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1、Module 3:Statistical Process Control(SPC)Methodology,2,PCS Elements,Create Measurement Plan,Establish Monitor(SPC),Implement Response Flow Checklist(RFC),Element 1,Element 2,Element 3,3,Contents,Introduction 簡介What is SPC 什麼是SPC?What is Stability 什麼是穩定性?What is a Control Chart 什麼是管制圖How to Set-up a
2、Control Chart 如何建立管制圖Type of Control Charts Available 管制圖的種類How to Calculate the Control Limits 如何計算管制界限SPC Trend Rules SPC法則When to Revise Control Limits 何時重新計算管制界限Process Capability Study 制程能力研討Spec limits VS Control Limits 規格界限 vs.管制界限Stability VS Capability 穩定性 vs.能力Control Chart Reduction/Elimi
3、nation 減少管制圖SPC Expectations,4,What is SPC?,Statistical 統計Anything that deals with the collection,analysis,interpretation&presentation of numerical data 關於數據資料的收集,分析,解釋與表現Gaining information for making informed decisions取得資訊來作有效的決定Process 制程Combination of machines,tools,methods,materials&people empl
4、oyed to attain process specification結合機器,治工具,方法,材料與人員來達到制程規格A similar procedure/event that is happening repetitively重覆發生的事件/類似程序Control 管制To keep something within a desired condition使某事/物保持在想要的情況Make something behave the way we want it to behave使某事/物依我們所想的來執行,The use of statistical techniques such a
5、s control charts to analyze a process,take appropriate actions to achieve&maintain a stable process,&improve process capability.,5,What is Stability?,A process is said to be Stable if it has the following properties:下列特性稱為穩定:Pattern appears random 隨機出現Constant process mean 平均值一定Uniform variability o
6、ver time 變異程度不隨時間改變No trends,runs,shifts,erratic ups&downs 不會偏向一邊Important for many reasons:穩定性為何重要?Increased productivity of engineering&manufacturing personnel提高生產性Predictable,repeatable results within a specified range結果有重覆性,可預測,6,What is a Control Chart?,A trend chart with control limits有管制界限的趨勢
7、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,以圖表表現制程性能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Evaluating whether a process is or is not in a state of statistical
8、 control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,7,Control Limits,A typical control chart consists of three lines:典型管制圖有三條線:,CL:The average(measure of location)process performance when the process is in-controlCL:制程的平均性能UCL&LCL:The range of usual proc
9、ess 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,制程性能的範圍,8,Control Chart Assumptions,Process Stability制程穩定The process must be in statistical controlNormality常態分布The underlying process distribution is normalNote:If th
10、e 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 assumptions are violated.若假設不成立,則管制界限將沒有意義,9,Test for Control Chart Assumptions 假設,Process Stability(no outliers)
11、穩定性Screen out outliers from the database before computing final control limits by using a control chart.Any point beyond either control limit is an outlier.Report number of outliers screened.-計算管制界限前,將超出點排除.所有超出管制界限的點都是 outlierNormality 常態性Plot a normal probability plot of the data or overlay a norm
12、al 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 用JMP W test 來計算常態性,10,Select appropriate type of control chart to be used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A minimum of 30 sub
13、groups is required over a time frame as determined by the sampling plan.抽樣計劃至少收集30組數據Plot the data in time order on a Trend Chart依序在趨勢圖上描點,How to Set-up a Control Chart?(I),11,Compute the control limits&plot them on the trend chart計算管制界線並畫在圖上Outliers identification&exclusion超出點的確認與排除Exclude the Out-
14、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Re-compute the control limits,excluding the OOC points重新計算管制界限If there are fewer than 30 points remaining at any time,collect more data.Its very important that the control limits a
15、re calculated using at least 30 subgroups.若資料點少於30再繼續收集.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.30 subgroups.,12,Validate the computed control limits against data collected by re-plotting the control chart with data&new control
16、 limitsDo the limits detect known problems?界限可以查覺已知的問題嗎?Are the limits too sensitive?Would they flag problems you do not know how to react to?界限是否太敏感?是否有問題你不曉得如何處理?Use the control limits established to monitor the critical parameter identified使用建立的管制圖來追蹤確認重要參數For each parameter,every machine should
