SPC-抽样教程ppt课件

1、SPC Part II:Sampling Plans for X-chartLearning ObjectivesRevision of SPC Fundamentals/SPC原理校正Misconceptions of SPC/SPC 误解Process Control Model/制程控制模型Two Basic Causes of Variability/2种根本变异缘由Review of X-R Chart and X-s Chart/均值极差及单值控制图回想Review of Attributes Control Charts属性控制图回想Designing the X-chart均值

2、控制图的设计Sampling Risks (a and b)抽样风险ARL0 and ARL1Determining Sampling Interval决议抽样时间间隔Determining Sample Size决议样本大小Misconceptions of SPCLets check our understanding by looking at the most common control chart, X-chart.经过回想根本的均值控制图，检阅我们对SPC的了解LSLUSLPutting USL & LSL on X-chart helps ensure that parts a

3、re meeting Cpk requirements.Myth No. 1It is alright to shrink USL & LSL down to, say, 70% or 80%, to establish UCL and LCL.Myth No. 2More myths and misconceptions on the X-chart.对均值控制图的误解LSLUSLFortunately, parts still meet customer spec. although process is out of controlMyth No. 3Process in control

4、: therefore parts meet customer spec. as well as Cpk requirementsMyth No. 4Misconceptions of SPCLSLUSLMore myths and misconceptions of the X-chart.对均值控制图的误解How did we establish the sampling plan?- Gut feel? - Passed-down figures?- Statistical calculation?- Technical judgement?5 pcs/2 hr Myth No. 6Mi

5、sconceptions of SPCMyth No. 5A2RWe know A2R = 3s. But which s? sx, sx, swithin, soverall?Process Control Model for Quality ControlRaw Material, Components& Sub-Assemblies原资料，零件及半废品 ProcessProductObservation察看:Data Collection数据搜集Evaluation评价:Data Analysis数据分析Diagnosis诊断:Fault Discovery错误发现Decision决策:

6、Formulate Action阐明行动Implementation推行:Take Action采取行动Uncontrollable Inputs不可控的输入Controllable Inputs可控的输入Statistical Process Control The process control model shifts focus to the home front, i.e. the manufacturing process, taking a preventive instead of reactive mode.制程控制模型具有前瞻性，如，制造制程，是采取预防措施而非直接处理问题

7、 It also has something which the old concept of product control lacked - statistics. This allows use of samples to understand the entire process.较早时期产品控制缺乏统计这一让我们明白整个制程的概念 The new emphasis had to have a name - Statistical Process Control (SPC).新的产品控制观念强调了SPC We owe the application of statistics as a

8、 tool for manufacturing to Dr Walter A. Shewhart.统计在制造中的运用应归功于修哈特博士Two Basic Causes of VariabilityChance Causes of Variation变异的偶因Due to the cumulative effect of many small unavoidable sources of variation.许多不可防止的小的变异源的累积Also known as:common variation普通变异random variation随机变异inherent variation内在变异natu

9、ral variation自然变异A process operating with only chance causes of variation is said to be “in statistical control.仅有偶因变异的制程处于统计控制Two Basic Causes of VariabilityAssignable (or Special) Causes of Variation变异的异因Variation in a process that is different from from chance variation; disturbs a process so tha

10、t what it produces seems unnatural.这种变异明显异常于偶因引起的变异，制程遭到明显的影响，显得不自然。Examples of such causes of variation are异因引起的变异的例子:improperly adjusted machine不正常的调机excessive tool wear过多运用工具defective raw material运用有缺陷的原资料A process operating in the presenceof assignable causes of variation issaid to be “out-of-co

11、ntrol异因引起的变异的制程处于不受控.Objectives of SPC ChartsAll control charts have one primary purpose!一切控制图均有一个根本的目的To detect assignable causes of variation探测严重引起制程变异的异因，因此：that cause significant process shift, so that:investigation and corrective action may be undertaken to rid the process of the assignable cau

12、ses of variation before too many non-conforming units are produced.大量不合格品产生前，必需调查研讨并采取改善行动，以消除起制程变异的异因in other words, to keep the process in statistical control.换句话说，使得制程处于统计控制Objectives of SPC ChartsThe following are secondary objectives or direct benefits of the primary objective:以下是采用控制图的益处To red

