SPC-抽樣教程ppt課件

1、SPC Part II:Sampling Plans for X-chartLearning ObjectivesRevision of SPC Fundamentals/SPC原理校正Misconceptions of SPC/SPC 誤解Process Control Model/制程控制模型Two Basic Causes of Variability/2種根本變異緣由Review of X-R Chart and X-s Chart/均值極差及單值控制圖回想Review of Attributes Control Charts屬性控制圖回想Designing the X-chart均值

2、控制圖的設(shè)計Sampling Risks (a and b)抽樣風(fēng)險ARL0 and ARL1Determining Sampling Interval決議抽樣時間間隔Determining Sample Size決議樣本大小Misconceptions of SPCLets check our understanding by looking at the most common control chart, X-chart.經(jīng)過回想根本的均值控制圖，檢閱我們對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.對均值控制圖的誤解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.對均值控制圖的誤解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原資料，零件及半廢品 ProcessProductObservation察看:Data Collection數(shù)據(jù)搜集Evaluation評價:Data Analysis數(shù)據(jù)分析Diagnosis診斷:Fault Discovery錯誤發(fā)現(xiàn)Decision決策:

6、Formulate Action闡明行動Implementation推行:Take Action采取行動Uncontrollable Inputs不可控的輸入Controllable Inputs可控的輸入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，是采取預(yù)防措施而非直接處理問題

7、 It also has something which the old concept of product control lacked - statistics. This allows use of samples to understand the entire process.較早時期產(chǎn)品控制缺乏統(tǒng)計這一讓我們明白整個制程的概念 The new emphasis had to have a name - Statistical Process Control (SPC).新的產(chǎn)品控制觀念強調(diào)了SPC We owe the application of statistics as a

8、 tool for manufacturing to Dr Walter A. Shewhart.統(tǒng)計在制造中的運用應(yīng)歸功于修哈特博士Two Basic Causes of VariabilityChance Causes of Variation變異的偶因Due to the cumulative effect of many small unavoidable sources of variation.許多不可防止的小的變異源的累積Also known as:common variation普通變異random variation隨機變異inherent variation內(nèi)在變異natu

9、ral variation自然變異A process operating with only chance causes of variation is said to be “in statistical control.僅有偶因變異的制程處于統(tǒng)計控制Two Basic Causes of VariabilityAssignable (or Special) Causes of Variation變異的異因Variation in a process that is different from from chance variation; disturbs a process so tha

10、t what it produces seems unnatural.這種變異明顯異常于偶因引起的變異，制程遭到明顯的影響，顯得不自然。Examples of such causes of variation are異因引起的變異的例子:improperly adjusted machine不正常的調(diào)機excessive tool wear過多運用工具defective raw material運用有缺陷的原資料A process operating in the presenceof assignable causes of variation issaid to be “out-of-co

11、ntrol異因引起的變異的制程處于不受控.Objectives of SPC ChartsAll control charts have one primary purpose!一切控制圖均有一個根本的目的To detect assignable causes of variation探測嚴(yán)重引起制程變異的異因，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.大量不合格品產(chǎn)生前，必需調(diào)查研討并采取改善行動，以消除起制程變異的異因in other words, to keep the process in statistical control.換句話說，使得制程處于統(tǒng)計控制Objectives of SPC ChartsThe following are secondary objectives or direct benefits of the primary objective:以下是采用控制圖的益處To red

13、uce variability in a process.減少制程的變異To help estimate the parameters of a process and establish its process capability.協(xié)助估計制程參數(shù)，建立制程才干Process Control制程控制Means that chance causes are the only source of variation present.偶因是制程變異的獨一因數(shù)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控制圖反映制程的聲音，我們僅需求制程的數(shù)據(jù)來決議制程能否受控.Quality characteristic is monitored to verify if it forms a stable distribution over time, with control limits computed from the process data only經(jīng)過監(jiān)控質(zhì)量特性，由制程數(shù)據(jù)計算制程的控制范圍，檢驗制程能否構(gòu)成在一定控制范圍內(nèi)的穩(wěn)定的分布. Just because a process is in cont

15、rol does not necessarily mean it is a capable process僅僅由于制程受控不可以確定制程是有才干.The “goodness of a process is measured by its process capability制程的好會是由它的才干來量度的.Compares “voice of the process with “voice of the customer, which is given in terms of customer specs. or requirements比較制程的聲音和客戶的聲音，客戶的聲音即由客戶給定規(guī)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衡量一個穩(wěn)定的制程如何滿足客戶的需求是看它的產(chǎn)品在客戶規(guī)格范圍內(nèi)的分布情況來確定.Process Capability制程才干Control Limits vs Spec. LimitsSpecification Limits (USL , LSL)規(guī)格極限determined by desig

