大1st distribution2nd distribution3rd distributionLower specUpper spec.Defects.Defec

27、ts& Distributions缺陷与分布形状 p(d)缺陷几率规范上限规范下限TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCAs the standard deviation incrProcess Capability过程能力TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCProcess CapabilityTUV德国莱茵技术六西格过程输入的变差已知有两种类型的过程变差:统计不受控: 与特殊原因有关统计受控: 与普通原因有关在研究过程表现时:特殊原因造成的变差往往表现为严重地偏离目标值，或不随机的平均值漂移普通原因造成的变差表现为

28、正态的随机分布过程能力分析适用于 普通原因造成的变差TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC过程输入的变差已知有两种类型的过程变差:TUV德国莱茵技术六Process Capability Indicators过程能力指数Process Potential : Ratio of the specification width to 6 times工艺潜能 a measure of the process variation工程规范的宽度与六倍的过程标准偏差的比值Cp = USL-LSL 6sPPp = USL-LSL 6sTCp is used when t

29、he process is in a state of statistical control as defined by standard control charting methods. Cp用于统计稳定的过程, 过程是否稳定可由统计控制图来确定Cp uses the pooled standard deviation. Cp使用分组汇合的标准偏差Pp is used when the process is NOT in a state of statistical control as defined by standard control charting methods. Pp u

30、ses the total standard deviation Pp用于统计不稳定的过程, 它使用整体的标准偏差TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCProcess Capability IndicatorsPNot indicatingif centeredhere . . .不论中心在哪Or here . . .或这儿Or here . . .或这儿Indicators with variables data:变量数据的指示CpPpTUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCNot indicatingOr here

31、. . .OTUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCTUV德国莱茵技术六西格码培训资料BasicStatistisPsTPooled standard deviation 分组汇合标准偏差Taken over a relatively short time period.相对较短时间内的数据Takes into account only the variation within a subset. 只计入小组内的变差Contains only common causes of variation. 只包含普通原因的变差Total or Overall sta

32、ndard deviation 整体标准偏差Taken over sufficient subsets to show the variation due to all common and special causes of variation.足够长时间内的数据以展示普通原因的变差和特殊原因的变差Calculated from many samples that represent the shift anddrift that occurs in the population due to all causes of variation.从很多样品中计算包含所有变差所带来的总体漂移Poo

33、led Vs Overall Standard Deviation分组汇合标准偏差与整体标准偏差TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCsPsTPooled standard deviation Actual Process Performance : Ratio of the difference between the process average and the nearest specification to 3 times a measure of the process variation 实际过程的表现:过程均值与最近的规范线的距离跟3倍的过

34、程标准偏差之比值Process Capability Indicators过程能力指数CPK = Min CPL, CPUCPL = X-LSL 3sPCPU = USL-X 3sPPPL = X-LSL 3sTPPU = USL-X 3sTPPK = Min PPL, PPUCpk is used when the process is in a state of statistical control as defined by standard control charting methods. Cp用于统计稳定的过程, 过程是否稳定可由统计控制图来确定Cpk uses the pool

35、ed standard deviation. Cpk使用分组汇合的标准偏差Ppk is used when the process is NOT in a state of statistical control as defined by standard control charting methods. Pp uses the total standard deviation Ppk用于统计不稳定的过程, 它使用整体的标准偏差TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCActual Process Performance : RIndicates Spre

36、ad & Distance分布宽度和距离的指示Width & positionare indicated here指示了分布宽度和位置and here . . .and here . . .CpkPpkTUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCIndicates Spread & Distance分布TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCTUV德国莱茵技术六西格码培训资料BasicStatisti计算 Cp / Cpk Cp=LSL140USL260200Cp=LSL140USL260200Cp=LSL140USL2602

37、00Cp=LSL140USL260200215sst = 20sst = 20sst = 10sst = 10Cpk=Cpk=Cpk=Cpk=TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC计算 Cp / Cpk Cp=LSLUSL200Cp=LSLCpPPCPKPPKCapability能力Overall Std DevNot in Control长期整体标准偏差统计不受控Pooled Std DevIn Control短期分组汇合标准偏差统计受控Performance表现CP represents “entitlement”!Cp代表改进的目标Relates s

38、td. deviationto tolerance 考察标准偏差与公差宽度Relates mean & std. deviation to spec.考察均值/标准偏差和工程规范Short TermLong Term“Snapshot” Look照相“Video” Look 录像TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCCpPPCapability能力Performance表Sample 3Sample 4Sample 5 s4 s3 s2 s1s5Total sT In a perfect state of control stotal = spPooled

39、 Standard Deviation分组汇合标准差“Average” Standard Deviation平均的标准偏差Assuming equal subgroup sizeSample 2Sample 1 TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCSample 3Sample 4Sample 5s4 s3 MondaySubgroup 1子组1TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCMondaySubgroup 1子组1TUV德国莱茵技术六西TuesdayFromMondaySubgroup 2子组2TUV德国莱茵技术

40、六西格码培训资料BasicStatisticsforSPCTuesdayFromSubgroup 2子组2TUV德国莱WednesdaySubgroup 3子组3FromMonday &TuesdayTUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCWednesdaySubgroup 3子组3FromTUV德ThursdaySubgroup 4 子组4FromMon, Tues,WedTUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCThursdaySubgroup 4 子组4FromTUV德This distribution is made

41、 up of many smaller time periods.这一分布是由一段时间内许多小分布组成Long Term DistributionSubgroups 1-4子组1-4TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCThis distribution is made up oMondayTuesdayWednesdayThursdayOVER TIME时间一长SHIFT HAPPENS漂移发生了TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCMondayTuesdayWednesdayThursdayWhich standa

42、rd deviation should we use?应该选用哪种标准偏差?It depends on what we are trying to do取决于我们要作什么If we want to know the best our process is capable of,如果我们想知道过程的最佳状态如何the process entitlement亦即过程的天赋能力use sst - the short term process capability使用短期标准差计算短期过程能力If we want to know what our customers see, 如果想了解客户是怎么看的

43、our actual performance,我们的表现use slt - the long term process capability使用长期标准差计算长期过程能力If we want to know our opportunity for improvementUSE BOTH!如果我们想知道改进的机会, 两者都用TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPCWhich standard deviation shoul0The difference between sst and slt representsThe Area for Process Imp

44、rovement 短期标准差与长期标准差的差距代表改进的空间The Focus of MAIC 改进的关注点Another way of thinking about it另一中思考角度0TUV德国莱茵技术六西格码培训资料BasicStatisticsforSPC0The difference between sst an YB 8207批号Y4092BY4092BY4092BY4092BY4092BY4092BY4092BY4092BY4092BY4095BY4095BY4095BY4095BY4095BY4095BY4095BY4095BY4095BY4095BY4095BMFI13.06

45、12.9512.3712.6013.1913.3312.7612.9712.7113.1912.2013.7012.0013.1612.2712.5712.7213.0213.0212.55批号Y4167BY4167BY4167BY4167BY4167BY4167BY4167BY4167BY4167BY4167BY4167BY4228BY4228BY4228BY4228BY4228BMFI12.8412.7413.0012.6012.6212.6413.0312.7413.1012.6012.6012.5612.8612.6014.0013.40批号Y4240BY4240BY4240BY4240BY4240BY4240BY4240BY4240BY4241BY4241BY4241BY4241BY4241BY4241BMFI12.5912.6011.9311.9712.9012.7512.3712.7013.0412.6012.9013.7012.4913.18Melt Flo