13、uce variability in a process.减少制程的变异To help estimate the parameters of a process and establish its process capability.协助估计制程参数，建立制程才干Process Control制程控制Means that chance causes are the only source of variation present.偶因是制程变异的独一因数Refers to “voice of the process, i.e. we only need data from the proce

14、ss to determine if a process is in control控制图反映制程的声音，我们仅需求制程的数据来决议制程能否受控.Quality characteristic is monitored to verify if it forms a stable distribution over time, with control limits computed from the process data only经过监控质量特性，由制程数据计算制程的控制范围，检验制程能否构成在一定控制范围内的稳定的分布. Just because a process is in cont

15、rol does not necessarily mean it is a capable process仅仅由于制程受控不可以确定制程是有才干.The “goodness of a process is measured by its process capability制程的好会是由它的才干来量度的.Compares “voice of the process with “voice of the customer, which is given in terms of customer specs. or requirements比较制程的声音和客户的声音，客户的声音即由客户给定规格或要

16、求.Measures how well a stable distribution (process in control) meets customer requirements by the proportion of products within or out of customer specs衡量一个稳定的制程如何满足客户的需求是看它的产品在客户规格范围内的分布情况来确定.Process Capability制程才干Control Limits vs Spec. LimitsSpecification Limits (USL , LSL)规格极限determined by desig

17、n considerations由设计来决议represent the tolerable limits of individual values of a product产品的个别值代表偏向usually external to variability of the process通常外在环境影响制程的变异Control Limits (UCL , LCL)控制极限derived based on variability of the process来源于制程的变异usually apply to sample statistics such as subgroup average or r

18、ange, rather than individual values通常运用于抽样统计，如子组平均或极差，而非个别值Spec. limits should not be placed on control charts for subgroups规格极限不应放在控制图上:Spec. limits involve individual values of the quality characteristic, while control limits involve sample statistics of the quality characteristic规格极限包括质量特性的个别值，控制

19、极限仅包括质量特性的抽样统计值.Spec. limits are imposed by external demands, & thus do not help identify assignable causes规格极限被运用于外部，不能识别异因.Points plotted within the control limits do not indicate directly that parts are meeting customer specs. or Cpk requirements点在控制线内不代表产品满足客户规格或Cpk要求. Spec. Limits has No Busine

20、ss in Control Charts!Shewhart Control Charts - Overview变量属性缺陷有缺陷的Review of X-R Charts均值极差图回想Central Limit Theorem and Normal DistributionShewhart variables control charts for subgroups work because of two important principles修哈特控制图运用于子组，由于以下2个重要原理:Central Limit Theorem中心极限定律Normal Distribution正态分布Sh

21、ewhart found that when the averages of subgroups from a constant-cause system are plotted in the form of a histogram, the normal distribution appears修哈特发现当把常量系统的子组平均值作成一个直方图时，就出现了常态分布. Construction of X-R ChartsThe X-R chart is the most versatile of control charts, and is used in most applications.均

22、值极差控制图是个通用控制图Charting of averages and charting of ranges are used to check if a constant-cause system exists均值图和极差图用于检验常量系统能否存在.X-chart measures variability between samples均值图丈量2个样本间的差别R-chart measures variability within samples极差图丈量样本内的差别The Center Line and Control Limits of a X-chart:The Center Li

23、ne and Control Limits of a R-chart:Construction of X-R ChartsFor sample size n 10, R loses its efficiency in estimating process sigma and R-chart may not be appropriate.样本数大于10时，极差不能用于估算制程规范差，极差图不适用Construction of X-R ChartsShewhart Constants修哈特常数How do we begin to set up an X-R chart from scratch?如

24、何建立均值极差控制图？Implementing the Control Chart控制图的推行Implementing the Control Chart1)Preparation of Sampling抽样预备2)Data Collection数据搜集3)Construct the Control Chart组建控制图4)Analysis & Interpretation分析5)Use the Control Chart as a Process Monitoring Tool运用控制图作为制程监控工具Indicators of Instability制程不稳定判别Primary Indic

