项目运作实例

（六西格玛管理）项目运作实例《6Sigma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。谢谢阅读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a2Pareto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《6Sigma项目运作实例》->《定义阶段》->我们在定义阶段做什么精品文档放心下载------------------------------------------------------------------------感谢阅读---------------------------感谢阅读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？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？4，绘制宏观图。5，描述项目的主线。6，完成目标陈述。7，组成项目小组，列出小组成员。8，完成财务评估。《6Sigma项目运作实例》->《定义阶段》->如何进行项目问题陈述精品文档放心下载------------------------------------------------------------------------精品文档放心下载---------------------------感谢阅读如何进行问题陈述？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？《6Sigma项目运作实例》->《定义阶段》->如何绘制宏观图谢谢阅读------------------------------------------------------------------------精品文档放心下载---------------------------感谢阅读如何绘制宏观图?绘制宏观图的顺序：供应商->输入->工序->输出->客户感谢阅读《6Sigma项目运作实例》->《定义阶段》->项目的目标陈述要点感谢阅读------------------------------------------------------------------------感谢阅读---------------------------谢谢阅读项目的目标陈述要点:1,目标陈述2，计算方法3，全年节省额确定TeamMembers成员:1，小组成员要包括技术人员2，包括维修人员（如果需要）3，包括操作者4，小组人员不超过5人(特殊情况除外)。《6Sigma项目运作实例》->《测量阶段》->如何进行项目描述精品文档放心下载------------------------------------------------------------------------精品文档放心下载---------------------------谢谢阅读如何进行项目描述:1，目标陈述2，Metric图3，月节省额如何绘制工艺流程图:召集小组:流程图绘制是集体努力的结果小组包括：流程负责人：项目结果的负责人工程部门-工艺，产品，设计及设备生产部门-操作员，各班次主管，培训员，操作班长，维修技师精品文档放心下载流程图所需信息脑力风暴观察/经历操作手册工程标准，工作指示六大方面（人，机，方法，测量，材料，环境）确定工艺范围:范围至观重要越窄越好！大量工艺步骤可能表明项目定义不佳或问题源于几个项目问题藏于问题中若问题可以由粗略分析解决，管理层会去做绘制可执行的工艺图你能确认缺陷来源吗？我们能有意识地改变输入指标变量吗？有意识的改变输入指标变量能直接影响输出结果吗？工艺流程图（PFD）:6Sigma工艺流程图的要素：所有工艺步骤包括隐形工厂数据采集点所有设备/工具各步骤表明增值性（VA）和非增值性（NVA）控制标准文件用标准符号绘制工艺流程：在MicrosoftOfficeTM等软件中可找到感谢阅读工艺流程图-程序:绘制工艺记载的工艺步骤包括所有检查点，测量指标和传运步骤确认所有数据采集点标示各工序标准控制文件各步骤标明为增值性（VA）或非增值性（NVA）确认各工艺步骤的X和Y标明可能消除的NVA步骤加入并标明“隐形工厂”工段标明为VA或NVA，标明可能消除的步骤标明须指定控制文件的步骤加入DUP，RTY，COPQ，循环周期等估计值标明须进行量具和工艺能力研究的步骤通过直接或秘密观察确认准确性文件记录/确认:文件记录的工艺流程首先绘制记录下来的工艺加入并标明隐形工厂步骤当所有步骤展示出来后，流程图就属于实际工艺确认流程图的准确性至关重要项目组必须花时间观察工艺秘密进行。观察导致行为改变确认实际工艺设置与记录的设置相同跨班跨机器观察工艺如何绘制工艺流程细图:工艺流程细图：6Sigma工艺流程图要素：工艺或产品是输出指标Y和输入指标X标准上下限和标准控制文件所用设备/工具绘制工艺流程细图工艺流程细图必须依工艺流程图而画。更改其一应在另一个中反映出来。