17、n considerations由設(shè)計來決議represent the tolerable limits of individual values of a product產(chǎn)品的個別值代表偏向usually external to variability of the process通常外在環(huán)境影響制程的變異Control Limits (UCL , LCL)控制極限derived based on variability of the process來源于制程的變異usually apply to sample statistics such as subgroup average or r

18、ange, rather than individual values通常運用于抽樣統(tǒng)計，如子組平均或極差，而非個別值Spec. limits should not be placed on control charts for subgroups規(guī)格極限不應(yīng)放在控制圖上:Spec. limits involve individual values of the quality characteristic, while control limits involve sample statistics of the quality characteristic規(guī)格極限包括質(zhì)量特性的個別值，控制

19、極限僅包括質(zhì)量特性的抽樣統(tǒng)計值.Spec. limits are imposed by external demands, & thus do not help identify assignable causes規(guī)格極限被運用于外部，不能識別異因.Points plotted within the control limits do not indicate directly that parts are meeting customer specs. or Cpk requirements點在控制線內(nèi)不代表產(chǎn)品滿足客戶規(guī)格或Cpk要求. Spec. Limits has No Busine

20、ss in Control Charts!Shewhart Control Charts - Overview變量屬性缺陷有缺陷的Review of X-R Charts均值極差圖回想Central Limit Theorem and Normal DistributionShewhart variables control charts for subgroups work because of two important principles修哈特控制圖運用于子組，由于以下2個重要原理:Central Limit Theorem中心極限定律Normal Distribution正態(tài)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修哈特發(fā)現(xiàn)當(dāng)把常量系統(tǒng)的子組平均值作成一個直方圖時，就出現(xiàn)了常態(tài)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、值極差控制圖是個通用控制圖Charting of averages and charting of ranges are used to check if a constant-cause system exists均值圖和極差圖用于檢驗常量系統(tǒng)能否存在.X-chart measures variability between samples均值圖丈量2個樣本間的差別R-chart measures variability within samples極差圖丈量樣本內(nèi)的差別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.樣本數(shù)大于10時，極差不能用于估算制程規(guī)范差，極差圖不適用Construction of X-R ChartsShewhart Constants修哈特常數(shù)How do we begin to set up an X-R chart from scratch?如

24、何建立均值極差控制圖？Implementing the Control Chart控制圖的推行Implementing the Control Chart1)Preparation of Sampling抽樣預(yù)備2)Data Collection數(shù)據(jù)搜集3)Construct the Control Chart組建控制圖4)Analysis & Interpretation分析5)Use the Control Chart as a Process Monitoring Tool運用控制圖作為制程監(jiān)控工具Indicators of Instability制程不穩(wěn)定判別Primary Indic

25、ators主要判別根據(jù)any point outside of a control limit恣意點出界Secondary Indicators次要判別根據(jù)any non-random pattern of points on a control chart恣意規(guī)律的點shift or run交替性Trend一定趨勢Stratification分層Mixture混合性Periodicity周期性MiniTabs Tests for InstabilitySecondary IndicatorsPrimary IndicatorWarning Limits警告線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控制線又叫行動線，假設(shè)點在這些線以外，必需采取行動.Sometimes, 2 warning limits are marked on a control chart to increase the sensitivity of the control chart.有時2警告線也標(biāo)示在圖上，以添加控制圖的敏銳性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?點在警告線以上如何辦？An important idea in control chart theory is the way we pull specimens to form a subgroup of data控制圖原理的一個重

28、要概念是我們將樣本組成數(shù)據(jù)子組的方法.This should follow what Shewhart called the rational subgroup concept這必需根據(jù)修哈特的合理子組概念.The rational subgroup concept requires that parts are pulled consecutively from the process when forming a subgroup修哈特的合理子組概念要求組成子組的樣本必需延續(xù)地從制程抽取.Rational Subgroups合理子組 Thus, the rational subgroup

29、concept implies that subgroups should be selected so that if assignable causes are present合理子組概念意味著選擇子組時，展現(xiàn)異因:the probability for differences between subgroups will be maximized/應(yīng)最大化2個子組的差別while the probability for differences within a subgroup will be minimized同時應(yīng)最小化子組內(nèi)的差別.Rational Subgroups合理子組 Co

