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1、Materials QualityPCS Training-Rev 3 May 21 20016/25/97Materials QualityPCS Training-Rev 3 May 21 2001Create Measurement PlanEstablish Monitor(SPC)Implement Response Flow Checklist(RFC)Element 1Element 2Element 32Materials QualityPCS Training-Rev 3 May 21 2001 Introduction 簡介簡介 What is SPC 什麼是什麼是SPC?

2、What is Stability 什麼是穩定性什麼是穩定性?What is a Control Chart 什麼是管制圖什麼是管制圖 How to Set-up a Control Chart 如何建立管制圖如何建立管制圖 Type of Control Charts Available 管制圖的種類管制圖的種類 How to Calculate the Control Limits 如何計算管制界限如何計算管制界限 SPC Trend Rules SPC法則法則 When to Revise Control Limits 何時重新計算管制界限何時重新計算管制界限 Process Capab

3、ility Study 制程能力研討制程能力研討 Spec limits VS Control Limits 規格界限規格界限 vs.管制界限管制界限 Stability VS Capability 穩定性穩定性 vs.能力能力 Control Chart Reduction/Elimination 減少管制圖減少管制圖 SPC Expectations3Materials QualityPCS Training-Rev 3 May 21 2001 Statistical 統計統計 Anything that deals with the collection,analysis,interpr

4、etation&presentation of numerical data 關於數據資料的收集關於數據資料的收集,分析分析,解釋與表現解釋與表現 Gaining information for making informed decisions 取得資訊來作有效的決定取得資訊來作有效的決定 Process 制程制程 Combination of machines,tools,methods,materials&people employed to attain process specification 結合機器結合機器,治工具治工具,方法方法,材料與人員來達到制程規格材料與人員來達到制程規

5、格 A similar procedure/event that is happening repetitively 重覆發生的事件重覆發生的事件/類似程序類似程序 Control 管制管制 To keep something within a desired condition 使某事使某事/物保持在想要的情況物保持在想要的情況 Make something behave the way we want it to behave 使某事使某事/物依我們所想的來執行物依我們所想的來執行The use of statistical techniques such as control chart

6、s to analyze a process,take appropriate actions to achieve&maintain a stable process,&improve process capability.4Materials QualityPCS Training-Rev 3 May 21 2001What is Stability?A process is said to be Stable if it has the following properties:下列特性稱為穩定下列特性稱為穩定:Pattern appears random 隨機出現隨機出現 Consta

7、nt process mean 平均值一定平均值一定 Uniform variability over time 變異程度不隨時間改變變異程度不隨時間改變 No trends,runs,shifts,erratic ups&downs 不會偏向一邊不會偏向一邊 Important for many reasons:穩定性為何重要穩定性為何重要?Increased productivity of engineering&manufacturing personnel 提高生產性提高生產性 Predictable,repeatable results within a specified rang

8、e 結果有重覆性結果有重覆性,可預測可預測5Materials QualityPCS Training-Rev 3 May 21 2001What is a Control Chart?A trend chart with control limits 有管制界限的趨勢圖有管制界限的趨勢圖 Graphical representation of process performance,where data is collected at regular time sequence of production 數據依生產順序定時間收集數據依生產順序定時間收集,以圖表表現制程性能以圖表表現制程性能

9、 Valuable tool for differentiating between common cause and special cause variation 將一般變異與特殊變異區分開的有用工具將一般變異與特殊變異區分開的有用工具 Evaluating whether a process is or is not in a state of statistical control 評估制程是否在統計管制中評估制程是否在統計管制中 It lets the data talk by itself&basis for data-driven decisions 讓數據說話並依數據導向作決定

10、讓數據說話並依數據導向作決定6Materials QualityPCS Training-Rev 3 May 21 2001Control LimitsA typical control chart consists of three lines:典型管制圖有三條線典型管制圖有三條線:Upper ControlLimit (UCL)Center Line(CL)Lower ControlLimit(LCL)CL:The average(measure of location)process performance when the process is in-controlCL:制程的平均性能

