6Sigma项目运作实例74

1、6 Sigma项目运作实例如何定义一个项目？ 项目定义是由冠军来完成的。我们简单介绍以下项目是如何定义的。1 确定主要商业问题：a目标b目的c 可交付使用的2对与生产来说： a 循环时间 b 质量 /缺陷水平 c 耗费3项目的选择a选择项目的工具a1 宏观图a2 Paretc图分析a3 鱼骨图a4因果矩阵图b项目的标准（评估）b1 减少缺陷的 70%b2 第一年节省 $175Kb3项目完成周期为4个月b4最少的资金总额b5黑带的第一个项目必须满足培训目标6 Sigma项目运作实例-定义阶段-我们在定义阶段做什么我们在定义阶段需要做什么？1，完成项目陈述。2，完成项目预测节省金额。3，完成问题陈

2、述：3.1 问题是什么？3.2 在哪里和什么时间发现的？3.3 问题将涉及哪些工序？4，5，6，7，8，3.4谁将受到影响？3.5问题的严重程度是什么？3.6你是如何得知这些的？ 绘制宏观图。 描述项目的主线。 完成目标陈述。组成项目小组，列出小组成员。完成财务评估。6 Sigma 项目运作实例 - 定义阶段 -如何进行项目问题陈述如何进行问题陈述？分六个方面进行问题陈述：1问题是什么？2在哪里和什么时间发现的？3问题将涉及哪些工序？4 谁将受到影响？5问题的严重程度是什么？6你是如何得知这些的？6 Sigma 项目运作实例 - 定义阶段 -如何绘制宏观图如何绘制宏观图 ?绘制宏观图的顺序：

3、供应商 -输入-工序 -输出-客户6 Sigma 项目运作实例 - 定义阶段 -项目的目标陈述要点项目的目标陈述要点 :1,目标陈述 2，计算方法日FMFMHATBilALHATBilAL EKFFBfiEKFFBfi UbrAlCovnUbrAlCovn 量具偏差（C measurement system ）真实值 精确度（量具偏差）观察值 测量系统的精确度（ P）：精确度包括重复性和复制性 测量系统的指标 -PT: 精确度与公差之比 -P/T 代表量具偏差占公差的部分 此部分通常用百分数来表示 最好的情形 P/T10%- 可接受的 P/TMake Patterned Data 准备量具研究

4、数据表 让员工测量所有无标识，随机次序的样本 分别让另外其他员工测量所有无标识，随机次序的样本 重复第五步及第六步循环三次。也尽量打乱员工次序当量具样本中的偏差代表真实工艺偏差时，P/TV 等于 P/SV定量型量具 R&R -使用方法说明 :此部分通常用百分率来表示最好情形 10% 量具可接受条件 4 ，可接受的： 3-4P/T 和 P/TV 的用处 :P/T （% 公差） 最常用于测量系统的精确度评估 将量具的精确度与公差要求进行对比 如果量具用来对生产样品进行分类 P/T 还可以P/SV （ %R&R ）-6 Sigma 首选 测量量具与量具研究偏差相比其性能如何 最适合进行工艺改进的评估

5、 使用时应小心。量具研究偏差并不一定代表真实的工艺偏差P/TV （ %R&R ） -6 Sigma 首选 测量量具与工艺偏差相比其性能如何 使用时应小心。量具研究偏差并不一定代表真实的工艺偏差8，用 Minitab 作下列两个分析StatQuality ToolsGage R&R Study(Crossed) StatQuality ToolsGage Run Chart 9，对测量系统能力研究结果进行分析10 ，确定适当的后续措施 定量型量具 R&R -Minitab 实例 : 一个黑带想对冶金工艺使用的温度表进行量具研究，他严格按前面一页的方法进行 实验，并将数据输进了 R&Rexampl

6、e.xls 中。运用 Minitab 分析数据并评估量具能力StatQuality ToolsGage R&R Study(Crossed).Minitab 量具 R&R 研究 -选项 输入该工艺公差和偏差，如果你想要 Minitab 帮你计算 P/T 和 P/TV 的话。 Minitab 默认计算 P/SV 量具 R&R 结果 -ANOVA 表 s for the space programP 值是变化源在统计上对总偏差影响是否不显著的概率 在这个例子中，部件和员工均为显著的偏差源另外，你能用 Minitab 的计算器计算总的平方和吗？这个值代表什么意思？6 Sigma 项目运作实例 - 分

7、析阶段 -失效模式及后果分析失效模式及后果分析Failure Modes and Effects Analysis (FMEA) Background:Failure Modes and Effects Analysis (FMEA) First developed in the 1950Appropriated by NASA in the 1960defect ”?Ford Motor Company was the first North American company to widely implement the use of FMEAsTypes of FMEASystem -