25、ators主要判别根据any point outside of a control limit恣意点出界Secondary Indicators次要判别根据any non-random pattern of points on a control chart恣意规律的点shift or run交替性Trend一定趋势Stratification分层Mixture混合性Periodicity周期性MiniTabs Tests for InstabilitySecondary IndicatorsPrimary IndicatorWarning Limits警告线The 3 control lim

26、its are also called action limits, i.e. investigation and corrective action are required when a point plots outside of these limits/ 3控制线又叫行动线，假设点在这些线以外，必需采取行动.Sometimes, 2 warning limits are marked on a control chart to increase the sensitivity of the control chart.有时2警告线也标示在图上，以添加控制图的敏锐性Lower Cont

27、rol LimitUpper Control LimitCenter LineSample Number or TimeSample Quality CharacteristicUpper Warning LimitLower Warning LimitSo what do you do if a point is above the Warning Limit?点在警告线以上如何办？An important idea in control chart theory is the way we pull specimens to form a subgroup of data控制图原理的一个重

28、要概念是我们将样本组成数据子组的方法.This should follow what Shewhart called the rational subgroup concept这必需根据修哈特的合理子组概念.The rational subgroup concept requires that parts are pulled consecutively from the process when forming a subgroup修哈特的合理子组概念要求组成子组的样本必需延续地从制程抽取.Rational Subgroups合理子组 Thus, the rational subgroup

29、concept implies that subgroups should be selected so that if assignable causes are present合理子组概念意味着选择子组时，展现异因:the probability for differences between subgroups will be maximized/应最大化2个子组的差别while the probability for differences within a subgroup will be minimized同时应最小化子组内的差别.Rational Subgroups合理子组 Co

30、nstruction of Subgroups子组构建Preferred method首选方法:Take consecutive units of production选取延续消费产品Because the specimens are collected within a short time-frame, this minimizes the chance of variability due to an assignable cause to appear within a sample only因样本在一短时间内搜集，可以最小化异因在一个样本内出现的时机.It maximizes the

31、 chance of variability due to an assignable cause to appear between samples可以最大化异因在不同样本内出现的时机.Good for detecting process shifts能很好地探测制程偏移Rational Subgroups合理子组 X-S ChartsThe Center Line and Control Limits of a X Chart areThe Center Line and Control Limits of a S Chart are_Shewhart ConstantsFor n 25A

32、ttributes Control Charts属性控制图43npcpuConstant常数Lot SizeVariable变数Lot SizeDefects(Poisson Distribution泊松分布)Defectives(Binomial Distribution二项分布)p ChartFraction Non-Conforming少数不合格Reject Rate / Defective Rate拒收率/缺陷率Percent Fallout20100Sample NumberProportionp Chart1P=0.21403.0SL=0.388

33、0-3.0SL=0.04000The underlying principles of the p chart are based on the binomial distribution/P 图的原理基于二项分布.The mean and variance of the distribution of ps are computed from the binomial equation, giving/P图分布的均值和偏向由二项分布公式计算而来: p Chartk = number of subgroups, should be between 20 to 25 before constru

34、cting control limits.建立控制线之前，子组数应选择在20到25之间Xk = number of defective units in subgroup k which has a total sample size of nk unitsp ChartFollowing Shewharts principle, the Center Line and Control Limits of a p chart are根据休哈特原理，中心线和控制线分别是:The p chart also assumes a symmetrical bell-shape distribution,

35、 with symmetrical control limits on each side of the center line/P图呈对称铃型分布，控制线对称地分布在中心线的两侧.This implies that the binomial distribution is approximately close to the shape of the normal distribution, which can happen under certain conditions of p and n这说名在p& n 一定的条件下，二项分布接近正态分布:p 1/2 and n 10 implyin

36、g np 5For other values of p, the general guideline is to have np 10 to get a satisfactory approximation of the normal to the binomial.假设P不等于1/2，通那么是使np10,这样就可以使二项分布得到称心的正态型p ChartIf the sample size is not constant, then the Control Limits of a p chart may be computed by either method假设样本大小不为常数，控制线可以