11、制程的平均性能UCL&LCL:The range of usual process performance when the process is stable.Lines drawn 3 standard deviations(3 sigma)on each side of the center line.UCL&LCL:制程穩定情況下制程穩定情況下,制程性能的範圍制程性能的範圍7Materials QualityPCS Training-Rev 3 May 21 2001Control Chart Assumptions Process Stability 制程穩定制程穩定 The pro

12、cess must be in statistical control Normality 常態分布常態分布 The underlying process distribution is normalNote:If the assumptions are not met,the control limits calculated are misleading&do not accurately indicate 3 sigma control limits.See your site statistician for advice on calculation methods when ass

13、umptions are violated.若假設不成立若假設不成立,則管制界限將沒有意義則管制界限將沒有意義8Materials QualityPCS Training-Rev 3 May 21 2001Test for Control Chart Assumptions 假設假設 Process Stability(no outliers)穩定性穩定性 Screen out outliers from the database before computing final control limits by using a control chart.Any point beyond ei

14、ther control limit is an outlier.Report number of outliers screened.-計算管制界限前計算管制界限前,將超出點排除將超出點排除.所有超出管制界限的點都是所有超出管制界限的點都是 outlier Normality 常態性常態性 Plot a normal probability plot of the data or overlay a normal curve over the histogram.Normally distributed data will roughly fall on a straight line.Te

15、st for normality by using Shapiro-Wilk W test in JMP 用用JMP W test 來計算常態性來計算常態性9Materials QualityPCS Training-Rev 3 May 21 2001 Select appropriate type of control chart to be used 選擇合適的管制圖型態選擇合適的管制圖型態 Gather data to establish the control chart.收集數據建立管制圖收集數據建立管制圖 A minimum of 30 subgroups is required

16、over a time frame as determined by the sampling plan.抽樣計劃至少收集抽樣計劃至少收集30組數據組數據 Plot the data in time order on a Trend Chart 依序在趨勢圖上描點依序在趨勢圖上描點How to Set-up a Control Chart?(I)10Materials QualityPCS Training-Rev 3 May 21 2001 Compute the control limits&plot them on the trend chart 計算管制界線並畫在圖上計算管制界線並畫在

17、圖上 Outliers identification&exclusion 超出點的確認與排除超出點的確認與排除 Exclude the Out-of Control(OOC)points or outliers for which there are verified/confirmed special causes from the chart 由於顯示是特殊原因造成故將排除超出點由於顯示是特殊原因造成故將排除超出點 Re-compute the control limits,excluding the OOC points 重新計算管制界限重新計算管制界限 If there are few

18、er than 30 points remaining at any time,collect more data.Its very important that the control limits are calculated using at least 30 subgroups.若資料點少於若資料點少於30再繼續收集再繼續收集.這是很重要的這是很重要的How to Set-up a Control Chart?(II)Note:Refer to Appendix A for Control Charts for Limited Production,i.e.=10 n=10 X -wh

19、en subgrouping is not applicable (Individual)due to single unit reading may take Chart a long time,unit reading is extremely expensive,etc.-when its common to have single measurement spaced time apart Control Charts For Variables 計量型計量型每次量測費時或昂貴每次量測費時或昂貴,使同一段時間內量使同一段時間內量測多次不適當測多次不適當每次量測值都非常相近每次量測值都非

20、常相近,同一段時間內量同一段時間內量測多次測多次14Materials QualityPCS Training-Rev 3 May 21 2001Why MR Method is used to determine Control Limits for Mean&Variability(Range&Standard Deviation)Chart?為什麼要使用移動全距方法為什麼要使用移動全距方法?Most batch production processes have a larger run-to-run variation than within-run variation 批量性生產時批

21、量性生產時,子群組間的變異大多會大於子群組內的子群組間的變異大多會大於子群組內的變異變異 Traditional control chart formulas developed in the 20s by Walter Shewhart considerably underestimate control limits,i.e.too narrow 傳統的方法將使管制界限太窄傳統的方法將使管制界限太窄15Materials QualityPCS Training-Rev 3 May 21 2001Traditional vs.MR Method859095100105110115OrderA

