Six-SigmaTrainingBook14825

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,*,按一下以編輯母片本文樣式,第二階層,第三階層,第四階層,第五階層,*,*,6推行教材,Six-Sigma,Training Book,Six-Sigma,1,BPTL Confidential,數据分布,2,BPTL Confidential,Normal,Exponential,Weibull,Lognormal,t,c,2,f,Continuous Distributions,Sampling Distributions,數据分布,3,BPTL Confidential,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.,正態分布,Plot is known as Probability Density Function,of X,4,BPTL Confidential,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, humidity change, vibrations, cutting angle variations, cutting tool wear, bearing wear, rotational speed 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.,正態分布,5,BPTL Confidential,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 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 Friedrich Gauss,6,BPTL Confidential,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,7,BPTL Confidential,A normal distribution can be completely described by knowing only the:,Mean (,m,),Variance (,s,2,),正態分布的一些特性,Distribution One,Distribution Two,Distribution Three,What is the difference between the 3 normal distributions?,X, N(,m,s,2,),1,8,BPTL Confidential,ANormal(,A,A,),BNormal(,B,B,),ANormal(,A,A,),BNormal(,B,B,),ANormal(,A,A,),BNormal(,B,B,),What is the difference,between process A & B,for each case?,正態分布的一些特性,9,BPTL Confidential,The mean, median and mode all 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 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.,正態分布的一些特性,10,BPTL Confidential,The area under sections of the curve can be used to estimate the cumulative probability of a certain “event” occurring:,Point of Inflection,1,s,+,-,68.27,%,95.45%,99.73%,m,+/- 3,s,is often referred to as the width of a normal distribution,3,正態分布的一些特性,11,BPTL Confidential,Lets compute the cumulative probabilities of 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,正態分布的一些特性,12,BPTL Confidential,MiniTab:,Calc,Probability Distributions,Normal.,Enter,m,value,Enter,s value,Enter,x value,正態分布的一些特性,13,BPTL Confidential,什么是 6,?,?,?,14,BPTL Confidential,6,簡介,15,BPTL Confidential,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 people have the,time, tools, and resources,they need to succeed.,16,BPTL Confidential,Customer Focus: A Model For Success,Technology,Technology,Capability,Capability,Organization,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 ?,17,BPTL Confidential,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 Six Sigma is to apply a structured, systematic approach to achieve breakthrough improvement across all areas of our business.,18,BPTL Confidential,PPM,Process,Capability,Defects per,Million Opp.,Six Sigma - Aggressive Goal,What purpose is Six-sigma ?,19,BPTL Confidential,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 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,BPTL Confidential,Statistical Definition of,6,This is the six-,sigma we said,LSL,LSL,USL,USL,Process Width,m,o,Design Width,- 3,s,st,+ 3,s,st,T,T,.001,ppm, USL,.001,ppm,2),b) 工序能力可 (C,p,=1 to 2),c) 工序能力差 (C,p,1.5),b)工序能力可(C,pk,=1 to 1.5),c)工序能力差(C,pk,1),a),C,p,= 2,C,pk,= 2,b),C,p,= 2,C,pk,= 1,c),C,p,= 2,C,pk, 1,43,BPTL Confidential,工序潛力与工序表現,(a) Poor Process Potential(b) Poor Process Performance,LSL,USL,LSL,USL,Experimental Design,to reduce variation,Experimental Design,to center mean,to reduce variation,44,BPTL Confidential,工序潛力与工序表現,a),C,p,= 2,C,pk,= 2,b),C,p,= 2,C,pk,= 1,c),C,p,= 2,C,pk, 1,45,BPTL Confidential,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 Process,Time,Unstable Process,ucl,lcl,ucl,lcl,46,BPTL Confidential,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 operating over a period of time. It includes sources of variation in addition to the short-term variability.,47,BPTL Confidential,WithinOverall,Sample Size30 50 units, 100 units,Number of Lotssingle lotseveral lots,Period of Timehours or daysweeks or months,Number of Operatorssingle operatordifferent operators,Process Potential C,p,P,p,Process Performance C,pk,P,pk,短期工序能力与長期工序能力,48,BPTL Confidential,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 process capability for this supplier.,The data is available in,Camshaft.MTW,. Data are collected in subgroups of 5 each.,49,BPTL Confidential,Example 4,Minitab:,S,tat,Q,uality Tools Capability,A,nalysis (Normal),50,BPTL Confidential,Example 4,51,BPTL Confidential,Example 5,Histogram 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 suppliers similar in performance?,If not, what are your recommendations?,52,BPTL Confidential,Example 5,MiniTab:,S,tat,Q,uality Tools Capability,S,ixpack(Normal),53,BPTL Confidential,Example 5,54,BPTL Confidential,Example 5,55,BPTL Confidential,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 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.,56,BPTL Confidential,If the process data are somewhat bell-shaped 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 轉化后的工序能力分析,57,BPTL Confidential,Minitab:,S,tat,Q,uality Tools Capability,A,nalysis (Normal),用Box-Cox 轉化后的工序能力分析,58,BPTL Confidential,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 轉化后的工序能力分析,59,BPTL Confidential,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 轉化后的工序能力分析,60,BPTL Confidential,Example 6,Cpk has increased from 0.41 to 0.81,用Box-Cox 轉化后的工序能力分析,61,BPTL Confidential,Whats “,6,” Quality Then,Original Definition by Motorola:,In the short term, the specification limits are at least 6, away from the process mean , i.e. C,p, 2,In the long run, the process will shift by less than 1.5, i.e. P,pk, 1.5,The process will yield less than 3.4 dppm rejected parts.,6,6,Shift,1.5,4.5,“Sigma Level” Capability,62,BPTL Confidential,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.,k, =,z, + 1.5,k, =,z, + 1.5,Shift,1.5,z,Note,:Sigma Capability = (dpmo),(dppm),“Sigma Level” Capability,63,BPTL Confidential,Types of Variation,1. Positional Variation,Same process, variation at differing locations simultaneously:,Temperature variations inside a thermal chamber,Cavity-to-cavity variations in an injection mold,2. Cyclical Variation,Sequential repetitions of a process over fairly short time, say, less than 15 mins:,Variations between consecutive batches of a process,Differences from lot to lot of raw materials,64,BPTL Confidential,Types of Variation,3. Temporal Variation,Variations over longer periods of time, such a several hours, days or weeks.,65,BPTL Confidential,谢谢观看,/,欢迎下载,BY FAITH I MEAN A VISION OF GOOD ONE CHERISHES AND THE ENTHUSIASM THAT PUSHES ONE TO SEEK ITS FULFILLMENT REGARDLESS OF OBSTACLES. BY FAITH I BY FAITH,