37、用以下恣意一放法得到:a) Variable Control Limits变量控制线where ni is the actual sample size of each sampling i这里n是每次抽样的实践数b) Control Limits Based on Average Sample Size控制线基于平均样本数where n is the average (or typical) sample size of all the samples这里n是一切样本数的平均值p ChartWhen to Use Control Limits Based on Average Sample

38、Size instead of Variable Control Limits当运用基于样本平均大小的控制线时Smallest subgroup size, nmin, is at least 30% of the largest subgroup size, nmax.最小样本大小至少是最大样本大小的30%Future sample sizes will not differ greatly from those previously observed.后来的样本大小与目前样本大小无较大区别When using Control Limits Based on Average Sample S

39、ize, the exact control limits of a point should be determined and examined relative to that value if当运用基于样本平均大小的控制线时，每一点的控制线由于那一点的值来决议假设:There is an unusually large variation in the size of a particular sample某一特别的样本的大小有明显的变化There is a point which is near the control limits.有一点接近控制线p Chart - Average

40、 Sample Sizenp ChartIf the sample size is constant, it is possible to base a control chart on the number nonconforming (np), rather than the fraction nonconforming (p).假设样本大小是常数，可以基于控制图的不合格品数，而非部分不合格品数The Center Line and Control Limits of an np chart are:Sample Size for p and np ChartsSample Size is

41、 determined based on the 2 criteria样本大小基于2个规范来决议:Assumption to approximate Binomial Distribution to a Normal Distribution假定二项分布近似正态分布To ensure that the LCL is greater than zero.确保下控制线大于0For p 0.5For p = other valuesc ChartDefects per Unit (DPU)单位缺陷Error Rate / Defect Rate缺陷率Defects per Opportunity20

42、10020100Sample NumberSample Countc ChartC=9.6503.0SL=18.97-3.0SL=0.3307c ChartIf the number of nonconformities (defects) per inspection unit is denoted by c, then假设每个检查单元的缺陷数为c,那么:The Center Line and Control Limits of a c chart are:u ChartIn cases where the number of inspection units is not constant

43、, the u chart may be used instead, with假设检查单元的数量不为常数，那么用u图:If the average number of defects per inspection unit is denoted by u, then假设每个检查单元的平均缺陷数用u表示，那么Where ci is the count of the number of defects in number of inspection units, ai这里ci 是数量为ai的检查单元的缺陷数u ChartThe Center Line and Control Limits of a

44、 u chart are:Sampling Plans for X Chart 均值图抽样方案Sampling frequency?抽样频率Sample size?样本大小Width of control limits?控制线宽度Sampling Frequency抽样频率 The most desirable situation with regards to detecting shifts would be to take large samples very frequently探测变化最理想的做法是频繁地抽取大的样本. But this is usually not economic

45、ally feasible, and the problem is one of resource allocation.由于资源分配的问题，这在经济上不可行 Should we take smaller samples at short intervals? Or larger samples at longer intervals?可以在较短时间内抽取小样本吗， 或在较长时间间隔内抽取较大样本吗 Current industry practice tends to favour smaller, more frequent samples目前业界的共识是频繁地抽去小样本Designing

46、an X-R Chart Sampling Frequency - ARL抽样频率-平均运转周期 A good way is to start evaluating sampling frequency is to determine the required sampling frequency statistically一个好的方法是评价抽样频率，统计地决议需求的抽样频率 - We use the Average Run Length (ARL) to do this我们运用平均运转周期来决议 Then finally weigh the computed results with sou

47、nd practical judgement最后根据计算结果和惯例来决议Designing an X-R Chart Control Charts Sampling RisksIf there is no change in the process, there is still a chance of getting a point out of the 3s control limits. What is the implication?假设制程没有改动，但有一点在3s控制线外，它表示什么呢3 s3 s99.73%Lower Control LimitCenter LineUpper Co

48、ntrol LimitWhat does each area of 0.% mean?每一个这样的区域代表什么？0.%0.%Control Charts Sampling RisksType I Error一类错误Concluding that the process is out of control when it is really in control制程受控，但却以为曾经失控 = probability of making Type I error范此类错误的能够性 = commonly known as the producers risk制造商的风险 = total of 0.2

