1、Dec 18 ,2001BPTL Confidential1 Six-Sigma Training Book 6推行教材BPTL Confidential24 數(shù)據(jù)分布 6推行教材BPTL Confidential34 NormalExponentialWeibullLognormaltc2fContinuous DistributionsSampling Distributions數(shù)據(jù)分布 6推行教材BPTL Confidential4The most widely used model for the distribution of continuous random variable.A

2、rises in the study of numerous physical phenomena, such as the velocity of molecules.正態(tài)分布正態(tài)分布 xe21xf2x21Plot is known as Probability Density Functionof X 6推行教材BPTL Confidential54Many natural phenomena and man-made processes are observed to have normal distributions, or can be closely represented as

3、normally distributed.4For 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 contaminat

4、ion level changes4If 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)分布正態(tài)分布 6推行教材BPTL Confidential64First introduced by French mathematician Abraham DeMoivre in 1733.4Made famous in 1809 by G

5、erman mathematician K.F. Gauss when he also developed a normal distribution independently and used it in his study of astronomy.4As a result, it is also known as the Gaussian distribution.4During mid to late nineteenth century, many statisticians believed that it was “normal” for most well-behaved d

6、ata to follow this curve.正態(tài)分布正態(tài)分布 - 歷程表歷程表Karl Friedrich Gauss 6推行教材BPTL Confidential74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)有力的分析方法來幫助人們做決定.4因此, 我們通常會試圖用正態(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.4它是分析過程能力的首選分布形式.正態(tài)分布正態(tài)分布 6推行教材BPTL Confidential84A normal distribution can be completely described by knowing only

7、 the:Mean (m)Variance (s2)正態(tài)分布的一些特性正態(tài)分布的一些特性Distribution OneDistribution TwoDistribution ThreeWhat is the difference between the 3 normal distributions? xe21xf2x21X N(m, s2)1 6推行教材BPTL Confidential9ANormal(m mA,s sA)BNormal(m mB,s sB)ANormal(m mA,s sA)BNormal(m mB,s sB)ANormal(m mA,s sA)BNormal(m mB

8、,s sB)What is the difference between process A & B for each case?正態(tài)分布的一些特性正態(tài)分布的一些特性 6推行教材BPTL Confidential104The mean, median and mode all coincide at the same value - m. There is perfect symmetry.+ - MeanMedianMode2The mean represents the arithmetic average of all observations in a data set.If

9、a set of observations is arranged in an increasing order of magnitude (ranked data), the middle value is called the median.lIf the number of observations is odd, the median is the value of the middle number.lIf the number of observations is even, there are 2 middle numbers, and the median is the ave

10、rage of the 2 values.The mode is the observation that occurs most frequently in the sample.正態(tài)分布的一些特性正態(tài)分布的一些特性 6推行教材BPTL Confidential114The area under sections of the curve can be used to estimate the cumulative probability of a certain “event” occurring:Point of Inflection1s s+ - 68.27%95.45%99.73%m

11、 +/- 3s is often referred to as the width of a normal distribution3正態(tài)分布的一些特性正態(tài)分布的一些特性 6推行教材BPTL Confidential12Lets compute the cumulative probabilities of the following distributions:+ - m = 3.5s = 0.61.8+ - 20.0m = 16.6s = 2.8+ - m = -1.5s = 0.9-2.80.5正態(tài)分布的一些特性正態(tài)分布的一些特性 6推行教材BPTL Confidential13Mini

12、Tab:Calc Probability Distributions Normal.Enter m valueEnter s valueEnter x value正態(tài)分布的一些特性正態(tài)分布的一些特性 6推行教材BPTL Confidential14什么是什么是 6? 6推行教材BPTL Confidential156 簡介 6推行教材BPTL Confidential16The Focus of Six Sigma4Identifying critical aspects of the business with problems or opportunities for improvemen

13、t.4Targeting those critical areas and designating improvement efforts as Six Sigma Black Belt projects.4Selecting top people to work on the projects-full time.4Ensuring these people have the time, tools, and resources they need to succeed. 6推行教材BPTL Confidential17Customer Focus: A Model For SuccessT

