西格玛改善阶段绿带教材ppt课件.ppt

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1、6Sigma绿带培训-改善阶段,6Sigma绿带培训-改善阶段,实验设计简介 2K因子实验设计简介23实验部分因子设计响应面方法（RMS）进化操作（EVOP）I阶段路径,目录,Introduction to Experimentation实验设计简介,The purpose of an experiment is to better understand the real world, not to understand the experimental data进行一个实验的目的是为了更好的了解真实的世界， 而不是了解实验数据。,William Diamond IBM-retired sta

2、tistician) IBM-已退休的统计员,Learning objectives学习目的,通过对本文章的学习，学员将能够 解释什么是DOE。 理解为什么使用DOE 解释一些DOE的术语 描述DOE的基本步骤 描述有效效果设计的一些阻碍 了解OFAT实验设计的局限性,What is Design of Experiments(DOE)什么是实验设计,DOE consists of purposeful changes of input variables (factors) to a process (or activity) in order to observe the correspo

3、nding changes in the output variables (Responses) 实验设计通过有目的地改变一个过程（或活动）的输入变量（因子），以观察输出变量（响应量）的相应变化。 It is a scientific approach which allows the researcher to gain Knowledge in order to better understand 它是一种科学的方法，使研究者更好地了解一个过程 并确定输入（因子）是如何影响输出（响应量）,What is Design of Experiments(DOE)什么是实验设计,Why Use

4、DOE为什么使用试验设计,试验设计是识别关键输入因子的最有效方法。 试验设计是帮助我们了解输入因子和响应变量关系的最高效途径。试验设计是建立响应变量与输入因子之间的数学关系模型的方法试验设计是确定优化输出并减少成本的输入设定值的途径。试验设计是设定公差的科学方法。,Benefit of DOE实验设计的益处,The benefits of DOE are:实验设计的益处如下 a) Process performance improvement 改善过程绩效水平 b) Costs reduction 降低成本 c) Shortening product development time. 缩短产

5、品开发时间和生产时间,Basic Terminology基本术语,Response 响应变量所关注的可测量的输出结果，如良率、强度等。Factors 因子可控制的变量，通过有意义的变动，可确定其对响应变量的影响，如温度、时间等。Level 水平 因子的取值或设定，如： e.g. Level 1 for time=2 hr Level2 for time=3 hr 举例：时间因子的水平12小时 时间因子的水平23小时,Basic Terminology基本术语,Treatment 处理 a set of specified factor levels for an experimental ru

6、n 某次实验的整套因子 e.g. Treatment1: time=2 hr and temperature=175 c Treatment1: time=3 hr and temperature=225 c 举例： 处理1：时间2小时， 温度175 c 处理1：时间3小时， 温度225 c,Basic Terminology基本术语,Repetition 重复 重复指在不重新组合实验设定的情况下，连续进行试验并收集数据。 Replication 复制 复制意味每个数据值在重新设定测试组合之后收集。 Randomization 随机化 适当安排实验次序，使每个实施被选出的机会都相等 目的:避免

7、噪音因子的变化对结果的影响.,Steps of DOE实验设计步骤,I、statement of the problem 陈述问题II、set the objective of the DOE 设立目标III、determine the output response(s) 确定输出变量IV、identify input factors(control factors and noise factors） 识别输入因子（可控因子/噪声因子）V、select the levels for each factors 选定每个因子的水平,Steps of DOE实验设计步骤,VI. Select t

8、he type of DOE 选择实验设计类型VII. Plan and prepare the resource for conducting the experiments 计划并为实施实验做准备.VIII. Conduct the experiments and record the data 实施实验并记录数据.IX. Analyze the data and draw conclusion 分析数据并得出结论.X. Run confirmatory experiments,if necessary. 必要时进行确认实验.,Step III: Determine the Respons

9、e(s)步骤三：确定响应变量,Use continuous responses whenever possible 尽量使用连续数据作输出变量. -Continuous data provide more information 连续数据提供更多的信息. -Attribute data needs larger sample size 计数型数据需要大样本量. Use response which can be measured precisely, accurately, and with stability. 尽量使用可精确，稳定测量的输出变量.,Step IV: Identify Inp