谢谢阅读应使用最新的控制文件标明所有隐形工厂步骤的输入输出指标工艺流程细图程序：1，从流程图中列出工艺步骤2，加入下列内容输出指标输出指标标准，若存在输入指标输入指标标准，若存在工艺能力或量具能力指标所用设备3，标明隐形工厂步骤4，标明各步骤属于增值性（VA）或非增值性（NVA）精品文档放心下载5，标明各步骤属于可控性的（C）或噪音性的（N）6，确认各设备的输入指标设置7，确认流程图准确性8，必要时更改及更新流程标准限和工艺能力：工艺及产品标准加入X的工艺设置加入Y的标准限标明未记录的Y和可控的X测量系统加入量具重复性及复验性数据标明须做测量系统分析的量具工艺能力展示RTY，DPU，CPK等的估计值标明哪些工艺步骤数据陈旧或不完整而需做工艺能力分析更改及更新：更改记住：6Sigma的目标之一是找出：Y=F（X）随着对工艺的深入了解，更新工艺图以反映新的信息更新项目最终成果之一是现有的工艺的流程图更新工艺图以反映任何工艺改变加入测量系统分析及工艺能力分析结果精简制造与5S:精简制造例似于日本的5S精简制造与5S:鱼骨图:鱼骨图一种系统确认所有可能导致问题(后果)产生的原因方法。谢谢阅读构造鱼骨图的方法：1.陈述问题，并置于右边的方框内2.朝方框画一水平箭头。3.在箭头上下写上传统因素类型名称*或你怀疑是的类型名称。用感谢阅读直线连到箭头线上。4.在各主要的类型范围内，集思广益并列出所有可能引起问题发生的因子。谢谢阅读5.进一步优化：对各种详细列出的因子再列出其输入变量。精品文档放心下载*6m--man,machine,method,measurement,mothernature(environment)感谢阅读(6M:人员，机器，测量方法，原材料，环境)定性测量系统研究:定性型量具R&R-术语:检验员分数（%）-在定性型R&R检验过程中，检验员前后一致的比例谢谢阅读定性数据--定性（合格/不合格）数据，可用来做记录和分析谢谢阅读定性型测量系统--把每个部件与标准进行比较，从而决定部件是否符合标准的测量精品文档放心下载系统。消费者偏见--员工倾向把合格产品判为废品%--在定性型R&R精品文档放心下载也一致的比例。标准值--由一个高准确度量具所测的平均值生产者偏差--员工倾向于把不合格（有缺陷的）产品判为合格感谢阅读筛选--用检验方法对产品进行100%的评估筛选有效性--定性量具系统区别合格与不合格的能力使用定性型量具R&R的目的:工艺评估评估你的检查标准或工作质量标准与客户要求的一致性确定所有班次，机器等的检查人员是否使用相同标准来决定合格与不合格感谢阅读量化检查人员准确重复其检验结果的能力确定检查人员与“已知标准”的一致性及倾向于消费者偏差还是生产者偏差感谢阅读工艺改进发现是否需要培训，缺少工序或缺乏标准定性型量具R&R的方法:准备从工艺中挑选30个部件，50%合格，50%次品可能的话，挑选近乎于合格和不合格样本挑选检查人员--受过完全培训的和有资格的实施要求每一个检查人员随机地检查部件，决定合格与不合格并重复此检查精品文档放心下载评估将结果载入文件如果必要，采取适当的措施调整测量工艺重做R&R试验，核实调整后的有效性定性型量具R&R--结论:检查员分数如果大多数员工都是100%，则培训作用极为有限筛选有效分数如果员工本身前后一致但是相互间不一致，则重新培训可帮助减少错误。谢谢阅读标准化分数如果员工时常与标准不一致，则需要改变测量系统（或局部标准）感谢阅读工艺能力分析:为何测量工艺能力?使我们根据数据分配资源！（这可不常见！）缺陷率得以量化确认可以改进机会分析工艺能力可使组织预测其所有产品和服务的真实质量水平感谢阅读确认工艺发生问题的本质-居中程度或分散度工艺能力研究连续数据离散数据1.确认标准限1.确认标准限2.收集数据2.收集数据3.确定短期偏差3.决定：短期还是长期？4.计算工艺能力指标：（通常是长期）a.短期：4.计算工艺能力指标：ⅠZU,ZLa.长期：ⅡCPⅠPPMⅢCPKⅡSigma水平ZLTⅣSigma水平ZSTⅢPPKb.长期：b.短期：ⅠSigma水平ZLTⅠSigma水平ZST精品文档放心下载ⅡPPKⅡCPK工艺能力计算实例一位技师负责医院设备的蒸汽杀菌过程。其中一个关键参数是控制“暴露”阶段的谢谢阅读温度。设备室温度和在最小饱和蒸汽浓度的周期时间决定杀菌程度在整个设备室维持前后谢谢阅读一致的温度范围很重要。第一步：确认标准这一阶段常被忽视。我们如何设定标准？设计部门-设计蓝图设计部门如何得到各项要求？工艺部门-标准由工艺以前能够做到的或开始使用时的能力定谢谢阅读这想法有错吗？客户我们总是对客户说可以吗？对上例而言：设备室目标温度是1250C±1.50C第二步：采集数据-合理编组应采集数据获得“短期”性能，如可能，“长期”性能通过固定时间区间采集一系列快照型数据应按合理编组采集快照数据什么是合理编组？从流程连续不断产生的零件或产品中合理取样以期捕获最小工艺偏差的方法感谢阅读组内偏差反映一般偏差平均标准差（用一种均方差方法平均）是对工艺应有能力的良好估计精品文档放心下载第二步：采样-例子例子：技师在暴露周期从控温探针读数中选取五个数据，并从连续七个杀菌运转周谢谢阅读期采集数据，数据列在ChamberTemp2.mtw文件的杆ChambTemp栏中精品文档放心下载第三步：确定短期偏差多数现有数据居于长期和短期之间为了估计真实短期数据：小心设计工艺能力研究方法确保编组策略合理某些工艺无法研究短期数据如低产量和长循环周期工艺采样昂贵或难以取样的工艺第三步：短期还是长期？一个指导思想：如果允许80%的输入指标在其自然范围内浮动，数据就是长期的短期及长期：组内及组间平均标准差与总标准差对各组方差取平均值可得到组内标准差的平均值总标准差由所有数据算出，不计编组平均标准差不计组间偏差，而总标准差计入组间偏差平均标准差是对组内标准差的最佳估计长期和短期指导思想短期数据在有限的周期或间隔采集数据在有限的机器和员工中采集差不多总是连续变量长期数据在很多的周期，间隔，机器和员工中采集可以是离散或连续数据离散数据几乎都是长期性的第四步：计算ZU和ZL:Z-分数提供统计数据以便用共同语言交流提供一个与标准上下限相关的工艺性能指标第四步：计算CP例子工艺平均值为325标准差为15标准上限为380，下限为270CP是多少？