17、have a separate control chart with separately computed control limits對每一參數,每台機器應有一獨立的管制圖與管制界限,How to Set-up a Control Chart?(III),13,Control Chart Classifications 類型,Classifications of control charts are depending onthe type of data 依數據型態可分類為:Variables data 計量型數據A characteristic measured on a contin
18、uous scale resulting in a numerical value 特性:連續性,可量測,有小數點Examples:Void Size,Bond Pull Strength,Coplanarity,Ball Height,etc.如尺寸,推拉力,平面度,高度Attributes data 計數型數據A characteristic measured by#of conforming&non-conforming to a specification.Output is classified as pass/fail or accept/reject.特性:計數的,合格/不合格,
19、E.g.Broken Wire,Lifted Bond,FM,Chipping,Bent Lead,etc.如:故障數,Can be expressed in terms of fraction,percentage,count or DPM 以分數,百分比,DPM單位表示,14,Control Chart,When to Use(Guidelines only)?,X-S,-when subgrouping of samples or,(Mean-Standard Deviation)Chart,measurements is applicable,-n=10 n=10,X,-when su
20、bgrouping 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,每次量測費時或昂貴,使同一段時間內量測多次不適當,每次量測值都非常相近,同一段時間內量測多次,15,Why MR Method is us
21、ed to determine Control Limits for Mean&Variability(Range&Standard Deviation)Chart?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,子群組間的變異大多會大於子群組內的變異Traditional control chart formulas developed in the 20s by Walter Shewhart considera
22、bly underestimate control limits,i.e.too narrow 傳統的方法將使管制界限太窄,16,Traditional vs.MR Method,Traditional control chart formulasare used.,Moving Range(MR)Method is used.,X-bar Control Chart,X-bar Control Chart,17,X-S Chart Concept,Consists of Two Portions:X ChartPlots the mean of the X values in the sam
23、ple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S ChartPlots the standard deviation of a sample以抽樣的標準差描點Shows the changes in dispersion or process variability of one sample to another顯示抽樣標準差的改變,18,Computing Control Limits for X-S Chart,Obtain at least k=30 subgroups獲得至少30
24、組子群組Compute the Mean for each subgroup of size n計算每子群組(個數n)的平均值Compute the Standard Deviation for each subgroup 計算每子群組(個數n)的標準差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,19,Computing Contro
25、l limits for X-S Chart,Compute the Overall Mean,X=(X1+X2+X3.+Xk)/kCompute the Average of Range,S=(S1+S2+S3.+Sk)/kCompute 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),=,20,Compute the Contro
26、l Limits:Draw the control limits on both the X-S chart respectively If LCL(S)0,put as 0 or N/A,X ChartUCL(X)=X+2.66MRXCL(X)=XLCL(X)=X-2.66MRX,=,=,=,Computing Control limits for X-S Chart,S ChartUCL(S)=S+2.66MRSCL(S)=SLCL(S)=S-2.66MRS,21,Observations,Mean,Moving Range,S.D.,Moving Range,Subgroup#,1,2,
27、3,4,5,(X-bar),(MRX,),(S),(MR,S,),1,8.0,7.7,8.1,8.0,7.8,7.92,-,0.16,-,2,7.1,6.9,7.4,7.3,7.2,7.18,0.74,0.19,0.03,3,8.0,7.5,7.6,7.8,7.9,7.76,0.58,0.21,0.02,:,:,30,7.5,7.8,7.9,7.8,7.6,7.72,0.70,0.16,0.04,Average,7.64,0.68,0.19,0.03,X ChartUCL(X)=X+2.66MRX=7.64+2.66(0.68)=9.45CL(X)=X=7.64LCL(X)=X-2.66MRX
28、=7.64-2.66(0.68)=5.83,Example of 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)=0.11,22,Open the dataset Thickness.jmp.1.Compute the mean for each lot.Select Summary from the Tables menu.Select Lot as the Group variabl
29、e.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(Thickness)as the Proce
30、ss 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 JMP,23,WARNINGS:Group/Sum
31、mary 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 making the control chart.,Example of Computing Control Limi
32、ts for X-S Chart using JMP,LCL(S)=0,24,Exercise 1,Open the dataset Exer1.jmp.Compute the X-S control limits using JMP for lead width.-What are the control limits?-Is the process stable?,25,Interpretation of X-S Chart,Some special causes of out-of-control forX ChartChanges in machine setting or adjus
33、tment參數設定被調整MS-to-MS technique inconsistentChanges in material材料變化S ChartMachine in need of repair or adjustment機器須維修New MsesMaterials are not uniform材料一致性不夠,26,Attributes Control Charts,Attribute control charts are useful when it is difficult or impractical to monitor a process numerically(on a con
34、tinuous scale)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A defect is an individual failure to meet a single requirement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,27,Control Charts For Attributes,28,p Chart Concept,It plots proportion of defective units in a sample每一抽樣點是以不良率
35、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,%,dpm來表示It allows us to chart production processes where sample size cannot be equal不同的抽樣數是允許的,29,Computing Control Limits for p Chart with MR-Method,Obtain at least k=30 subgroups or lots.Data coll