10、ut Factors步骤四：识别输入因子,Generally，input factors can be identified through:通常可通过以下工具识别输入因子： - Fishbone diagram 鱼骨图 - C&E matrix 因果矩阵 - FMEA 潜在失效模式效果分析,Control Factors vs. Noise Factors可控因子与噪声因子,Controllable (Control) factors are factors for which we can set and maintain a desired level during a process

11、normal operation.可控（控制）因子是我们在工序的正常操作时能设定并且维持在期望水平的因子。Noise factors are factors that vary during normal Operation，and we cannot control them.Or，we prefer Not to control them because doing so would be very expensive. 噪音因子是在正常的操作期间变化的因子，而且我们不能够控制他们；或者我们宁愿不控制他们，因为这么做会很昂贵。,Step V:Select Levels for Each F

12、actor步骤五：选择输入因子的水平,Levels can be either quantitative or qualitative.因子水平可以是定量的，也可是定性的。Quantitative example.定量举例 温度：100 和120 压力： 20 psi 和25 psi 旋转度：3000RPM vs.3500RPM Qualitative example- 定性举例 Machine A vs. Machine B 机器A和机器B Shift A, B, C 曲线A, B, C Material type: New vs old 材料类型：新和旧,Step V:Select Lev

13、els for each Factor步骤五：选择输入因子的水平,Levels are selected based on DOE objective.因子水平的选择是基于实验目的。Objective#1: Determine vital few inputs from a large number of variables(Screening)筛选DOE：从大量的变量中确定出重要的少数输入因子 Set “Bold ” levels extremes of current capabilities 将当前能力的极限值设定为“大胆”水准,Step V:Select Levels for each

14、 Factor步骤五：选择输入因子的水平,Objective#2: To understand factor relationships and interactions量化DOE：了解因素关系及交互作用 Once critical inputs are identified, reduced spacing of the levels is used to identify interactions among Inputs 一旦确定重要的输入因子，通过减少水平间距来确定输入因子间的关系和交互作用Objective#3:To identify the operating window of

15、a set of input variables (Process Optimization)优化/稳健DOE：确定一组输入变量的操作参数（过程最优化) Close settings are again used 水平设定进一步接近,Step VI: Select the type of DOE步骤六：选择DOE类型,Step VII:Plan conducting the experiment步骤七：实施实验的计划,实施实验的计划应解决以下问题： 费用如何？我们已经与内部客户讨论过吗？需要多长时间？有必要做试运行吗？我们需要提案及许可吗？谁来进行实验？,Step VIII & IX: Con

16、duct experiments,obtain data and analyze data步骤八和九：实施实验，获取数据并分析数据,Obtain the data 获取数据 -Validate the data collection and data values 确认数据,收集数据值 -Validate that special conditions did not influence 确认特别情况不会产生影响Analyze the data using Minitab 用Minitab 分析数据 We will cover this in later modules 我们将在接下来的课程里

17、讲解,Barriers to Effective DOE实施实验的阻碍,Problem not clear 问题不清Objectives not clear 目标不明 Inadequate brainstorming 集体讨论不充分Results of the experiment unclear 实验结果不清DOE is too costly 实验设计费用过高DOE is too time consuming 实验设计耗时过长 Lack of understanding DOE strategies 对实验设计策略缺乏理解,Barriers to Effective DOE实施实验的阻碍,N

18、ot confident during the early stages实验初期缺乏信心Lack of management support缺乏管理支持Need for instant results过于迫切需要结果Lack of adequate coaching/support缺乏足够的指导/支持,Advantages 优点,DOE实验可以实现对多因子在多水平上的分析。这要比传统上被称为OFAT（一次一个因子）的假设检验技术快得多。DOE实验在分析初期阶段可以用来筛选大量因子DOE实验可以分析出因子间的潜在“交互作用”。OFAT实验却不可以。这就称为因子效率。设想你在进行一次一个因子（OF

19、AT)实验，每次只变动一个因子,Advantages 优点,你得到的只是在其他因子不变的情况下对一个因子的估计;并假设其他因子的效果都不变以及这些效果可以叠加; 但是 当其他因子的数值变动时，一个因子的最佳数值可能发生变化.,Advantages 优 点,In Factorial Experiment, No matter the optimal value changes or not. 在因子实验里，不管最佳值是否发生变化It detects and estimates the effect among different factors and even their interactio