若平均值为355而标准差不变CP又是多少？Cp与工艺应有能力Cp是工艺应有能力的良好指标工艺应有能力--一个工艺观察到的最好的短期性能机会--工艺长期性能与工艺应有能力间的差距Sigma项目--致力与把长期性能与工艺应有能力的差距缩短感谢阅读定量测量系统研究:定性型量具R&R--模型测量系统μ总和=μ工艺+Δμ测量系统偏离度：观察值=实际真实值+测量偏移通过“校准计划”Δ测量偏移来评估真实值测量值（准确度）测量系统σ2总合=σ2工艺+σ2测量系统偏离度：观察的偏差=工艺的偏差+测量的偏差通过“校准计划”来评估真实值测量值（准确度）测量系统的指标:量具R&R结果->量具偏差（σmeasurementsystem）感谢阅读真实值精确度（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/T<10%--可接受的P/T<30%谢谢阅读测量系统的测量方法--P/TV:精确度与总偏差之比代表量具偏差占据总偏差的部分此部分通常用百分率来表示最好情形<10%量具可接受条件<30%测量系统的指标--分辨指数:分辨指数是测量系统从工艺数据中可辨认的不同读数的数量感谢阅读分辨指数是一个分辨率指标分辨指数是重复性和复制性的函数最好情形：>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）--6Sigma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感谢阅读P/TV（%R&R）--6Sigma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谢谢阅读当量具样本中的偏差代表真实工艺偏差时，P/TV等于P/SV谢谢阅读定量型量具R&R--使用方法说明:1，校准量具或确认最近校准仍然有效2，收集10个代表工艺偏差全部范围的样本3，从每日使用这种测量方法的员工中选出检验员4，运用Clac>MakePatternedData>准备量具研究数据表感谢阅读5，让员工测量所有无标识，随机次序的样本6，分别让另外其他员工测量所有无标识，随机次序的样本精品文档放心下载7，重复第五步及第六步循环三次。也尽量打乱员工次序8，用Minitab作下列两个分析Stat>QualityTools>GageR&RStudy(Crossed)精品文档放心下载Stat>QualityTools>GageRunChart精品文档放心下载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感谢阅读实验，并将数据输进了R&Rexample.xls中。谢谢阅读运用Minitab分析数据并评估量具能力Stat>QualityTools>GageR&RStudy(Crossed)...感谢阅读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。精品文档放心下载Minitab默认计算P/SV量具R&R结果--ANOVA表P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？感谢阅读《6Sigma项目运作实例》->《分析阶段》->失效模式及后果分析谢谢阅读------------------------------------------------------------------------谢谢阅读---------------------------精品文档放心下载失效模式及后果分析:FailureModesandEffectsAnalysis(FMEA)感谢阅读Background:FailureModesandEffectsAnalysis(FMEA)精品文档放心下载Firstdevelopedinthe1950’sAppropriatedbyNASAinthe1960’sforthespaceprogram精品文档放心下载FordMotorCompanywasthefirstNorthAmericancompanytowidely精品文档放心下载implementtheuseofFMEAsTypesofFMEASystem–Top-level,earlystageanalysisofcomplexsystems感谢阅读Design–Systems,subsystems,parts&componentsearlyindesign谢谢阅读stageProcess–Focusesonprocessflow,sequence,equipment,tooling,精品文档放心下载gauges,inputs,outputs,setpoints,etc感谢阅读Who?When?WhoconstructstheFMEA?TheBlackBeltistheteamleader.谢谢阅读TheprocessownerinheritsthefinishedFMEA.精品文档放心下载Usetheprocessmapping,C&Ematrixteam.谢谢阅读Mayneedtoaddarepfromquality,asupplier,reliability感谢阅读WhenshouldtheFMEAbeconstructed?