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1、Dec 18,2001,BPTL Confidential,1,Six-Sigma Training Book,Six-Sigma,BPTL Confidential,2,數据分布,BPTL Confidential,3,NormalExponentialWeibullLognormaltc2f,Continuous Distributions,Sampling Distributions,數据分布,BPTL Confidential,4,The most widely used model for the distribution of continuous random variable.
2、Arises in the study of numerous physical phenomena,such as the velocity of molecules.,正態分布,Plot is known as Probability Density Functionof X,BPTL Confidential,5,Many natural phenomena and man-made processes are observed to have normal distributions,or can be closely represented as normally distribut
3、ed.For example,the length of a machined part is observed to vary about its mean due to:temperature drift,humidity change,vibrations,cutting angle variations,cutting tool wear,bearing wear,rotational speed variations,fixturing variations,raw material changes and contamination level changesIf these so
4、urces of variation are small,independent and equally likely to be positive or negative,the length will closely approximate a normal distribution.,正態分布,BPTL Confidential,6,First introduced by French mathematician Abraham DeMoivre in 1733.Made famous in 1809 by German mathematician K.F.Gauss when he a
5、lso developed a normal distribution independently and used it in his study of astronomy.As a result,it is also known as the Gaussian distribution.During mid to late nineteenth century,many statisticians believed that it was“normal”for most well-behaved data to follow this curve.,正態分布-歷程表,Karl Friedr
6、ich Gauss,BPTL Confidential,7,正態分布易于理解,具有特性,統計學提供了許多基于正態分布的強有力的分析方法來幫助人們做決定.因此,我們通常會試圖用正態分布去近似模擬其它分布(如可能)或轉化數据以“使”它遵從正態分布.它是分析過程能力的首選分布形式.,正態分布,BPTL Confidential,8,A normal distribution can be completely described by knowing only the:Mean(m)Variance(s2),正態分布的一些特性,What is the difference between the 3
7、 normal distributions?,X N(m,s2),1,BPTL Confidential,9,What is the difference between process A&B for each case?,正態分布的一些特性,BPTL Confidential,10,The mean,median and mode all coincide at the same value-m.There is perfect symmetry.,MeanMedianMode,2,The mean represents the arithmetic average of all obse
8、rvations in a data set.,If a set of observations is arranged in an increasing order of magnitude(ranked data),the middle value is called the median.If the number of observations is odd,the median is the value of the middle number.If the number of observations is even,there are 2 middle numbers,and t
9、he median is the average of the 2 values.,The mode is the observation that occurs most frequently in the sample.,正態分布的一些特性,BPTL Confidential,11,The area under sections of the curve can be used to estimate the cumulative probability of a certain“event”occurring:,Point of Inflection,1s,+,-,68.27%,95.4
10、5%,99.73%,m+/-3s is often referred to as the width of a normal distribution,3,正態分布的一些特性,BPTL Confidential,12,Lets compute the cumulative probabilities of the following distributions:,m=3.5s=0.6,1.8,20.0,m=16.6s=2.8,m=-1.5s=0.9,-2.8,0.5,正態分布的一些特性,BPTL Confidential,13,MiniTab:Calc Probability Distribu
11、tions Normal.,Enter m value,Enter s value,Enter x value,正態分布的一些特性,BPTL Confidential,14,什么是 6,?,?,?,BPTL Confidential,15,6 簡介,BPTL Confidential,16,The Focus of Six Sigma,Identifying critical aspects of the business with problems or opportunities for improvement.Targeting those critical areas and desi
12、gnating improvement efforts as Six Sigma Black Belt projects.Selecting top people to work on the projects-full time.Ensuring these people have the time,tools,and resources they need to succeed.,BPTL Confidential,17,Customer Focus:A Model For Success,Technology,Technology,Capability,Capability,Organi
13、zation,Organization,People,People,Processes,Processes,商務上的生存競爭有賴于我們多大程度上讓我們的客戶滿意.客戶滿意才能体現品質,价格,和貨期的意義.品質,成本,准時走貨無不依耐于工序能力.,What purpose is Six-sigma?,BPTL Confidential,18,Six Sigma Vision,The Vision of Six Sigma is to delight customers by delivering world-class quality products through the achieveme
