1、Dec 18 ,2001,BPTL Confidential,1,Six-Sigma Training Book,Six-Sigma,天馬行空官方博客： ；QQ:1318241189；QQ群：175569632,BPTL Confidential,2,數(shù)據(jù)分布,天馬行空官方博客： ；QQ:1318241189；QQ群：175569632,BPTL Confidential,3,Normal Exponential Weibull Lognormal t c2 f,Continuous Distributions,Sampling Distributions,數(shù)據(jù)分布,BPTL Confiden

2、tial,4,The most widely used model for the distribution of continuous random variable. Arises in the study of numerous physical phenomena, such as the velocity of molecules.,正態(tài)分布,Plot is known as Probability Density Function of X,BPTL Confidential,5,Many natural phenomena and man-made processes are o

3、bserved to have normal distributions, or can be closely represented as normally distributed. 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 spe

4、ed variations, fixturing variations, raw material changes and contamination level changes If these sources of variation are small, independent and equally likely to be positive or negative, the length will closely approximate a normal distribution.,正態(tài)分布,BPTL Confidential,6,First introduced by French

5、 mathematician Abraham DeMoivre in 1733. Made famous in 1809 by German mathematician K.F. Gauss when he also 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 st

6、atisticians believed that it was “normal” for most well-behaved data to follow this curve.,正態(tài)分布 - 歷程表,Karl Friedrich Gauss,BPTL Confidential,7,正態(tài)分布易于理解, 具有特性, 統(tǒng)計(jì)學(xué)提供了許多基于正態(tài)分布的強(qiáng)有力的分析方法來(lái)幫助人們做決定. 因此, 我們通常會(huì)試圖用正態(tài)分布去近似模擬其它分布 (如可能) 或轉(zhuǎn)化數(shù)據(jù)以“使”它遵從正態(tài)分布. 它是分析過(guò)程能力的首選分布形式.,正態(tài)分布,BPTL Confidential,8,A normal distrib

7、ution can be completely described by knowing only the: Mean (m) Variance (s2),正態(tài)分布的一些特性,What is the difference between the 3 normal distributions?,X N(m, s2),1,BPTL Confidential,9,What is the difference between process A & B for each case?,正態(tài)分布的一些特性,BPTL Confidential,10,The mean, median and mode all

8、 coincide at the same value - m. There is perfect symmetry.,Mean Median Mode,2,The mean represents the arithmetic average of all observations 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

9、 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 the median is the average of the 2 values.,The mode is the observation that occurs most frequently in the sample.,正態(tài)分布的一些特性,BPTL Confidential,11,The area under s

10、ections of the curve can be used to estimate the cumulative probability of a certain “event” occurring:,Point of Inflection,1s,+ ,- ,68.27%,95.45%,99.73%,m +/- 3s is often referred to as the width of a normal distribution,3,正態(tài)分布的一些特性,BPTL Confidential,12,Lets compute the cumulative probabilities of

11、the following distributions:,m = 3.5 s = 0.6,1.8,20.0,m = 16.6 s = 2.8,m = -1.5 s = 0.9,-2.8,0.5,正態(tài)分布的一些特性,BPTL Confidential,13,MiniTab: Calc Probability Distributions Normal.,Enter m value,Enter s value,Enter x value,正態(tài)分布的一些特性,BPTL Confidential,14,什么是 6,?,?,?,BPTL Confidential,15,6 簡(jiǎn)介,BPTL Confiden

12、tial,16,The Focus of Six Sigma,Identifying critical aspects of the business with problems or opportunities for improvement. Targeting those critical areas and designating improvement efforts as Six Sigma Black Belt projects. Selecting top people to work on the projects-full time. Ensuring these peop

13、le have the time, tools, and resources they need to succeed.,BPTL Confidential,17,Customer Focus: A Model For Success,Technology,Technology,Capability,Capability,Organization,Organization,People,People,Processes,Processes,商務(wù)上的生存競(jìng)爭(zhēng)有賴于我們多大程度上讓我們的客戶滿意. 客戶滿意才能體現(xiàn)品質(zhì), 價(jià)格, 和貨期的意義. 品質(zhì),成本, 準(zhǔn)時(shí)走貨無(wú)不依耐于工序能力.,What

14、 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 achievement of Six Sigma levels of performance in everything we do.,What purpose is Six-sigma ?,Six Sigma Philosophy,The philosophy of

15、Six Sigma is to apply a structured, systematic approach to achieve breakthrough improvement across all areas of our business.,BPTL Confidential,19,PPM,Process Capability,Defects per Million Opp.,Six Sigma - Aggressive Goal,What purpose is Six-sigma ?,BPTL Confidential,20,Statistical Definition of n-

16、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 reflects process capability. The sigma scale of measure is perfectly correlated to such characteristics as defects-per-u

17、nit, 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,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 Confid

18、ential,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,Characterize Optimize Breakthrough,USL,T,LSL,USL,T,LSL,T,USL,LSL,USL,LSL,The Strategy,BPTL Confidential,

19、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&effect analysis Fishbone and C&E matrix,Dot plot , Box plot,Histogram chart, Pareto chart,The Breakthr

20、ough 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 18 ,2001,BPTL Confidential,27,工 序 能 力 分 析,BPTL Confidential,28,學(xué) 習(xí) 目 標(biāo),工序控制與工序能力 工序能力: 規(guī)格, 工藝和控制