49、7% for control limits of +/- 3s对于+/- 3s控制线，范此类错误的能够性为0.27%Lower Control LimitUpper Control LimitCenter LineSample Number or Time0.%0.%Is process really out of control? Or is the point outside due to random variation?Control Charts Sampling RisksType I Error and Tampering一类错误及干涉 If the process is rea

50、lly in control, and process adjustment is made because of Type I error, it is called tampering with the process.制程受控但由于范一类错误而调整制程，这叫干涉制程 Tampering has been shown to actually increase the variability of the process!干涉制程实践是给制程添加变异Control Charts Sampling RisksType II Error二类错误Concluding that the proces

51、s is in control when it is really out of control制程不受控但却以为它受控 = probability of making Type II error范此类错误的能够性 = commonly known as the consumers risk客户的风险0.%0.%Lower Control LimitUpper Control LimitCenter LineSample Number or Time0.%0.%Is process really in control? Or is the point inside due to random

52、variation of the shifted process?Shifted ProcessAverage Run Length (ARL)ARL refers to the average number of samples (or points) plotted to see an out-of-control signalFor a process that is in-control, For a process that is out-of-control,ARLs are used to help evaluate decisions on sample size and sa

53、mpling frequency平均运转周期用来协助决议抽样大小和频率Sampling Frequency: In-Control ARL (ARL0)受控平均运转周期For the X-chart with 3s limits, a = 0.0027Therefore, in-control ARL = 1/0.0027 = 370.This means that if the processremains unchanged, one out-of-control signal will be generated every 370 samples制程不变条件下，每370个样本能够产生一个

54、失控信号.If the sampling interval is 1 hr,one false alarm will be seenevery 370 hrs typically.假设取样间隔为1小时，那么每370小时就会看到1个错误报警Designing an X-R Chart 0.%0.%Sampling Frequency: Out-of-Control ARL (ARL1)失控平均运转周期Now suppose the process has drifted by 3s.现假定制程偏移3sProbability of X still within the 3s limits = 0.

55、5均值在3s 线内的能够性为0.5Thus, out-of-control ARL = 1/(1 - 0.5) = 2.This means from the time theprocess shifted, the chart needs 2 samples to detect the shift.这意味着从制程开场发生偏移时，控制图需求2个样本才干探测得到这种偏移If the sampling interval is 1 hr,Average Time to Signal (ATS)or exposure is 2 hrs typically.假设抽样间隔是1小时，那么这种变化要2小时才干

56、知道Designing an X-R Chart 0.%0.%Sample Size样本大小What about sample size? How do we compute the adequate sample size statistically?如何计算足够的样本大小Recall that the sample size helps to control or limit the amount of TypeII error (b).样本大小帮组控制或限制二类错误Recall also that sample size is a function of several paramete

57、rs:样本大小是几个参数的函数n = f a , b , D , s Hence, each parameter needs to be established before we can compute sample size因此，计算样本大小前，需求先建立各个参数Designing an X-R Chart Sampling Interval & Sample Size Procedure抽样间隔和样本大小选择程序Using 3s limits, a = 0.27% ARL0 = 1/a = 370 Define the required false alarm rate确定需求的错误报警

58、率: F.A. rate = Ave. # of production hrs to get 1 false alarm得到一个错误报警消费的平均时间From above information, determine the required sampling interval (S.I.) using following equation根据上面的资料，用以下等式确定抽样间隔: ARL0 x S.I. F.A. rate Round up S.I. (hrs) to next higher convenient number四舍五入抽样间隔时间到最正确Define the required

59、exposure rate:决议需求的发生率Exp. rate = Ave. # of production hrs before detecting shift探测到变异前的平均消费时间Designing an X-R Chart Sampling Interval & Sample Size Procedure抽样间隔和样本大小选择程序Bring S.I. & Exp. rate into following equation to compute the required ARL1抽样间隔和发生率代入以下公式计算ARL1 : ARL1 x S.I. Exp. rate From comp

60、uted ARL1, establish the required b, or (1 b), using ARL1 = 1/(1 b)计算b, or (1 b), At this juncture, sampling interval is already established & some parameters already established for sample size calculation到如今曾经有了计算样本大小的一些参数: n = f a , b , D , s Designing an X-R Chart Sampling Interval & Sample Size