14、nt of Six Sigma levels of performance in everything we do.,What purpose is Six-sigma?,Six Sigma Philosophy,The philosophy of Six Sigma is to apply a structured,systematic approach to achieve breakthrough improvement across all areas of our business.,BPTL Confidential,19,PPM,ProcessCapability,Defects
15、 per Million Opp.,Six Sigma-Aggressive Goal,What purpose is Six-sigma?,BPTL Confidential,20,Statistical Definition of n-Sigma,LSL,LSL,USL,USL,Process Width,m,o,Design Width,T,T,scale,LSL,LSL,USL,USL,scale,T,T,+n,s,scale,-n,s,This is the so-called n-sigma,Sigma is a statistical unit of measure that r
16、eflects process capability.The sigma scale of measure is perfectly correlated to such characteristics as defects-per-unit,parts-per million defective,and the probability of a failure/error.,BPTL Confidential,21,Statistical Definition of 6,This is the six-sigma we said,LSL,LSL,USL,USL,Process Width,m
17、,o,Design Width,+3,s,st,T,T,.001,ppm,USL,.001,ppm,LSL,scale,LSL,LSL,USL,USL,scale,T,T,+6,s,st,scale,BPTL Confidential,22,3 Sigma,6 Sigma,5 Sigma,4 Sigma,93.32%,99.379%,99.9767%,99.99966%,Historical,Current,Intermediate,Long-Run,Sigma,Long-Term Yield,Standard,6-Performance Target,BPTL Confidential,23
18、,CharacterizeOptimizeBreakthrough,USL,T,LSL,USL,T,LSL,T,USL,LSL,USL,LSL,The Strategy,BPTL Confidential,24,Characterization,Phase 1:,Measurement,Phase 2:,Analysis,Optimization,Phase 3:,Improvement,The Breakthrough Phases,BPTL Confidential,25,Phase 2:,Analysis,Capability study(Cpk),GR&R study,Cause&ef
19、fect analysisFishbone and C&E matrix,Dot plot,Box plot,Histogram chart,Pareto chart,The Breakthrough Phases Analysis tool and method,BPTL Confidential,26,Improvement,Analysis rolled throughput yield,Set up process Map,Set up FMEA,and control,.,The Breakthrough Phases Improvement tool and method,Dec
20、18,2001,BPTL Confidential,27,工 序 能 力 分 析,BPTL Confidential,28,學 習 目 標,工序控制与工序能力工序能力:規格,工藝和控制的界限工序潛力与工序表現短期与長期工序能力“6”品質,BPTL Confidential,29,工序控制与工序能力,1.工序控制意即工序運作處于統計控制狀態,換言之,普遍的原因是變化的僅有來源.鑒于“用事實說話”,即一個人僅需要用源于工序的數据 來判定工序是處于受控狀態.過程的跟蹤表現來証實它是否建立了長時間穩定的數据分布表現,典型地,用帶有“僅從工序中的數据計算出的”控制圖表.“而且一個工序在受控”并不一定意味
21、著它是一個好工序.,BPTL Confidential,30,工序控制与工序能力,2.工序能力“好處”是工序能力可被度量比較“工序的現狀”与“客戶的要求”,均須以規格為依据度量一個穩定的工序狀態(受控制)在多大程度上能滿足客戶的規格.,BPTL Confidential,31,變化的類型,固有的或定值的變化許多微小又不可避免的原因導致的累積效果只有微小的机會導致變化的運作工序稱為“統計控制”,BPTL Confidential,32,變化的類型,特定或確定的變化可能由于 a)不正確的調机 b)操作者錯誤 c)有缺陷的原材料一個工序如果出現上面的變化則稱為“失控”.,BPTL Confident
22、ial,33,工序能力,工序能力 研究能:顯示工序輸出的恒定性顯示輸出符合規格的程度用于和另一工序或競爭對手比較,BPTL Confidential,34,工序能力與規格极限,a),b),c),a)工序能力高b)工序能力能夠滿足c)工序能力不足夠,BPTL Confidential,35,三種极限類型,規格极限(LSL and USL)created by design engineering in response to customer requirements to specify the tolerance for a products characteristic 工序极限(LPL
23、and UPL)measures the variation of a processthe natural 6 limits of the measured characteristic 控制极限(LCL and UCL)measures the variation of a sample statistic(mean,variance,proportion,etc),BPTL Confidential,36,工序能力指數,工序能力的兩种度量:工序潛力Cp工序表現CpuCplCpk,BPTL Confidential,37,工序潛力,Cp 指標顯示實際工差(6)是否超出規格.,公式,BPTL
24、 Confidential,38,工序潛力,傳統上,Cp 有 1.0 時顯示工序能力被判為“有能力考核成績”.若數据集中于工程工差內,將僅有0.27%的工件會超差.Cp 拒貨率1.000.270%1.330.007%1.506.8 ppm2.002.0 ppb,BPTL Confidential,39,工序潛力,a),b),c),a)工序能力高(Cp2)b)工序能力可(Cp=1 to 2)c)工序能力差(Cp1),BPTL Confidential,40,工序潛力,The Cp index compares the allowable spread(USL-LSL)against the pr
25、ocess spread(6).It fails to take into account if the process is centered between the specification limits.,Process is centered,Process is not centered,BPTL Confidential,41,工序表現,The Cpk index relates the scaled distance between the process mean and the nearest specification limit.,BPTL Confidential,4
26、2,工序表現,Cpk 不良率1.00.13 0.27%1.10.05 0.10%1.20.02 0.03%1.348.1 96.2 ppm1.413.4 26.7 ppm1.5 3.4 6.8 ppm1.6 794 1589 ppb1.7 170 340 ppb1.8 33 67 ppb1.9 6 12 ppb2.0 1 2 ppb,BPTL Confidential,43,工序表現,a)工序能力高(Cpk1.5)b)工序能力可(Cpk=1 to 1.5)c)工序能力差(Cpk1),BPTL Confidential,44,工序潛力与工序表現,(a)Poor Process Potential