22、vg=99.1LCL=96.5UCL=101.8Mean of Meas.708090100110120130OrderAvg=99.1LCL=76.7UCL=121.5Mean(Meas.)Traditional control chart formulasare used.Moving Range(MR)Method is used.X-bar Control ChartX-bar Control Chart16Materials QualityPCS Training-Rev 3 May 21 2001X-S Chart ConceptConsists of Two Portions:X

23、 Chart Plots the mean of the X values in the sample 以抽樣的平均值描點以抽樣的平均值描點 Shows the changes of the mean of one sample to another 顯示抽樣平均值的改變顯示抽樣平均值的改變 S Chart Plots the standard deviation of a sample 以抽樣的標準差描點以抽樣的標準差描點 Shows the changes in dispersion or process variability of one sample to another 顯示抽樣標

24、準差的改變顯示抽樣標準差的改變17Materials QualityPCS Training-Rev 3 May 21 2001Computing Control Limits for X-S Chart Obtain at least k=30 subgroups 獲得至少獲得至少30組子群組組子群組 Compute the Mean for each subgroup of size n 計算每子群組計算每子群組(個數個數n)的平均值的平均值 Compute the Standard Deviation for each subgroup 計算每子群組計算每子群組(個數個數n)的標準差的標

25、準差 Compute the Moving Range for each subgroup mean,MRXi=|Xi-Xi-1|計算每子群組平均值的移動全距計算每子群組平均值的移動全距 Compute the Moving Range for each subgroup range,MRSi=|Si-Si-1|計算每子群組標準差的移動全距計算每子群組標準差的移動全距18Materials QualityPCS Training-Rev 3 May 21 2001Computing Control limits for X-S Chart Compute the Overall Mean,X=

26、(X1+X2+X3.+Xk)/k Compute the Average of Range,S=(S1+S2+S3.+Sk)/k Compute the Average of Moving Range for the mean,MRX=(MRX2+MRX3+MRX4.+MRXk)/(k-1)Compute the Average of Moving Range for the range,MRS=(MRS2+MRS3+MRS4.+MRSk)/(k-1)=19Materials QualityPCS Training-Rev 3 May 21 2001 Compute the Control L

27、imits:Draw the control limits on both the X-S chart respectively If LCL(S)0,put as 0 or N/AX ChartUCL(X)=X+2.66MRXCL(X)=XLCL(X)=X-2.66MRX=Computing Control limits for X-S ChartS ChartUCL(S)=S+2.66MRSCL(S)=SLCL(S)=S-2.66MRS20Materials QualityPCS Training-Rev 3 May 21 2001ObservationsMeanMoving RangeS

28、.D.Moving RangeSubgroup#12345(X-bar)(MRX)(S)(MR S)18.07.78.18.07.87.92-0.16-27.16.97.47.37.27.180.740.190.0338.07.57.67.87.97.760.580.210.02:307.57.87.97.87.67.720.700.160.04Average7.640.680.190.03 X ChartUCL(X)=X+2.66MRX=7.64+2.66(0.68)=9.45CL(X)=X=7.64LCL(X)=X-2.66MRX=7.64-2.66(0.68)=5.83Example o

29、f Computing Control Limits for X-S Chart S ChartUCL(S)=S+2.66MRS=0.19+2.66(0.03)=0.27CL(S)=S=0.55 LCL(S)=S-2.66MRS=0.19-2.66(0.03)=0.1121Materials QualityPCS Training-Rev 3 May 21 2001Open the dataset Thickness.jmp.1.Compute the mean for each lot.Select Summary from the Tables menu.Select Lot as the

30、 Group variable.Highlight Thickness&select Mean from the Statistics menu.Then,highlight Thickness&select Std Dev from the Statistics menu.Click OK.2.Create an individuals control chart using the table of lot means&ranges.Select Control Chart from the Graph menu.Select Mean(thickness)&StdDev(Thicknes

