TRAINING SIX-SIGMA（PPT 66页）.pptx

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1、 Six-Sigma Training Book Dec 18 ,20011 6推行教材4 數据分布2 6推行教材4 NormalExponentialWeibullLognormaltc2fContinuous DistributionsSampling Distributions數据分布3 6推行教材The most widely used model for the distribution of continuous random variable.Arises in the study of numerous physical phenomena, such as the veloc

2、ity of molecules.正態分布正態分布 xe21xf2x21Plot is known as Probability Density Functionof X4 6推行教材4Many natural phenomena and man-made processes are observed to have normal distributions, or can be closely represented as normally distributed.4For example, the length of a machined part is observed to vary

3、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 changes4If these sources of variation are small, independent and equally li

4、kely to be positive or negative, the length will closely approximate a normal distribution.正態分布正態分布5 6推行教材4First introduced by French mathematician Abraham DeMoivre in 1733.4Made famous in 1809 by German mathematician K.F. Gauss when he also developed a normal distribution independently and used it

5、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 data to follow this curve.正態分布正態分布 - 歷程表歷程表Karl Friedrich Gauss6 6推行教材4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

6、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.4它是分析過程能力的首選分布形式.正態分布正態分布7 6推行教材4A normal distribution can be completely described by knowing only the:Mean (m)Variance (s2)正態分布的一些特性正態分布的一些特性Distribution OneDistribution TwoDistribution ThreeWhat is the difference between the 3 norma

7、l distributions? xe21xf2x21X N(m, s2)18 6推行教材ANormal(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,s sB)What is the difference between process A & B for each case?正態分布的一些特性正態分布的一些特性9 6推行教材4The mean, median and mode all coincide at the same value - m.

8、There is perfect symmetry.+ - MeanMedianMode2The 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.lIf the number of observations is odd, the median is

9、 the value of the middle number.lIf 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.正態分布的一些特性正態分布的一些特性10 6推行教材4The area under sections of the curve can be used to estim

10、ate the cumulative probability of a certain “event” occurring:Point of Inflection1s s+ - 68.27%95.45%99.73%m +/- 3s is often referred to as the width of a normal distribution3正態分布的一些特性正態分布的一些特性11 6推行教材Lets compute the cumulative probabilities of the following distributions:+ - m = 3.5s = 0.61.8+ - 2

11、0.0m = 16.6s = 2.8+ - m = -1.5s = 0.9-2.80.5正態分布的一些特性正態分布的一些特性12 6推行教材MiniTab:Calc Probability Distributions Normal.Enter m valueEnter s valueEnter x value正態分布的一些特性正態分布的一些特性13 6推行教材什么是什么是 6?14 6推行教材6 簡介15 6推行教材The Focus of Six Sigma4Identifying critical aspects of the business with problems or oppor

12、tunities for improvement.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.16 6推行教材Customer Focus: A Model For Su

13、ccessTechnologyTechnologyCapabilityCapabilityOrganizationOrganizationPeoplePeopleProcessesProcesses 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客戶滿意才能体現品質, 价格价格, 和貨期的意義和貨期的意義. 品質品質,成本成本, 准時走貨無不依耐于工序能力准時走貨無不依耐于工序能力.What purpose is Six-sigma ? 17 6推行教材Six Sigma VisionThe Vision of

14、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 breakthroug

15、h improvement across all areas of our business. 18 6推行教材2308,537366,80746,210523363.4s sPPMProcessCapabilityDefects per Million Opp.Six Sigma - Aggressive GoalWhat purpose is Six-sigma ? 19 6推行教材Statistical Definition of n-SigmaLSLLSLUSLUSLProcess WidthmoDesign WidthTTscaleLSLLSLUSLUSLscaleTT+n s ss

16、cale- 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 of a failure/error.20 6推行教材Statistical De

17、finition 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 = 1c)Cp = 2Cpk 143 6推行教材工序潛力与工序表現工序潛力与工序表現(a) Poor Process

18、Potential(b) Poor Process PerformanceLSLUSLLSLUSLExperimental Design to reduce variationExperimental Design to center mean to reduce variation44 6推行教材工序潛力与工序表現工序潛力与工序表現a)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2Cpk USLPPM USLPPM USLPPM USLPPM USLPPM USLPPM USLPPM USLPPM USLPPM LSLPpkPPLPPUPpCpmCpkCPLCPUC

19、pStDev (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. Overall PerformanceExp. Within PerformanceObserved PerformanceOverall CapabilityPotential (With

20、in) CapabilityProcess DataWithinOverallCpk has increased from 0.41 to 0.81用用Box-Cox 轉化后的工序能力分析轉化后的工序能力分析61 6推行教材Whats “6s” Quality Then4Original Definition by Motorola:4In the short term, the specification limits are at least 6s away from the process mean m, i.e. Cp 2,4In the long run, the process w

21、ill 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” Capability62 6推行教材Whats 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 =

22、 zs + 1.5s Shift1.5szsNote: Sigma Capability = (dpmo) (dppm)“Sigma Level” Capability63 6推行教材Types of Variation1. Positional VariationSame process, variation at differing locations simultaneously:Temperature variations inside a thermal chamberCavity-to-cavity variations in an injection mold2. Cyclica

23、l VariationSequential 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 materials64 6推行教材Types of Variation3. Temporal VariationVariations over longer periods of time, such a several hours, days or weeks. 65 6推行教材Measurement System Analysis ApproachThere are two types of measurements possible:4VariableData can be described on a continuous scale4AttributeData cannot be adequately described on a continuous scalePass / Fail, very low counts Each must be approached differently.66