27、(b)Poor Process Performance,Experimental Design to reduce variation,Experimental Design to center mean to reduce variation,BPTL Confidential,45,工序潛力与工序表現,BPTL Confidential,46,工序穩定性,A process is stable if the distribution of measurements made on the given feature is consistent over time.,Time,Stable
28、Process,Time,Unstable Process,BPTL Confidential,47,短期工序能力与長期工序能力,短期工序能力(previously called short-term capability)shows the inherent variability of a machine/process operating within a brief period of time.長期工序能力(previously called long-term capability)shows the variability of a machine/process operati
29、ng over a period of time.It includes sources of variation in addition to the short-term variability.,BPTL Confidential,48,WithinOverallSample Size30 50 units 100 unitsNumber of Lotssingle lotseveral lotsPeriod of Timehours or daysweeks or monthsNumber of Operatorssingle operatordifferent operatorsPr
30、ocess Potential Cp PpProcess Performance Cpk Ppk,短期工序能力与長期工序能力,BPTL Confidential,49,實戰演練,The length of a camshaft for an automobile engine is specified at 600 2 mm.Control of the length of the camshaft is critical to avoid scrap/rework.The camshaft is provided by external suppliers.Assess the proces
31、s capability for this supplier.The data is available in Camshaft.MTW.Data are collected in subgroups of 5 each.,BPTL Confidential,50,Example 4,Minitab:Stat Quality Tools Capability Analysis(Normal),BPTL Confidential,51,Example 4,BPTL Confidential,52,Example 5,Histogram of the camshaft length suggest
32、s mixed populations.Further investigation revealed that there are two suppliers for the camshaft.Data were now collected on camshafts from each source without combining both.Subgroup size is 5 for each supplier.Are the two suppliers similar in performance?If not,what are your recommendations?,BPTL C
33、onfidential,53,Example 5,MiniTab:Stat Quality Tools Capability Sixpack(Normal),BPTL Confidential,54,Example 5,BPTL Confidential,55,Example 5,BPTL Confidential,56,用Box-Cox 轉化后的工序能力分析,When the process data are not normal,the Cpk or Ppk indices are not accurate or reliable,because these indices are com
34、puted on the basis that the data are normally distributed.Dppm values associated with the indices will not be near to the actual performance when the normal curve does not model the actual data well.,BPTL Confidential,57,If the process data are somewhat bell-shaped but skewed,Box-Cox transformation
35、can be used to make the data normal before we assess the process capability.Remember to transform the specification limits too before we compute Cpk or Ppk!,用Box-Cox 轉化后的工序能力分析,BPTL Confidential,58,Minitab:Stat Quality Tools Capability Analysis(Normal),用Box-Cox 轉化后的工序能力分析,BPTL Confidential,59,Exampl
36、e 6,Open the file named Dimension.MTW in the Day-2 folder again.Compute the process capability with the specification limits:LSL:0.1USL:10Are the data normally distributed?Compute the process capability again with Box-Cox transformation.,用Box-Cox 轉化后的工序能力分析,BPTL Confidential,60,Cpk of 0.41 is report
37、ed in the SSAT package.This value is not reliable or accurate if the data are not normal.,Data is not normal,Example 6,用Box-Cox 轉化后的工序能力分析,BPTL Confidential,61,Whats Six Sigma Quality Now,Mikel J Harry claims that the process mean between lots will vary,with an average process shift of 1.5.,Shift1.5
38、,Note:Sigma Capability=(dpmo)(dppm),“Sigma Level”Capability,BPTL Confidential,62,Types of Variation,1.Positional VariationSame process,variation at differing locations simultaneously:Temperature variations inside a thermal chamberCavity-to-cavity variations in an injection mold2.Cyclical VariationSe
39、quential repetitions of a process over fairly short time,say,less than 15 mins:Variations between consecutive batches of a processDifferences from lot to lot of raw materials,BPTL Confidential,63,Types of Variation,3.Temporal VariationVariations over longer periods of time,such a several hours,days or weeks.,