31、s)as the Process variable.Select Lot as the Sample Label variable.Verify option settings.Chart Type is “IR”.Individual Measurement box is selected.Moving Range box is not selected.K-sigma is selected,and K=3.Range Span=2.Click on OK.Example of Computing Control Limits for X-S Chart using JMP22Materi

32、als QualityPCS Training-Rev 3 May 21 2001WARNINGS:Group/Summary will sort the new table in alphabetical order of the grouping variable.Control charts must always be plotted in time order.Therefore,if the summary table is not in time order,you will have to sort the table in correct time order before

33、making the control chart.Example of Computing Control Limits for X-S Chart using JMPLCL(S)=023Materials QualityPCS Training-Rev 3 May 21 2001Exercise 1Open the dataset Exer1.jmp.Compute the X-S control limits using JMP for lead width.-What are the control limits?-Is the process stable?24Materials Qu

34、alityPCS Training-Rev 3 May 21 2001Interpretation of X-S ChartSome special causes of out-of-control for X Chart Changes in machine setting or adjustment 參數設定被調整參數設定被調整 MS-to-MS technique inconsistent Changes in material 材料變化材料變化 S Chart Machine in need of repair or adjustment 機器須維修機器須維修 New Mses Mat

35、erials are not uniform 材料一致性不夠材料一致性不夠25Materials QualityPCS Training-Rev 3 May 21 2001Attributes Control Charts Attribute control charts are useful when it is difficult or impractical to monitor a process numerically(on a continuous scale)若無法以量測數值來監控制程或有困難時若無法以量測數值來監控制程或有困難時,可使用計數型管制圖可使用計數型管制圖 A def

36、ect is an individual failure to meet a single requirement 不良是指無法滿足單一要求不良是指無法滿足單一要求 A defective unit is a unit that contains one or more defects 不良品不只包含一項缺點不良品不只包含一項缺點26Materials QualityPCS Training-Rev 3 May 21 2001Control Charts For AttributesControl Chart Symbol Descriptionp Chartp%Defectivenp cha

37、rtnp#defective27Materials QualityPCS Training-Rev 3 May 21 2001p Chart Concept It plots proportion of defective units in a sample 每一抽樣點是以不良率來描點每一抽樣點是以不良率來描點 The proportion of defective units in a sample can be in terms of fraction,percent or dpm 不良的比率可以是分數不良的比率可以是分數,%,dpm來表示來表示 It allows us to chart

38、 production processes where sample size cannot be equal 不同的抽樣數是允許的不同的抽樣數是允許的28Materials QualityPCS Training-Rev 3 May 21 2001Computing Control Limits for p Chart with MR-Method Obtain at least k=30 subgroups or lots.Data collected in#of units inspected&#of units rejected.至少至少30組子群組組子群組.以檢驗數與拒收數來收集數據

39、以檢驗數與拒收數來收集數據 Compute the defective rate from the ith lot(i=1,2,.,k),pi=#of units rejected/#of units inspected Compute the control limits using:UCL(p)=p+2.66MRp CL(p)=pLCL(p)=p-2.66MRp When LCL UCL or Point LCL 至少須使用第至少須使用第 1 條條 For an automated SPC system with automated application of SPC trend rul

40、es,its highly recommended to add 5th rule to detect large shifts in mean,(i.e.2 out of 3 rule)若若spc系統是自動的系統是自動的,非常建議增加第非常建議增加第 5 條條 Add other rules depending upon process knowledge ability to respond criticality of the monitor sensitivity requirements for the monitor Intel does recommend as a goal t

41、o use rules 1,2,5,&6 when appropriate Intel建議使用建議使用1,2,5,&6 條條48Materials QualityPCS Training-Rev 3 May 21 2001Trend Rule Recommendations Only use the trend rules that signal process instabilities for which you are capable of responding 在你有能力反應處理的不穩定制程在你有能力反應處理的不穩定制程,才使用趨勢規則才使用趨勢規則 Justification nee