20、ns, it also provide a better discrimination power than OFAT 它能够察觉及估计不同因子的效果，甚至它们的交互作用，它也比“一次一个因子”实验提供更好的判别能力.,OFAT vs DOE单因子实验vs实验设计,OFAT vs DOE单因子实验vs实验设计,OFAT vs DOE单因子实验vs实验设计,OFAT vs DOE单因子实验vs实验设计,One Factor at a Time(OFAT) Strategy单次单因子（OFAT）方法,A sequence of experimental runs in which only one

21、 factor is manipulated while the values of all other factors are held constant, followed by a sequence of experimental runs in which a second factor is manipulated and all other factors are held constant,and so on 通常固定所有其他因子不变，而只变动一个因子进行实验；然后变动第二个因子（固定其他因子），以此类推。 Optimum operating point identified i

22、s often misleading. 这样确定的“最优点”常常有误导性。,Introduction To 2k Factorial Experiment 2k 因子实验设计简介,Learning Objectives学习目的,完成对本模块的学习后，学员将能够： 描述一个全因子实验 说明用于一个全因子实验计划的标志。 解释说明主要效果和交互作用。 用Minitab设定和分析一个2 x 2全因子实验,Agenda 教程,From previous module “Introduction to Design of Experiments” recap basis of DOE 从前面的章节“实验

23、设计简介”复习实验设计基本原理。What is a full factorial experiment? 什么是全因子实验？“Main effect” and “Interaction” “主效果”和“交互作用”Two Factor Example （using Minitab） 两个因子例题（用Minitab),Introduction To2k Factorial Experiment 2k 因子实验设计简介,Why do we use factorial experiment? 我们为什么需要进行因子实验？,Introduction To2k Factorial Experiment 2

24、k 因子实验设计简介,Vocabularies, Definitions & Notations 词汇、定义和标识,DOE Vocabulary实验设计词汇,Experimental Design； 实验设计对于实施实验的计划叫做“实验设计”又叫做“实验模式”或“设计矩阵”特意改变变量的一个或一系列实验，目的是观察和识别响应变量改变的原因它是一个选择响应变量、因子、区块和组合的计划所用的工具包括计划组合、随机化、重复和/或复制,Definition & Notation定义和标识,FULL factorial experiment: experiment with all combinatio

25、ns of factors in each of their levels 全因子实验：组合所有因子和每个因子所有水平的实验Design Notation: 设计标识：Factors 因子Upper case A, B, C，etc 大写字母A,B,C NUMBER OF FACTORS 因子数量K,Definition & Notation定义和标识,High and Low levels of factors 因子的高水平和低水平+，signsNumber of replicates 复制的数量NTreatment combinations 组合Lower case notation 小写

26、字母,Definition & Notation定义和标识,Example: 例子：For experiments using two levels of all the factors a shorthand is used:对于所有因子都使用两个水平的实验，可使用速记： 2ke.g23 =there factors at two levels each 例如23三个因子，每个因子都有两个水平,Definition & Notation定义和标识,For the number of runs needed, just multiply 为计算出需要的运行次数，就进行乘积 e.g 2 x 2=

27、4 runs, 2 x 2 x 2=8 runs, 24 =16 runsThe following session will focus on the 2 x 2or 22 design 我们现在将学习于2 x2或22设计,Main Effect 主效果,The Main Effect of a factor is the average effect on the response variable, by switching between the levels of the factor the example below has factors: Consistence and Ca

28、talyze. The output variable is yield 一个因子的主效果定义为一个因子在多水平下的变化导致输出变量的平均变化。参考下表，其中有两个因子，浓度与催化剂。输出变量是良率,Main Effect 主效果,The Main Effect for Consistence=The change in Yield across Catalyzes: 浓度的主效果:,When consistence is changed from Level 1 to level 2, yield is 4当浓度从水平1增加到水平2时，良率是4个点。,Likewise, the Main E

29、ffect for Catalyze is: 同样，催化剂的主效果:,Conc = ,= 4,When catalyzer is changed from Level 1 to level 2, yield is -12当催化剂从水平1增加到水平2时，良率是-12个点。,32+382,Main Effect Plot 主效果图,Table or simple plot e.g. 表格或简单的图示，例如Data file: 数据文件 Expt22.mtw Large slopes imply main effect is significant-but be aware of the choic