36、ected in#of units inspected&#of units rejected.至少30組子群組.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 inspectedCompute the control limits using:UCL(p)=p+2.66MRp CL(p)=pLCL(p)=p-2.66MRp,When LCL 0,put LCL=0 or N/A Draw the control limits on p char
37、t,30,Notes:The MR-Method describes how the control limits are calculated assuming equal(or near-equal)sample sizes.If the sample sizes vary by more than 50%of each other,you should consult a statistician.MR-Method的管制線是假設抽樣數相同的情況下得出的.若抽樣數差異超過50%時,則須請較統計學家.np Chart is applicable when all subgroups hav
38、e constant sample sizes.In terms of practicality,p Chart can/should be used when sample sizes are equal as p carry more meaning than#of rejected units(np)P Chart也可以是相同抽樣數,Computing Control Limits for p Chart,31,Open the dataset pchart.jmp.Select Control Chart from the Graph menu.Select%Defectives as
39、 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 p Chart,32,Exercise 2,The datas
40、et Exer2.jmp contains defect levels for undissolved flux.The number of units inspected&the number of units containing undissolved flux were recorded over several lots.-Make a p Chart for Undissolved Flux-Interpret the control chart,33,Interpretation of p Chart,Some special causes affecting the p Cha
41、rt:超出管制界限的原因:Changes in variable data specifications規格變更Changes in inspection procedures檢驗方法變更Changes in technician skills,e.g.new technicians測試員變更Changes in pieceparts quality零件品質變更,34,Time-related condition where consecutive data values are correlated(i.e.dependent)連貫的數據有關連性Data values collected n
42、earby in time are very similar 鄰近時間的數據非常相似Data values collected far apart in time may be very different 較久時間的數據差異大Tend to drift over time;some drift gradually,others may have occasional sudden changes in direction between periods of relative stability 傾向隨時間漂移,一般逐漸改變,有的會突然改變方向,Autocorrelation關連性,35,C
43、aution When Using MR Method,If there is autocorrelation,MR(Summary Stat)will underestimate the true process variation&the control limits will be too narrow 如果數據有關連性,MR方法會低估制程變異,界限會太窄.If autocorrelation is evident,use Sigma(Std Dev)Method for control limits computation(Refer to Appendix B)如果確定數據有關連性,
44、使用sigma方法計算管制界限.,36,sigma方法計算管制界限,N=the number of lots,=the mean from the ith lot(i=1,2,.,N),=the mean of the lot means,=the standard deviation of the lot means,where,Compute the control limits using:,37,Control Chart Trend Rules 趨勢規則,Purpose:Improve the responsiveness of the control chart增進管制圖的反應De
45、tect more subtle shifts in the process more quickly更快地察覺制程中細微的變化Detect irregularities beyond normal 3 that indicate non-randomness in process察覺在正常3 界限內的非隨機性變化,38,How to Interpret a Control Chart?,It is based on the Normal Distribution.,39,SPC Trend Rules,Rule#1:A single point beyond either control l
46、imit規則1:單獨點超出管制界限Uses:Detects very large/sudden shifts用途:察覺重大/突然的偏差False alarm rate:0.27%機率:0.27%Example:,40,SPC Trend Rules,Rule#2:9 consecutive points on the same side of the centerline規則2:連續9點在中心線同側Uses:Detects small shifts or trends用途:察覺微小/趨勢性的偏差False alarm rate:0.39%機率:0.39%Example:,41,SPC Tren
47、d Rules,Rule#3:6 consecutive points steadily increasing orDecreasing規則3:連續6點持續上升或下降Uses:Detects strong trends用途:察覺強烈趨勢Example:,42,SPC Trend Rules,Rule#4:14(or more)consecutive points are alternating up and down.規則4:相鄰14點規則性上下變動Uses:Detects systematic effects,such as alternating machines,operators,su
48、ppliers,etc.用途:察覺系統性的效性.如交替機台,人員,供應商等.Example:,43,SPC Trend Rules,Rule#5:2 out of 3 consecutive points at least 2 stddev beyond the centerline,on the same side規則5:連續同側3點中,2點落在同側2標準差之外Uses:Detects large changes用途:察覺大改變False alarm rate:0.30%機率:0.30%Example:,44,SPC Trend Rules,Rule#6:4 out of 5 consecu
49、tive points on the chart are more than 1 std dev away from the CL 規則6:連續同側5點中,4點超出1標準差Uses:Detects moderate-sized changes 用途:察覺中度改變False alarm rate:0.53%機率:0.53%Example:,45,SPC Trend Rules,Rule#7:15(or more)consecutive points are within 1 std dev of the CL 規則7:連續15點在1標準差內Uses:Detects a decrease in p
50、rocess variation 用途:察覺制程變異的降低Example:,46,SPC Trend Rules,Rule#8:8(or more)consecutive points are on both sides of the CL,but none are within 1 std dev of it.規則8:連續不同側8點,沒有一點在1標準差內.Uses:Detects an increase in process variation 用途:察覺制程變異的增加Example:,47,Selection of Trend Rules,Using a large#of trend ru