30、nstruction of Subgroups子組構(gòu)建Preferred method首選方法:Take consecutive units of production選取延續(xù)消費產(chǎn)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因樣本在一短時間內(nèi)搜集，可以最小化異因在一個樣本內(nèi)出現(xiàn)的時機.It maximizes the

31、 chance of variability due to an assignable cause to appear between samples可以最大化異因在不同樣本內(nèi)出現(xiàn)的時機.Good for detecting process shifts能很好地探測制程偏移Rational Subgroups合理子組 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屬性控制圖43npcpuConstant常數(shù)Lot SizeVariable變數(shù)Lot SizeDefects(Poisson Distribution泊松分布)Defectives(Binomial Distribution二項分布)p ChartFraction Non-Conforming少數(shù)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 圖的原理基于二項分布.The mean and variance of the distribution of ps are computed from the binomial equation, giving/P圖分布的均值和偏向由二項分布公式計算而來: p Chartk = number of subgroups, should be between 20 to 25 before constru

34、cting control limits.建立控制線之前，子組數(shù)應(yīng)選擇在20到25之間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根據(jù)休哈特原理，中心線和控制線分別是:The p chart also assumes a symmetrical bell-shape distribution,

35、 with symmetrical control limits on each side of the center line/P圖呈對稱鈴型分布，控制線對稱地分布在中心線的兩側(cè).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這說名在p& n 一定的條件下，二項分布接近正態(tài)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.假設(shè)P不等于1/2，通那么是使np10,這樣就可以使二項分布得到稱心的正態(tài)型p ChartIf the sample size is not constant, then the Control Limits of a p chart may be computed by either method假設(shè)樣本大小不為常數(shù)，控制線可以

37、用以下恣意一放法得到:a) Variable Control Limits變量控制線where ni is the actual sample size of each sampling i這里n是每次抽樣的實踐數(shù)b) Control Limits Based on Average Sample Size控制線基于平均樣本數(shù)where n is the average (or typical) sample size of all the samples這里n是一切樣本數(shù)的平均值p ChartWhen to Use Control Limits Based on Average Sample

38、Size instead of Variable Control Limits當(dāng)運用基于樣本平均大小的控制線時Smallest subgroup size, nmin, is at least 30% of the largest subgroup size, nmax.最小樣本大小至少是最大樣本大小的30%Future sample sizes will not differ greatly from those previously observed.后來的樣本大小與目前樣本大小無較大區(qū)別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當(dāng)運用基于樣本平均大小的控制線時，每一點的控制線由于那一點的值來決議假設(shè):There is an unusually large variation in the size of a particular sample某一特別的樣本的大小有明顯的變化There is a point which is near the control limits.有一點接近控制線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).假設(shè)樣本大小是常數(shù)，可以基于控制圖的不合格品數(shù)，而非部分不合格品數(shù)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樣本大小基于2個規(guī)范來決議:Assumption to approximate Binomial Distribution to a Normal Distribution假定二項分布近似正態(tài)分布To ensure that the LCL is greater than zero.確保下控制線大于0For p 0.5For p = other valuesc ChartDefects per Unit (DPU)單位缺陷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假設(shè)每個檢查單元的缺陷數(shù)為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假設(shè)檢查單元的數(shù)量不為常數(shù)，那么用u圖:If the average number of defects per inspection unit is denoted by u, then假設(shè)每個檢查單元的平均缺陷數(shù)用u表示，那么Where ci is the count of the number of defects in number of inspection units, ai這里ci 是數(shù)量為ai的檢查單元的缺陷數(shù)u ChartThe Center Line and Control Limits of a

44、 u chart are:Sampling Plans for X Chart 均值圖抽樣方案Sampling frequency?抽樣頻率Sample size?樣本大小Width of control limits?控制線寬度Sampling Frequency抽樣頻率 The most desirable situation with regards to detecting shifts would be to take large samples very frequently探測變化最理想的做法是頻繁地抽取大的樣本. But this is usually not economic

45、ally feasible, and the problem is one of resource allocation.由于資源分配的問題，這在經(jīng)濟上不可行 Should we take smaller samples at short intervals? Or larger samples at longer intervals?可以在較短時間內(nèi)抽取小樣本嗎， 或在較長時間間隔內(nèi)抽取較大樣本嗎 Current industry practice tends to favour smaller, more frequent samples目前業(yè)界的共識是頻繁地抽去小樣本Designing