8、Top-level, early stage analysis of complex systems Design - Systems, subsystems, parts & components early in designstageProcess - Focuses on process flow, sequence, equipment, tooling, gauges, inputs, outputs, set points, etcWho? When?Who constructs the FMEA?The Black Belt is the team leader.The pro

9、cess owner inherits the finished FMEA.Use the process mapping, C&E matrix team.May need to add a rep from quality, a supplier, reliability When should the FMEA be constructed?After the process map & the C&E matrixBefore or after the control plan, depending on the maturity of the processWhy?Warm up e

10、xercise:You have 60 seconds to document:What would you want to know about aFor the process:FMEA improves the reliability of the process An FMEA identifies problems before they occurFMEA serves as a record of improvement & knowledge For the future:FMEA helps evaluate the risk of process changesFMEA i

11、de ntifies areas for other studies - multi-vari, ANOVA, DOE图形技术分析 :6s Process FMEA - TerminologyFMEA: A systematic analysis of a process used to identify potential failures and to prevent their occurrencePotential Failure mode: The manner in which the process could potentially fail to meet the proce

12、ss requirements.Potential Failure Effect: The results of the failure mode on the customer.Severity: An assessment of the seriousness of a failure mode. Severity applies to the effects only.Cause: How the failure could occur, described in terms of something that can be corrected or controlled.Occurre

13、nce: The likelihood that a specific failure mode is projected to occur.Detection: The effectiveness of current process controls to identify the failure mode (or the failure effect) prior to occurring, prior to release to production, or prior to shipment to the customer.RPN - Risk Priority Number: Th

14、e product of Severity, Occurrence & DetectionFMEA ExamplesPlating ExampleAn aerospace plating company was shipping product to its customers with nickel plating that was too thin. Parts were failing corrosion testing at the customer.Shipping ExampleThe shipping department of an electronics company is

15、 unable to ship an assembly without its clam shell protective packaging. This causes occasional late shipments to the customer.In the following examples, a single line from the FMEA is used as an illustration for each of the above examples.CTC CT +=Graphical MethodsProcess VariationNoise variation f

16、rom discrete inputsDifferent operators, machines, setupsDifferent days, shiftsDifferent batches, mixtures, raw materialsNoise variation from continuous inputs Ambient temperature, humidity, pressureWear, drift, erosion, chemical depletion) ,., , ( 2 1 k Process x x x f y =) ,., , ( 2 1 k Noise n n n

17、 f +Intentional Unwanted The equation just means that any output is determined by the intentional process settings and the unwanted noise variation.Common Classification of Noise VariablesPositional (within part variation) Variation within a single production unitThickness variation across a plated

18、partVariation across a unit containing many partsVariation across a semiconductor wafer with many dieVariation by position in a batch processCavity-to-cavity variations in an injection molding operationCyclical (part-to-part variation)Variation between consecutive production unitsBatch-to-batch aver

19、age differences - consecutive batchesTemporal (time-to-time variation)Shift-to-shift, Day-to-Day, Setup-to-setupVariation not accounted for by Positional or CyclicalTemporal Cycli cal Positional Noise 6Grap hical An alysis - Exam pieInjection molding is used to make a type of socket, four pieces at

20、a time, one piece per slot. Measurements of the sockets consist of thickness values in excess of 5.00 millimeters. The gauges measure in hundredths of a millimeter. The specification i s 11 6.Four times a day the supervisor would go to the press and gather up the parts produced by five consecutive c

21、ycles of the press. Since each cycle produced four parts, he would have 20 parts to measure every two hours. The supervisor kept track of the cycle and the cavity from which each part came and wrote his twenty measurements in an array like this:The supervisor collected samples four times a day for f

22、ive days (20 samples total, 20 parts per sample). Calculate the process capability and use a Multi-Vari chart to help determine sources of variation.A BCDES118 19 20 19 21S213 16 14 13 13S310 11 13 10 13S411 12 13 13 13Exercise: Determine CapabilityUsing Minitab, analyze the Thick data in SocketData

23、.mtw for process capabilityRemember, the specifications are: 11What is the short-term process capability? What is the long-term process capability?Are these good or bad values?Remember, one goal of Six Sigma is to reduce variation, which will increasecapability. It is always important to understand

24、the process capability.Preparing Data for Marginal Plot byMarginal plots require both variables to be defined numerically We need to convert “Slot ” to a numeric column firstSlot ”Step 1: ConvertManipCodeText to Numeric Manip Code Text to NumericSlot ”Multi-Vari Analysis - DefinedA graphical analysi