42、ded for not using other SPC trend rules Std dev&range charts may choose not to react to Point LCL,however a LCL on these charts can be valuable for detecting metrology problems or unexpected process improvement 若點若點 1.0有潛在問題有潛在問題,1 Definitely a problem:|Change Ratio|1.5確定有問題確定有問題 1.554Materials Qual

43、ityPCS Training-Rev 3 May 21 2001Given Thickness.jmp example:UCLcurrent=130.0LCLcurrent=70.0Newly collected data resulted the following:UCLcalc=119.41LCLcalc=78.72 run-run(calc)=2.66 MR/3=20.35/3=6.78UCL Change Ratio=(UCLcalc-UCLcurrent)/run-run(calc)=-1.56LCL Change Ratio=(LCLcurrent-LCLcalc)/run-r

44、un(calc)=-1.28=Indicates a need to change the current control limits!Change Ratio ExampleMaterials QualityPCS Training-Rev 3 May 21 2001Process Capability20040060080010001300103050LSLUSL25507550150250350LSLUSL Process capability is the ability of a process to meet specifications.A process must be st

45、able before its capability can be computed.Not Capable Capable A capability index is a statistic that quantifies&describes the capability of a process56Materials QualityPCS Training-Rev 3 May 21 2001Specification Limits The region where product is known to function well in terms of performance,yield

46、,reliability,or other desired outcome Acceptable range of values for a product parameter Define what is acceptable/unacceptable product Determined by Design requirements&simulation models Engineering judgement(typically product eng.&integration)Customer agreement/requirements Data driven validation:

47、Process window characterization Historical data identifying in-line or EOL problems Used to determine process capability57Materials QualityPCS Training-Rev 3 May 21 2001Control Limits Calculated from data,based on actual process performance Describe the natural range of performance of a stable proce

48、ss Describe the amount of natural process variation Used to determine process stability58Materials QualityPCS Training-Rev 3 May 21 2001Spec Limits vs.Control LimitsSpec Limits Based on performance required of the product What the customer wants -“what we want”Tells us when to disposition the produc

49、t/material Apply only to individual(raw)data valuesControl Limits Based on actual historical process performance What the process delivers -“what we get”Tells us when to take action on the process/equipment Apply to summary statistics(e.g.:X-bar,std dev,range,etc.charts)Never use spec limits on a co

50、ntrol chart!59Materials QualityPCS Training-Rev 3 May 21 2001Stability vs.Capability A process is said to be in statistical control when the only source of variation is of natural causes,(i.e.no special causes variation present)A process is said to be capable when variation from natural causes is re

51、duced such that it can meet product specification tolerance when the control limits are well within the specification limits A process is said to be not capable if the control limits are outside the specification limits60Materials QualityPCS Training-Rev 3 May 21 2001Exercise 30204060801001201401601

52、8020002468specspeccontrolcontrol02468020406080100120140160180200specspeccontrolcontrolInterpretation:Y/N_Stable_CapableInterpretation:Y/N_Stable_Capable61Materials QualityPCS Training-Rev 3 May 21 200102468020406080100120140160180200specspeccontrolcontrolInterpretation:Y/N_Stable_CapableInterpretati

53、on:Y/N_Stable_CapableExercise 302468020406080100120140160180200specspeccontrolcontrol62Materials QualityPCS Training-Rev 3 May 21 2001Measuring Process Capability A minimum of 30 data points are needed before calculating process capability indices Always use a histogram or with specification limits

54、to visually represent the process distribution&capability63Materials QualityPCS Training-Rev 3 May 21 2001Measuring Process Capability:Cpk Cpk is a common measure of process capability:Cpk=minimum(Cpu,Cpl)USL-XX-LSLCpu=Cpl=3sindiv 3sindivwhere:USL,LSL-spec limits for individual data valuessindiv=std