14、echnologyTechnologyCapabilityCapabilityOrganizationOrganizationPeoplePeopleProcessesProcesses 商務(wù)上的生存競爭有賴于我們多大程度上讓我們的客戶滿意商務(wù)上的生存競爭有賴于我們多大程度上讓我們的客戶滿意. 客戶滿意才能體現(xiàn)品質(zhì)客戶滿意才能體現(xiàn)品質(zhì), 價(jià)格價(jià)格, 和貨期的意義和貨期的意義. 品質(zhì)品質(zhì),成本成本, 準(zhǔn)時(shí)走貨無不依耐于工序能力準(zhǔn)時(shí)走貨無不依耐于工序能力.What purpose is Six-sigma ? 6推行教材BPTL Confidential18Six Sigma VisionThe

15、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 PhilosophyThe philosophy of Six Sigma is to apply a structured, systematic approach to achieve b

16、reakthrough improvement across all areas of our business. 6推行教材BPTL Confidential192308,537366,80746,210523363.4s sPPMProcessCapabilityDefects per Million Opp.Six Sigma - Aggressive GoalWhat purpose is Six-sigma ? 6推行教材BPTL Confidential20Statistical Definition of n-SigmaLSLLSLUSLUSLProcess WidthmoDes

17、ign WidthTTscaleLSLLSLUSLUSLscaleTT+n s sscale- n s sThis 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-unit, parts-per million defective, and the probability

18、 of a failure/error. 6推行教材BPTL Confidential21Statistical Definition of 6This is the six- sigma we said LSLLSLUSLUSLProcess WidthmoDesign Width- 3s sst+ 3s sstTT.001 ppm USL.001 ppm 2)b) 工序能力可工序能力可 (Cp=1 to 2)c) 工序能力差工序能力差 (Cp1.5)b)工序能力可工序能力可(Cpk=1 to 1.5)c)工序能力差工序能力差(Cpk1)a)Cp = 2Cpk = 2b)Cp = 2Cpk

19、= 1c)Cp = 2Cpk 1 6推行教材BPTL Confidential44工序潛力與工序表現(xiàn)工序潛力與工序表現(xiàn)(a) Poor Process Potential(b) Poor Process PerformanceLSLUSLLSLUSLExperimental Design to reduce variationExperimental Design to center mean to reduce variation 6推行教材BPTL Confidential45工序潛力與工序表現(xiàn)工序潛力與工序表現(xiàn)a)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2C

20、pk USLPPM USLPPM USLPPM USLPPM USLPPM USLPPM USLPPM USLPPM USLPPM LSLPpkPPLPPUPpCpmCpkCPLCPUCpStDev (Overall)StDev (Within)Sample NMeanLSLTargetUSL12352.05 1486.4110865.64 8685.19 876.04 7809.1510000.00 0.0010000.000.770.770.990.88 *0.810.811.040.920.09904330.09401751000.999990.77268 *1.29420Exp. Ov

21、erall PerformanceExp. Within PerformanceObserved PerformanceOverall CapabilityPotential (Within) CapabilityProcess DataWithinOverallCpk has increased from 0.41 to 0.81用用Box-Cox 轉(zhuǎn)化后的工序能力分析轉(zhuǎn)化后的工序能力分析 6推行教材BPTL Confidential62Whats “6s” Quality Then4Original Definition by Motorola:4In the short term, th

22、e specification limits are at least 6s away from the process mean m, i.e. Cp 2,4In the long run, the process will shift by less than 1.5s, i.e. Ppk 1.5,4The process will yield less than 3.4 dppm rejected parts.6s6sShift1.5s4.5s“Sigma Level” Capability 6推行教材BPTL Confidential63Whats Six Sigma Quality NowMikel J Harry claims that the process mean between lots will vary, with an average process shift of 1.5s.ks = zs + 1.5s ks = zs + 1.5s Shift1.5szsNote: Sigma Capability = (dpmo) (dppm)“Sigma Level” Capability 6推行教材BPTL Confidential64Types of Variation1. Positional VariationSame process, variat