谢谢阅读Aftertheprocessmap&theC&Ematrix感谢阅读Beforeorafterthecontrolplan,dependingonthematurity感谢阅读oftheprocessWhy?Warmupexercise:Youhave60secondstodocument:感谢阅读Whatwouldyouwanttoknowabouta“defect”?感谢阅读Fortheprocess:FMEAimprovesthereliabilityoftheprocess精品文档放心下载AnFMEAidentifiesproblemsbeforetheyoccur感谢阅读FMEAservesasarecordofimprovement&knowledge谢谢阅读Forthefuture:FMEAhelpsevaluatetheriskofprocesschanges谢谢阅读FMEAidentifiesareasforotherstudies–谢谢阅读multi-vari,ANOVA,DOE6sProcessFMEA--Terminology精品文档放心下载FMEA:Asystematicanalysisofaprocessusedtoidentifypotential精品文档放心下载failuresandtopreventtheiroccurrence感谢阅读PotentialFailuremode:Themannerinwhichtheprocesscould精品文档放心下载potentiallyfailtomeettheprocessrequirements.谢谢阅读PotentialFailureEffect:Theresultsofthefailuremodeonthe精品文档放心下载customer.Severity:Anassessmentoftheseriousnessofafailuremode.精品文档放心下载Severityappliestotheeffectsonly.感谢阅读Cause:Howthefailurecouldoccur,describedintermsofsomething谢谢阅读thatcanbecorrectedorcontrolled.感谢阅读Occurrence:Thelikelihoodthataspecificfailuremodeisprojected精品文档放心下载tooccur.Detection:Theeffectivenessofcurrentprocesscontrolstoidentify精品文档放心下载thefailuremode(orthefailureeffect)priortooccurring,priorto精品文档放心下载releasetoproduction,orpriortoshipmenttothecustomer.精品文档放心下载RPN--RiskPriorityNumber:TheproductofSeverity,Occurrence精品文档放心下载&DetectionFMEAExamplesPlatingExampleAnaerospaceplatingcompanywasshippingproducttoits感谢阅读customerswithnickelplatingthatwastoothin.Partswerefailing精品文档放心下载corrosiontestingatthecustomer.感谢阅读ShippingExampleTheshippingdepartmentofanelectronicscompanyisunableto谢谢阅读shipanassemblywithoutitsclamshellprotectivepackaging.This谢谢阅读causesoccasionallateshipmentstothecustomer.感谢阅读Inthefollowingexamples,asinglelinefromtheFMEAisusedasan感谢阅读illustrationforeachoftheaboveexamples.精品文档放心下载图形技术分析:GraphicalMethodsProcessVariationNoisevariationfromdiscreteinputs感谢阅读Differentoperators,machines,setups感谢阅读Differentdays,shiftsDifferentbatches,mixtures,rawmaterials感谢阅读Noisevariationfromcontinuousinputs精品文档放心下载Ambienttemperature,humidity,pressure精品文档放心下载Wear,drift,erosion,chemicaldepletion精品文档放心下载),...,,(21kProcessxxxfy=),...,,(21kNoisennnf+精品文档放心下载IntentionalUnwantedTheequationjustmeansthatanyoutputis谢谢阅读determinedbytheintentionalprocesssettings谢谢阅读andtheunwantednoisevariation.