25、s toolUses logical sub-groupingAnalyzes the effects of discrete XA capability and process analysis toolcontisnuoonus Y sData collected for a relatively short timeData can estimate capability, stability, and y = f(x) Major focus: study uncontrolled noise variation firstVariation in noise variables pr

26、oduces chronic and acute mean shifts, changes in variability, and instabilityNoise variation must be reduced or eliminated in order toleverage the important controllable variables systematically Multi-vari analysis is a very useful toolfor graphically identifying sources of variation, especially noi

27、se variation. Later this week, we will be studying correlation & regression (an analysis of the effect of continuous X s on continuous Y s), analysisof variance (ANOVA) and the General LinearModel (GLM), both numerical analyses of variance data.Multi-vari analyses will help identify thevariation sou

28、rces with the purpose of reducing or eliminating them.A Multi-Vari Plan 1. Clearly state the objective2. List the Xs and Y s to be studied3. Ensure measurement system capability4. Describe the sampling plan5. Describe the data collection & storage plan (who, what, when, etc.)6. Describe the procedur

29、e and settings used to run the process7. Assemble and train the team. Define responsibilities8. Collect the data9. Analyze the data10. Verify the results 11. Draw conclusions. Report results. Make recommendationsInjection Molding Example1. Clearly state the objectiveDetermine the process capability

30、of the injection molding process Determine the major sources of noise variation2. List the Xs and Y s to be studiedOutput: ThicknessInputs: Cavity (slot), cycle, sample3. Ensure measurement system capabilityAn MSA was conducted and the system was found capable4. Describe the sampling planOne sample

31、from each slot, five consecutive runs, four times a day for five days.5. Describe the data collection & storage plan (who, what, when, where, etc.)The supervisor collected the data and entered it in a worksheet6. Describe the procedure and settings used to run the processStandard, constant process s

32、ettings.7. Assemble and train the team. Define responsibilities.For a small project, the supervisor did all the work8. Collect the data.The data are in Minitab worksheet SocketData.mtw9. Analyze the dataAnalysis is on the following slides中心限理论 :Central Limit TheoremQ: Why Are So Many Distributions N

33、ormal?Why is something this complicated so common?Science has shown us that variables that vary randomly are distributed normally. So a normal distribution is actually a random distribution.Another reason why some distributions are normally distributed is because measurements are actually averages o

34、ver time of many sub-measurements. The single measurement that we think we are making is actually the average (or sum) of many measurements. The Central LimitTheorem, discussed in the following slides, provides an explanation of why averages of non-normal data appear normal.from the mainDice Demonst

35、ration (Integer Distribution)What does a probability distribution from a single die look like?What is the mean?What is the standard deviation?Construct a dataset in MinitabSelect Calc Random Data Integer menuGenerate 1,000 rows of data in C1: Min = 1, Max = 6Use Minitab s Graphical Summary routine f

36、or analysisStat Basic Statistics Display Descriptive StatisticsMinitab Output (Typical)The probability distribution of the possible outcomes of the roll of a single die is obviously non-normal.A perfect distribution would have had all six bars exactly equal, but even with10,000 data points, there is

37、 still some differences in the histogram. If a better estimate is required, a different data set could be constructed with exactly equal counts of each possible outcome. Try it and see if the numbers are any different.Sampling a Non-normal Distribution- ExerciseEach person in the class is to toss a

38、single die sixteen times and record the data.Calculate the mean and standard deviation of each sample of sixteenRecord the means and standard deviations from each person in the class in a Minitab worksheetfromUse Minitab s Graphical Summary routine for analysisStat Basic Statistics Display Descripti

39、ve Statistics Alternately, a sample of sixteen throws of the dice can be simulated in Minitab asfollows:Select: Calc Random Data Integer the main menuGenerate 16 rows of data in C1: Min = 1, MaxAnalyze the Sample DataWhat is the mean of the sample averages?Mean 3.5What is the standard deviation of t

40、he sample averages?Sigma M0.4Is the distribution normal?What is the p-value?What is the relationship between the average of the sample means and the population average?What is the relationship between the sigma of the averages and the sigma of the individuals?The Central Limit TheoremFormal Definiti

41、on:If random samples of n measurements are repeatedlydraw n from a popu lati on with a fin ite mean 卩卩卩 nd a sta ndard deviation TTT T , then, when n is large, the relative frequency histogram for the sample means (calculated from the repeated samples) will be approximately normal with amean 卩 卩卩卩 a

42、nd a standard deviation equal to the population standard deviation ,(T , divided by the square root of n.(Note: The approximation becomes more precise as n increases.)Cen tral Limit Theorem - ExerciseFrom a Minitab analysis of the uniformly distributed data:For an exercise, verify that the Central L