55、 dev of individual(raw)measurements64Materials QualityPCS Training-Rev 3 May 21 2001LSLUSLABTail Closerto Spec LimitCpk =B/AA=3sB=-LSLx Cpk compares the upper half of the distribution to the upper spec&lower half of the distribution to the lower specMeasuring Process Capability:Cpk65Materials Qualit

56、yPCS Training-Rev 3 May 21 2001Cpk=0.7Cpk=0.7Cpk=1.0Cpk=1.0Cpk=1.3Cpk=1.3 The value of Cpk is affected by:where the process is centered process variation The higher the Cpk value,the better it is For one-sided specification,Cpk=Cpu if only USL exists Cpk=Cpl if only LSL existsMeasuring Process Capab

57、ility:Cpk66Materials QualityPCS Training-Rev 3 May 21 2001 A simple measure of process capability is CpUSL-LSLCp=-6sindiv Cp does not consider where the process is centered,therefore it assumes the process is centered on target.Therefore,Cp Cpk.Cp is often called process potential:How the process co

58、uld perform if it was on target Cp can only be computed for processes with two-sided spec limitsMeasuring Process Capability:Cp67Materials QualityPCS Training-Rev 3 May 21 2001Example1020306007509001050120013505101520600800100012001400Cpk=1.44,Cp=1.45Target&mean are close together:Cpk&Cp are similar

59、LSL=700,Target=1000,USL=1300Mean=1003.8,Std dev=68.6Cpk=0.52,Cp=0.87Target&mean are offset significantly:Cpk is much less than CpLSL=700,Target=1000,USL=1300Mean=1196,Std dev=115.068Materials QualityPCS Training-Rev 3 May 21 2001LSLUSLDCBADistribution capable?(Y/N)Cpk 1 Cpk=1 Cpk 1.3 A B C D Exercis

60、e 5For each of the 4 distributions below,check if you think Cpk 1.369Materials QualityPCS Training-Rev 3 May 21 2001Cp&Cpk Assumptions Process Stability The process must be in statistical control Representative Samples The obtained samples are representative of the population.Random sampling is impo

61、rtant in this regard.Normality The underlying process distribution is normalNote:If the assumptions are not met,the process capability indices calculated are misleading&do not accurately indicate the capability of the process.Seeyour site statistician for advice on calculation methods when assumptio

62、ns are violated.70Materials QualityPCS Training-Rev 3 May 21 2001Test for Cp&Cpk Assumptions Process Stability(no outliers)Screen out outliers from the database before computing Cpk by using control chart.Any point beyond either control limit is an outlier.Report number of outliers screened.Normalit

63、y Plot a normal probability plot of the data or overlay a normal curve over the histogram.Normally distributed data will roughly fall on a straight line.Test for normality by using Shapiro-Wilk W test in JMP 71Materials QualityPCS Training-Rev 3 May 21 2001No Large Outliers51525050100200300400510152

64、0050100150200250The example below illustrates the Cpk results with&without 2 large outliers.With outliers:Cpk=0.522 outliers points removed:Cpk=0.8872Materials QualityPCS Training-Rev 3 May 21 2001Are Data Normally Distributed?20406014001180012200126001300051525507090110140170200230Processes with la

65、rge systematic effects or other non-normal signature often result in an underestimated Cpk.73Materials QualityPCS Training-Rev 3 May 21 2001Cpk vs.DPM Out-of-SpecIf we assume that the process distribution is Normal,we can relate Cpk to the estimated dpm of product that is out-of-spec.Cpk,Cpu,Cpl0.00

66、0.010.020.030.040.050.060.070.080.090.13820893707003594243482683372433263553156143050262945982843390.22742532643472546272450972357632266272176952069702004541921500.31840601761861685281610871538641468591400711335001271431210010.4115070109349103835985269341888508837937927074933707810.5668076300959380559185261649472464794363240929383640.6359303362531443293792742925588238522221620675192260.71786516586153861426213209122251130410444964288940.881987549694763875868538649394527414537930.93466316728902635