谢谢阅读CommonClassificationofNoiseVariables谢谢阅读Positional(withinpartvariation)谢谢阅读Variationwithinasingleproductionunit精品文档放心下载Thicknessvariationacrossaplatedpart感谢阅读Variationacrossaunitcontainingmanyparts谢谢阅读Variationacrossasemiconductorwaferwithmanydie感谢阅读Variationbypositioninabatchprocess谢谢阅读Cavity-to-cavityvariationsinaninjectionmoldingoperation谢谢阅读Cyclical(part-to-partvariation)谢谢阅读Variationbetweenconsecutiveproductionunits谢谢阅读Batch-to-batchaveragedifferences–consecutivebatches精品文档放心下载Temporal(time-to-timevariation)谢谢阅读Shift-to-shift,Day-to-Day,Setup-to-setup精品文档放心下载VariationnotaccountedforbyPositionalorCyclical感谢阅读2222TemporalCyclicalPositionalNoiseσσσ++=感谢阅读GraphicalAnalysis–ExampleInjectionmoldingisusedtomakeatypeofsocket,fourpiecesatatime,one感谢阅读pieceperslot.Measurementsofthesocketsconsistofthicknessvaluesin感谢阅读excessof5.00millimeters.Thegaugesmeasureinhundredthsofa感谢阅读millimeter.Thespecificationis11±6.谢谢阅读Fourtimesadaythesupervisorwouldgotothepressandgatherupthe精品文档放心下载partsproducedbyfiveconsecutivecyclesofthepress.Sinceeachcycle感谢阅读producedfourparts,hewouldhave20partstomeasureeverytwohours.感谢阅读Thesupervisorkepttrackofthecycleandthecavityfromwhicheachpart精品文档放心下载cameandwrotehistwentymeasurementsinanarraylikethis:Thesupervisorcollectedsamplesfourtimesadayforfivedays(20samples精品文档放心下载total,20partspersample).CalculatetheprocesscapabilityanduseaMulti-Vari谢谢阅读charttohelpdeterminesourcesofvariation.感谢阅读ABCDES11819201921S21316141313S31011131013S41112131313Exercise:DetermineCapability感谢阅读UsingMinitab,analyzetheThickdata精品文档放心下载inSocketData.mtwforprocesscapability感谢阅读Remember,thespecificationsare:11±6感谢阅读Whatistheshort-termprocesscapability?精品文档放心下载Whatisthelong-termprocesscapability?感谢阅读Arethesegoodorbadvalues?Remember,onegoalofSixSigmaisto精品文档放心下载reducevariation,whichwillincrease感谢阅读capability.Itisalwaysimportantto感谢阅读understandtheprocesscapability.精品文档放心下载PreparingDataforMarginalPlotby“Slot”谢谢阅读Marginalplotsrequirebothvariablestobedefinednumerically感谢阅读Weneedtoconvert“Slot”toanumericcolumnfirst精品文档放心下载Step1:Convert“Slot”Manip>Code>TexttoNumericManip>Code>TexttoNumericMulti-VariAnalysis–Defined谢谢阅读AgraphicalanalysistoolUseslogicalsub-groupingAnalyzestheeffectsofdiscreteX’soncontinuousY’s感谢阅读Acapabilityandprocessanalysistool谢谢阅读Datacollectedforarelativelyshorttime谢谢阅读Datacanestimatecapability,stability,andy=f(x)’s谢谢阅读Majorfocus:studyuncontrollednoisevariationfirst谢谢阅读Variationinnoisevariablesproduceschronicandacute感谢阅读meanshifts,changesinvariability,andinstability谢谢阅读Noisevariationmustbereducedoreliminatedinorderto感谢阅读leveragetheimportantcontrollablevariablessystematically精品文档放心下载Multi-varianalysisisaveryusefultool谢谢阅读forgraphicallyidentifyingsourcesof感谢阅读variation,especiallynoisevariation.Later精品文档放心下载thisweek,wewillbestudyingcorrelation&感谢阅读regression(ananalysisoftheeffectof感谢阅读continuousX’soncontinuousY’s),analysis谢谢阅读ofvariance(ANOVA)andtheGeneralLinear精品文档放心下载Model(GLM),bothnumericalanalysesof感谢阅读variancedata.Multi-varianalyseswillhelpidentifythe感谢阅读variationsourceswiththepurposeofreducing感谢阅读oreliminatingthem.AMulti-VariPlan1.Clearlystatetheobjective感谢阅读2.ListtheX’sandY’stobestudied感谢阅读3.Ensuremeasurementsystemcapability精品文档放心下载4.Describethesamplingplan5.Describethedatacollection&storageplan(who,what,when,etc.)精品文档放心下载6.Describetheprocedureandsettingsusedtoruntheprocess精品文档放心下载7.Assembleandtraintheteam.Defineresponsibilities精品文档放心下载8.Collectthedata9.Analyzethedata10.Verifytheresults11.Drawconclusions.Reportresults.Makerecommendations精品文档放心下载InjectionMoldingExample1.Clearlystatetheobjective感谢阅读Determinetheprocesscapabilityoftheinjectionmoldingprocess谢谢阅读Determinethemajorsourcesofnoisevariation感谢阅读2.ListtheX’sandY’stobestudied谢谢阅读Output:ThicknessInputs:Cavity(slot),cycle,sample精品文档放心下载3.Ensuremeasurementsystemcapability精品文档放心下载AnMSAwasconductedandthesystemwasfoundcapable感谢阅读4.DescribethesamplingplanOnesamplefromeachslot,fiveconsecutiveruns,fourtimesa感谢阅读dayforfivedays.5.Describethedatacollection&storageplan(who,what,when,where,谢谢阅读etc.)Thesupervisorcollectedthedataandentereditinaworksheet精品文档放心下载6.Describetheprocedureandsettingsusedtoruntheprocess精品文档放心下载Standard,constantprocesssettings.谢谢阅读7.Assembleandtraintheteam.Defineresponsibilities.感谢阅读Forasmallproject,thesupervisordidallthework谢谢阅读8.Collectthedata.ThedataareinMinitabworksheetSocketData.mtw感谢阅读9.AnalyzethedataAnalysisisonthefollowingslides感谢阅读中心限理论:CentralLimitTheoremQ:WhyAreSoManyDistributionsNormal?感谢阅读Whyissomethingthiscomplicatedsocommon?Sciencehasshownusthatvariablesthat精品文档放心下载varyrandomlyaredistributednormally.So感谢阅读anormaldistributionisactuallyarandom精品文档放心下载distribution.Anotherreasonwhysomedistributions感谢阅读arenormallydistributedisbecause精品文档放心下载measurementsareactuallyaveragesover谢谢阅读timeofmanysub-measurements.The感谢阅读singlemeasurementthatwethinkweare感谢阅读makingisactuallytheaverage(orsum)of精品文档放心下载manymeasurements.TheCentralLimit谢谢阅读Theorem,discussedinthefollowingslides,感谢阅读providesanexplanationofwhyaveragesof精品文档放心下载non-normaldataappearnormal.