46、an X-R Chart Sampling Frequency - ARL抽樣頻率-平均運轉(zhuǎn)周期 A good way is to start evaluating sampling frequency is to determine the required sampling frequency statistically一個好的方法是評價抽樣頻率，統(tǒng)計地決議需求的抽樣頻率 - We use the Average Run Length (ARL) to do this我們運用平均運轉(zhuǎn)周期來決議 Then finally weigh the computed results with sou

47、nd practical judgement最后根據(jù)計算結(jié)果和慣例來決議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?假設(shè)制程沒有改動，但有一點在3s控制線外，它表示什么呢3 s3 s99.73%Lower Control LimitCenter LineUpper Co

48、ntrol LimitWhat does each area of 0.% mean?每一個這樣的區(qū)域代表什么？0.%0.%Control Charts Sampling RisksType I Error一類錯誤Concluding that the process is out of control when it is really in control制程受控，但卻以為曾經(jīng)失控 = probability of making Type I error范此類錯誤的能夠性 = commonly known as the producers risk制造商的風(fēng)險 = total of 0.2

49、7% for control limits of +/- 3s對于+/- 3s控制線，范此類錯誤的能夠性為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一類錯誤及干涉 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類錯誤而調(diào)整制程，這叫干涉制程 Tampering has been shown to actually increase the variability of the process!干涉制程實踐是給制程添加變異Control Charts Sampling RisksType II Error二類錯誤Concluding that the proces

51、s is in control when it is really out of control制程不受控但卻以為它受控 = probability of making Type II error范此類錯誤的能夠性 = commonly known as the consumers risk客戶的風(fēng)險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平均運轉(zhuǎn)周期用來協(xié)助決議抽樣大小和頻率Sampling Frequency: In-Control ARL (ARL0)受控平均運轉(zhuǎn)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制程不變條件下，每370個樣本能夠產(chǎn)生一個

54、失控信號.If the sampling interval is 1 hr,one false alarm will be seenevery 370 hrs typically.假設(shè)取樣間隔為1小時，那么每370小時就會看到1個錯誤報警Designing an X-R Chart 0.%0.%Sampling Frequency: Out-of-Control ARL (ARL1)失控平均運轉(zhuǎn)周期Now suppose the process has drifted by 3s.現(xiàn)假定制程偏移3sProbability of X still within the 3s limits = 0.

55、5均值在3s 線內(nèi)的能夠性為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.這意味著從制程開場發(fā)生偏移時，控制圖需求2個樣本才干探測得到這種偏移If the sampling interval is 1 hr,Average Time to Signal (ATS)or exposure is 2 hrs typically.假設(shè)抽樣間隔是1小時，那么這種變化要2小時才干

56、知道Designing an X-R Chart 0.%0.%Sample Size樣本大小What about sample size? How do we compute the adequate sample size statistically?如何計算足夠的樣本大小Recall that the sample size helps to control or limit the amount of TypeII error (b).樣本大小幫組控制或限制二類錯誤Recall also that sample size is a function of several paramete

57、rs:樣本大小是幾個參數(shù)的函數(shù)n = f a , b , D , s Hence, each parameter needs to be established before we can compute sample size因此，計算樣本大小前，需求先建立各個參數(shù)Designing an X-R Chart Sampling Interval & Sample Size Procedure抽樣間隔和樣本大小選擇程序Using 3s limits, a = 0.27% ARL0 = 1/a = 370 Define the required false alarm rate確定需求的錯誤報警

58、率: F.A. rate = Ave. # of production hrs to get 1 false alarm得到一個錯誤報警消費的平均時間From above information, determine the required sampling interval (S.I.) using following equation根據(jù)上面的資料，用以下等式確定抽樣間隔: ARL0 x S.I. F.A. rate Round up S.I. (hrs) to next higher convenient number四舍五入抽樣間隔時間到最正確Define the required

59、exposure rate:決議需求的發(fā)生率Exp. rate = Ave. # of production hrs before detecting shift探測到變異前的平均消費時間Designing an X-R Chart Sampling Interval & Sample Size Procedure抽樣間隔和樣本大小選擇程序Bring S.I. & Exp. rate into following equation to compute the required ARL1抽樣間隔和發(fā)生率代入以下公式計算ARL1 : ARL1 x S.I. Exp. rate From comp

60、uted ARL1, establish the required b, or (1 b), using ARL1 = 1/(1 b)計算b, or (1 b), At this juncture, sampling interval is already established & some parameters already established for sample size calculation到如今曾經(jīng)有了計算樣本大小的一些參數(shù): n = f a , b , D , s Designing an X-R Chart Sampling Interval & Sample Size