30、e of levels 斜度越大表示主效果大- 但要小心对水平的选择,Interaction 交互作用,If influence of the effect of 1factor is changed by changing the levels of one or more other factors,we say that an Interaction is found between factors. 在有些实验中，我们发现当改变其他因子的不同水平时，一个因子的水平的主效果有所改变。在这种情况下因子间具有交互作用。,Cata 1催化剂 1,Cata 2催化剂 2,浓度 1,浓度 2,32

31、,54,38,24,浓度与催化剂的交互作用：(24+32)/2-(54+38)/2=-18,Interaction 交互作用,For Example 参考下列数据组：At the first level of the CATALYZER Factor,the effect for Consistence is:在催化剂因子的第一个水平下，浓度效果为： Conc=54-32=22And at the second level of the CatalyzerFactor,the effect for Consistence is:而在催化剂因子的第二个水平下，浓度效果为： Conc=24-38=

32、-14,Interaction 交互作用,Lines on this plot which areNot parallel imply an interaction此图中的两条直线不平行表示存在交互作用Stat ANOVAInteractions Plot,Interaction 交互作用,Since the effect of Temperature on Yield depends on the level of Pressure, we can conclude that there is an interaction between Temperature and Pressure.

33、In this case the trend of increasing with temperature is even reversed. 因为浓度对良率的效果取决与催化剂水平，就表示浓度与催化剂之间存在交互作用。在这种情况下，由浓度产生的良率的增加趋势甚至被逆转。,Contrast 对 比,REMARKWhen we calculate the main effect of a factor 当我们计算一个因子的主效果时 Main Effect=yThe numerator before averge is called the linear contrast of the factor

34、 在平均前的分子叫作因子的线性对比E.g Contrasting level of Catalyze from prev. example is 例如：以上例子中催化剂的对比水平是（38+24）-（32+54）,Introduction To 2k Factorial Experiment 2k因子实验步骤,2 x 2 Example Using Minitab 2 x 2 例题（使用 Minitab),Step1: Identify Problem步骤1：识别问题,Step1:Practical Problem:To determine the effect of temperature a

35、nd pressure on the yield of two different products. Use the following data: 第一步：实际问题：确定浓度与催化剂在两个不同的水平,对产品的良率上产生的效果。使用下列数据：,Step2:Define Factors & Levels步骤2：确定因子与水平,Step 2：State the factors and levels of interest, create a Minitab experiment data sheet, Put the values of each response variable in one

36、 column. Each input and output has a separate column. 第二步：说明所关注因子与水平，建立一个Minitab 实验数据表，将每个相应变量的数值置于一列内。每个输入与输出列于不同的列。,Stat DOE Create Factorial Design Choose 选择Choose “2”选择“2”Choose “Designs”选择“Designs”,Step3: Tabulate the findings步骤3：记录结果,数据录入Minitab,Step4: Amalyze the data步骤4：分析数据,Menu: StatDOEAna

37、lyze Factorial Design,The model Yield=f(Consistence,Catalyze) includes both factors and their interaction模型良率f(浓度，催化剂），包含两个因子与其交互作用,Step5:Interpret the result步骤5:理解结果,Factorial Fit: Yield versus Cata, Conc Estimated Effects and Coefficients for Yield (coded units)Term Effect CoefConstant 37.000Cata

38、-12.000 -6.000Conc 4.000 2.000Cata*Conc -18.000 -9.000Analysis of Variance for Yield (coded units)Source DF Seq SS Adj SS Adj MS F PMain Effects 2 160.0 160.0 80.00 * *2-Way Interactions 1 324.0 324.0 324.00 * *Residual Error 0 * * *Total 3 484.0,Not enough data(degrees of freedom) to calculate无足够的数

39、据（自由度）来计算,Step6：Plot Chart步骤6:制作图表,Menu: StatDOEAnalyze Factorial Design,Step7：Pareto/Normal Plot步骤7：柏拉图/正态图,There no line on the plot defining statistical significance 图中没有线显示统计的显著性 BUT the AB interaction is the largest contributor, followed by pressure & temperature 但AB交互作用是最大的因素， 然后才是催化剂和浓度 There

