six sigma training(66)6sigma推行教材ppt課件

1、 Six-Sigma Training Book Six-Sigma . 數(shù)據(jù)分布. NormalExponentialWeibullLognormaltc2fContinuous DistributionsSampling Distributions數(shù)據(jù)分布.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P

2、lot is known as Probability Density Functionof X.Many natural phenomena and man-made processes are observed 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, humi

3、dity change, vibrations, cutting angle variations, cutting tool wear, bearing wear, rotational speed variations, fixturing variations, raw material changes and contamination level changesIf these sources of variation are small, independent and equally likely to be positive or negative, the length wi

4、ll closely approximate a normal distribution.正態(tài)分布.First introduced by French 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

5、 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(tài)分布 - 歷程表Karl Friedrich Gauss.正態(tài)分布易于了解, 具有特性, 統(tǒng)計學(xué)提供了許多基于正態(tài)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(tài)分布去近似模擬其它分布 (如能夠) 或轉(zhuǎn)化數(shù)據(jù)以“使它遵從正態(tài)分布.它是分析過程才干的首選

6、分布方式.正態(tài)分布.A normal distribution can be completely described by knowing only the:Mean (m)Variance (s2)正態(tài)分布的一些特性Distribution OneDistribution TwoDistribution ThreeWhat is the difference between the 3 normal distributions?X N(m, s2)1.ANormal(A,A)BNormal(B,B)ANormal(A,A)BNormal(B,B)ANormal(A,A)BNormal(B,

7、B)What is the difference between process A & B for each case?正態(tài)分布的一些特性.The 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 a set of observations is arranged in an in

8、creasing 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 the median is the average of the 2 values.The mode is the observa

9、tion that occurs most frequently in the sample.正態(tài)分布的一些特性.The area under sections of the curve can be used to estimate the cumulative probability of a certain “event occurring:Point of Inflection1s+ - 68.27%95.45%99.73%m +/- 3s is often referred to as the width of a normal distribution3正態(tài)分布的一些特性.Lets

10、 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.MiniTab:Calc Probability Distributions Normal.Enter m valueEnter s valueEnter x value正態(tài)分布的一些特性.什么是 6?.6 簡介.The Focus of Six SigmaIdentifying critical a

11、spects 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 people have the time, tools, and resources they need to succ

12、eed.Customer Focus: A Model For SuccessTechnologyTechnologyCapabilityCapabilityOrganizationOrganizationPeoplePeopleProcessesProcesses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.客戶滿意才干體現(xiàn)品質(zhì), 價錢, 和貨期的意義.品質(zhì),本錢, 準(zhǔn)時走貨無不依耐于工序才干.What purpose is Six-sigma ? .Six Sigma VisionThe Vision of Six Sigma is to delight customers by

13、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 breakthrough improvement across all areas of our

14、 business. .PPMProcessCapabilityDefects per Million Opp.Six Sigma - Aggressive GoalWhat purpose is Six-sigma ? .Statistical Definition of n-SigmaLSLLSLUSLUSLProcess WidthmoDesign WidthTTscaleLSLLSLUSLUSLscaleTT+nsscale- n sThis is the so-called n-sigma Sigma is a statistical unit of measure that ref

15、lects 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.Statistical Definition of 6This is the six- sigma we said LSLLSLUSLUSLProcess WidthmoDesign Width- 3sst+ 3sstT

16、T.001 ppm USL.001 ppm 2)b) 工序才干可 (Cp=1 to 2)c) 工序才干差 (Cp1.5)b)工序才干可(Cpk=1 to 1.5)c)工序才干差(Cpk1)a)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2Cpk 1.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 var

17、iation.工序潛力與工序表現(xiàn)a)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2Cpk 1.工序穩(wěn)定性A process is stable if the distribution of measurements made on the given feature is consistent over time.TimeStable ProcessTimeUnstable Processucllclucllcl.短期工序才干與長期工序才干短期工序才干(previously called short-term capability) shows the inheren

18、t variability of a machine/process operating within a brief period of time.長期工序才干(previously called long-term capability) shows the variability of a machine/process operating over a period of time. It includes sources of variation in addition to the short-term variability.WithinOverallSample Size30

19、50 units 100 unitsNumber of Lotssingle lotseveral lotsPeriod of Timehours or daysweeks or monthsNumber of Operatorssingle operatordifferent operatorsProcess Potential Cp PpProcess Performance Cpk Ppk短期工序才干與長期工序才干.實戰(zhàn)演練The length of a camshaft for an automobile engine is specified at 600 2 mm. Control

20、 of the length of the camshaft is critical to avoid scrap/rework.The camshaft is provided by external suppliers. Assess the process capability for this supplier.The data is available in Camshaft.MTW. Data are collected in subgroups of 5 each.Example 4Minitab:Stat Quality Tools Capability Analysis (N

21、ormal).Example 4.Example 5Histogram of the 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 supplier

22、s similar in performance?If not, what are your recommendations?.Example 5MiniTab:Stat Quality Tools Capability Sixpack(Normal).Example 5.Example 5.用Box-Cox 轉(zhuǎn)化后的工序才干分析When the process data are not normal, the Cpk or Ppk indices are not accurate or reliable, because these indices are computed on the b

23、asis 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.If the process data are somewhat bell-shaped but skewed, Box-Cox transformation can be used to make the data norma

24、l before we assess the process capability.Remember to transform the specification limits too before we compute Cpk or Ppk! 用Box-Cox 轉(zhuǎn)化后的工序才干分析.Minitab:Stat Quality Tools Capability Analysis (Normal)用Box-Cox 轉(zhuǎn)化后的工序才干分析.Example 6Open the file named Dimension.MTW in the Day-2 folder again. Compute the

25、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(zhuǎn)化后的工序才干分析.Cpk of 0.41 is reported in the SSAT package. This value is not reliable or accurate if the data are not normal.Data i

26、s not normalExample 6用Box-Cox 轉(zhuǎn)化后的工序才干分析.Example 6Cpk has increased from 0.41 to 0.81用Box-Cox 轉(zhuǎn)化后的工序才干分析.Whats “6 Quality ThenOriginal Definition by Motorola:In the short term, the specification limits are at least 6 away from the process mean , i.e. Cp 2,In the long run, the process will shift by less than 1.5, i.e. Ppk 1.5,The process will yield less than 3.4 dppm rejected parts.66Shift1.54.5“Sigma Level Capability.Whats Six Sigma Quality NowMikel J Harry claims that the process mean between lots will vary, with an average p