21、的界限 工序潛力與工序表現(xiàn) 短期與長(zhǎng)期工序能力 “6” 品質(zhì),BPTL Confidential,29,工序控制與工序能力,1. 工序控制 意即工序運(yùn)作處于統(tǒng)計(jì)控制狀態(tài) , 換言之,普遍的原因是變化的僅有來(lái)源. 鑒于 “用事實(shí)說(shuō)話”,即一個(gè)人僅需要用源于工序的數(shù)據(jù) 來(lái)判定工序是處于受控狀態(tài). 過(guò)程的跟蹤表現(xiàn)來(lái)証實(shí)它是否建立了長(zhǎng)時(shí)間穩(wěn)定的數(shù)據(jù)分布表現(xiàn),典型地, 用帶有“僅從工序中的數(shù)據(jù)計(jì)算出的”控制圖表 . “而且一個(gè)工序在受控” 并不一定意味著它是一個(gè)好工序 .,BPTL Confidential,30,工序控制與工序能力,2. 工序能力 “好處” 是工序能力可被度量 比較 “工序的現(xiàn)狀” 與

22、 “客戶的要求 ”, 均須以規(guī)格為依據(jù) 度量一個(gè)穩(wěn)定的工序狀態(tài)(受控制)在多大程度上能滿足客戶的規(guī)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?qū)е碌睦鄯e效果 只有微小的機(jī)會(huì)導(dǎo)致變化的運(yùn)作工序稱為“統(tǒng)計(jì)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(diào)機(jī) b) 操作者錯(cuò)誤 c) 有缺陷的原材料 一個(gè)工序如果出現(xiàn)上面的變化則稱為“失控” .,BPTL Confidential,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(guī)格的程度 用于和另一工序或競(jìng)爭(zhēng)對(duì)手

23、比較,BPTL Confidential,34,工序能力與規(guī)格極限,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,35,三種極限類型,規(guī)格極限 (LSL and USL) created by design engineering in response to customer requirements to specify the tolerance for a products characteristic 工序極限 (LPL and UPL) measures the variation of a process the

24、 natural 6 limits of the measured characteristic 控制極限 (LCL and UCL) measures the variation of a sample statistic (mean, variance, proportion, etc),BPTL Confidential,36,工序能力指數(shù),工序能力的兩種度量: 工序潛力 Cp 工序表現(xiàn) Cpu Cpl Cpk,BPTL Confidential,37,工序潛力,Cp 指標(biāo)顯示實(shí)際工差 (6)是否超出規(guī)格.,公式,BPTL Confidential,38,工序潛力,傳統(tǒng)上, Cp 有 1

25、.0 時(shí)顯示工序能力被判為“有能力考核成績(jī)”. 若數(shù)據(jù)集中于工程工差內(nèi), 將僅有0.27% 的工件會(huì)超差. Cp 拒貨率 1.000.270 % 1.330.007 % 1.506.8 ppm 2.002.0 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 process spread

26、 (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(xiàn),The Cpk index relates the scaled distance between the process mean and the nearest specification limit.,BPTL Confidential,42,工序表現(xiàn),Cpk

27、 不良率 1.00.13 0.27 % 1.10.05 0.10 % 1.20.02 0.03 % 1.348.1 96.2 ppm 1.413.4 26.7 ppm 1.5 3.4 6.8 ppm 1.6 794 1589 ppb 1.7 170 340 ppb 1.8 33 67 ppb 1.9 6 12 ppb 2.0 1 2 ppb,BPTL Confidential,43,工序表現(xiàn),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,工序潛力與工序表現(xiàn),(a) Poor Process Po

28、tential(b) Poor Process Performance,Experimental Design to reduce variation,Experimental Design to center mean to reduce variation,BPTL Confidential,45,工序潛力與工序表現(xiàn),BPTL Confidential,46,工序穩(wěn)定性,A process is stable if the distribution of measurements made on the given feature is consistent over time.,Time

29、,Stable Process,Time,Unstable Process,BPTL Confidential,47,短期工序能力與長(zhǎng)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(zhǎng)期工序能力(previously called long-term capability) shows the variability of a machine/proc

30、ess operating over a period of time. It includes sources of variation in addition to the short-term variability.,BPTL Confidential,48,WithinOverall Sample Size30 50 units 100 units Number of Lotssingle lotseveral lots Period of Timehours or daysweeks or months Number of Operatorssingle operatordiffe

31、rent operators Process Potential Cp Pp Process Performance Cpk Ppk,短期工序能力與長(zhǎng)期工序能力,BPTL Confidential,49,實(shí)戰(zhàn)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 supplie

32、rs. Assess the process 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 th

33、e camshaft length suggests 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 a

34、re your recommendations?,BPTL Confidential,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(zhuǎn)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 relia

35、ble, because these indices are computed 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

36、 but skewed, Box-Cox transformation 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(zhuǎn)化后的工序能力分析,BPTL Confidential,58,Minitab: Stat Quality Tools Capability Analysis (Normal),用Box-Cox

37、 轉(zhuǎn)化后的工序能力分析,BPTL Confidential,59,Example 6,Open the file named Dimension.MTW in the Day-2 folder again. Compute the process capability with the specification limits: LSL: 0.1USL: 10 Are the data normally distributed? Compute the process capability again with Box-Cox transformation.,用Box-Cox 轉(zhuǎn)化后的工序能力

38、分析,BPTL Confidential,60,Cpk of 0.41 is reported 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(zhuǎn)化后的工序能力分析,BPTL Confidential,61,Example 6,Cpk has increased from 0.41 to 0.81,用Box-Cox 轉(zhuǎn)化后的工序能力分析,BPTL Confidential,62,Whats “6” Quality Then,Original Definition by Motorola: In the short term, the specification limits are at least 6 away from