40、 no label on the plot defining statistical significance 图中无标识显示统计显著性,Step8: Main Effects Plots步骤8：主效果图,Menu: StatDOEFactorial Factorial plots,Step8: Main Effects Plots步骤8：主效果图,Main Effects Plot(data means) for Yield Note: 备注 The main effect of a factor is defined as the average change in the output

41、variable produced by a change in the levels of a factor. 一个因子的主效果是由于 改变因子的水平而导致输出的 变量的平均变化。 As Consistence in changed from level one to level two the average sample yield increases from 24 to 31 随着浓度从水平一达到水平二样本的平均良率从24增加到31 Make an equivalent statement for Catalyze 对催化剂作出同等的陈述,Step8: Interaction Plo

42、ts交互作用图,Menu: StatDOE Factorial Factorial plots,note:备注：In some experiments it was found that the main effect between the levels of one factor is not the same for different levels of the other factors. In this case we have an interaction between factors.在有些实验中，我们发现对于其他因子的不同水平，一个因子的水平间的主效果并不相同。在这种情况下

43、因子间具有交互作用。,In this case there is clearly an interaction between consistence and catalyze as far as yield2 is concerned-recall what the pareto chart showed.这里，浓度与催化剂之间存在着影响良率2的明显的交互作用-回想柏拉图的显示。,STEP8:INTERACTION PIOT步骤8：交互作用图,Introduction To 2k Factorial Experiment 2k 因子实验简介,Repeats, Replicates & Ran

44、domization 重复、复制和随机化,Repeats & Replicates 重复和复制,Definitions 定义Repeat-the same experiment conducted more than once in a sequential manner 重复-相同的实验一个接一个连续。Replicate-whole or part of the experimental design conducted more than once at different times and even in different orders 复制-整个或部分实验设计实施多次，在不同的时期

45、，也可能以不同的次序。,Repeats & Replicates 重复和复制,Advantages 优点Repeats improve signal-to-noise ratio. Especially if gauges are incapable . Repeats enable us to calculate the sample & analysis variance 重复有助于改善信噪比，尤其是当量仪的检测能力很低时-它能使我们计算样本以及分析方差。Replicates are even more valuable . Replicates enable us to estimate

46、 the total variability affecting the experiment e.g. set-up differences and therefore, we can have an estimate of the errors of the effects of the variables 复制就更有用-它能使我们估计影响实验的总变异。例如：设定差异，我们因此可以估计变量效果的误差。,Analysis with Replicates复制分析,Assuming we re-run the earlier example(Yield) with two replicates

47、假如我们已经对较早的例题（良率）做了两次复制The data sets will look like this 数据组如下（they are also in Expt 2 2 Replicates.mtw).,Consistence 1浓度 1,Consistence 2浓度 2,Cata 1催化剂 1,Cata 2催化剂 2,Conc 1,Conc 2,Catalyze 1,Catalyze 2,34,54,40,22,32,54,38,24,Analysis with Replicates复制分析,Analysis with Replicates复制分析,Factorial Fit: Yi

48、eld versus catalyzer, consistence Estimated Effects and Coefficients for Yield (coded units)Term Effect Coef SE Coef T PConstant 36.750 0.6614 55.56 0.000catalyzer -11.500 -5.750 0.6614 -8.69 0.001Consistence 1.500 0.750 0.6614 1.13 0.320catalyzer*consistence -17.500 -8.750 0.6614 -13.23 0.000S = 1.

49、87083 R-Sq = 98.44% R-Sq(adj) = 97.26%Analysis of Variance for Yield (coded units)Source DF Seq SS Adj SS Adj MS F PMain Effects 2 269.00 269.00 134.500 38.43 0.0022-Way Interactions 1 612.50 612.50 612.500 175.00 0.000Residual Error 4 14.00 14.00 3.500 Pure Error 4 14.00 14.00 3.500Total 7 895.50,现

50、在我们可以评估统计显著性,Analysis with Replicates复制分析,On the Pareto plot we can find the line indicating the significant effects to its right 在柏拉图中我们可以看到说明有 显著效果的直线在其右侧 On the normal plot we can find the annotation forthose with significant effects在正态图中我们可以看到有显著效果的标注,Analysis with Replicates复制分析,The main effect