43、imit Theorem is valid for this uniform dataVariable N Mean StDev n=1 (Individuals) 10000 -0.00331 0.57918n=2 (Means) 10000 0.00259 0.40613 n=5 (Means) 10000 -0.00113 0.25953 n=30 (Means) 10000 -0.00237 0.10559相关性及简单线性回归Regression & CorrelationIntroductionUsed for quantitative variables (Xs and Y s)F

44、or review: What is the focus of Six Sigma?Q. What does this equation represent?A. A mathematical model of a processPurpose of Regression: to predict Y from a setting of x Examples:Distance = f(acceleration, initial velocity, time) Product yield = f(concentrations of reactants) Hardness = f(alloy, an

45、neal temperature) ( x f Y =Remember, the focus of Six Sigma is to determine the defining equation of the process. It is to identify the important input variables, determine the relationship to the outputs, determine the optimum values of the critical inputs and then control the inputs at the optimum

46、 settings.To do this, the Black Belt must know the relationship between the inputs and the outputs. This module discusses linear modeling techniques for identifying the relationship between continuous variable inputs and continuous variable outputs.A Simple Linear ModelLinear equations require conti

47、nuous input and output variables. One other assumption is that the independent variable (input) is known and fixed and that all of the variation is in the dependent variable (output). This is not usually the case, but often the inputs are settings on dials or gauges or software that seems fixed and

48、invariable. Many times the variation in the output is a function of the inability of the input controller to hold the input at the same value.Collecting Data (y & x) - A Few ThoughtsPg 8 ?March 01, Breakthrough Management Group. Unpublished proprietary work available only under license. All rights r

49、eserved. March 16, 2001Make sure the process settings cover the likely production range (but not too far).Too great a range points outside the normal range may have too great an effect on the model.Too small a range Error term may dominate the fit.Take several replicates at each input setting (x).Re

50、plicate runs help increase the model accuracy.Randomize runs whenever practical.Run order is often significant factor.The output (y) at different inputs (x 抯 ) is not always independent of previous settings.A good spread in the data is required for a good model. Consider two examples: All of the dat

51、a is collected at the normal process settings. In this case, regression will try to fit a linear model to a combination of random process variation and random measurement variation. The results will be of no value.The second case is when most of the data is clustered around the standard settings exc

52、ept for a couple of points at the extreme ranges. In this case, the extreme points control the fit of the model. If one of the extreme points is a flyer, then the model will be in error due to the flyer.The ideal case is for the Black Belt to collect a range of data throughout the process space.置信区间

53、 :Confidence IntervalsA population is the set of all measurements of interest to the experimenter A sample is a subset of measurements selected from the population An inference is a statement about a population parameter based oninformation contained in a sample Two types of inference s reaction to

54、aEstimationA poll has been devised to determine the public new political scandal. The purpose is to estimate the reactionof all Americans by polling a representative sample Hypothesis testingA vaccine for Lyme disease has been developed but the rate of negative side effects is 1.45%. A new vaccine h

55、as been developed and it is desired to know if the rate of negative side effects is lower than 1.45%.The other branch of statistics is descriptive. Its purpose is merely to describe a set of measurements.Inferential statistics is used to guess whatGod knows about a population from a sample.Within in

56、ferential statistics, there are two types: estimation and hypothesis testing.Estimation is trying to guess the population statistics from a sample. Hypothesis testing concerns evaluating a sample statistic and comparing it to some hypothetical value.Estimates and the CLTWhat is the best estimate of

57、the population mean using sample data? The sample mean!How good of an estimate is the sample mean?What factors influence the accuracy of the estimate of the mean from sample data?Recall that:The variation in the distribution of sample means is a function of the variance of the Population and the sam

58、ple size! n Pop X /What About Small Samples?If the population standard deviation is known (it almost never is) use the previous formula for small samples, tooIf the population sigma is unknown (it usually is): The estimate for standard deviation (s) is usedThe t-distribution is used instead of the n

59、ormal (Z) distributionQ: What is a t-distribution?The t-distribution is a family of bell-shaped (normal-like) distributions that are dependent on sample sizeThe smaller the sample size n, the wider and flatter the distributions t X n n 1 , 2 / 1 , 2 / + a a 5 and nx(1-p)5尸 nxp and(r2 = nxp x(1 -p)Bi

60、nomial distributions are discussed in almost every statistics textbook. Calculations with them is not necessarily difficult, but it is tedious if it must be done manually. Minitab has routines, however, that greatly simplifies the calculations.If the binomial approximation applies and the data can b