精品文档放心下载DiceDemonstration(IntegerDistribution)谢谢阅读Whatdoesaprobabilitydistribution谢谢阅读fromasingledielooklike?Whatisthemean?Whatisthestandarddeviation?感谢阅读ConstructadatasetinMinitab感谢阅读SelectCalc>RandomData>Integer…fromthemain谢谢阅读menuGenerate1,000rowsofdatainC1:Min=1,Max=6谢谢阅读UseMinitab’sGraphicalSummaryroutineforanalysis谢谢阅读Stat>BasicStatistics>DisplayDescriptiveStatistics…感谢阅读MinitabOutput(Typical)Theprobabilitydistributionofthe感谢阅读possibleoutcomesoftherollofasingledie谢谢阅读isobviouslynon-normal.Aperfectdistributionwouldhavehad精品文档放心下载allsixbarsexactlyequal,butevenwith谢谢阅读10,000datapoints,thereisstillsome谢谢阅读differencesinthehistogram.Ifabetter谢谢阅读estimateisrequired,adifferentdataset精品文档放心下载couldbeconstructedwithexactlyequal感谢阅读countsofeachpossibleoutcome.Tryit谢谢阅读andseeifthenumbersareanydifferent.谢谢阅读SamplingaNon-normalDistribution–Exercise谢谢阅读Eachpersonintheclassistotossasinglediesixteen感谢阅读timesandrecordthedata.Calculatethemeanandstandarddeviationofeach谢谢阅读sampleofsixteenRecordthemeansandstandarddeviationsfromeach谢谢阅读personintheclassinaMinitabworksheet精品文档放心下载UseMinitab’sGraphicalSummaryroutineforanalysis精品文档放心下载Stat>BasicStatistics>DisplayDescriptiveStatistics…谢谢阅读Alternately,asampleofsixteenthrows感谢阅读ofthedicecanbesimulatedinMinitabas谢谢阅读follows:Select:Calc>RandomData>Integer…from谢谢阅读themainmenuGenerate16rowsofdatainC1:Min=1,Max谢谢阅读=6AnalyzetheSampleDataWhatisthemeanofthesampleaverages?精品文档放心下载Mean≈3.5Whatisthestandarddeviationofthesampleaverages?精品文档放心下载Sigma≈0.4Isthedistributionnormal?Whatisthep-value?Whatistherelationshipbetweentheaverageofthe精品文档放心下载samplemeansandthepopulationaverage?精品文档放心下载Whatistherelationshipbetweenthesigmaofthe精品文档放心下载averagesandthesigmaoftheindividuals?精品文档放心下载TheCentralLimitTheoremFormalDefinition:Ifrandomsamplesofnmeasurementsarerepeatedly精品文档放心下载drawnfromapopulationwithafinitemeanμμμμandastandard谢谢阅读deviationσσσσ,then,whennislarge,therelativefrequency精品文档放心下载histogramforthesamplemeans(calculatedfromthe感谢阅读repeatedsamples)willbeapproximatelynormalwitha感谢阅读meanμμμμandastandarddeviationequaltothepopulation感谢阅读standarddeviation,σσσσ,dividedbythesquarerootofn.精品文档放心下载(Note:Theapproximationbecomesmorepreciseasn谢谢阅读increases.)CentralLimitTheorem–Exercise感谢阅读FromaMinitabanalysisoftheuniformlydistributed感谢阅读data:Foranexercise,verifythattheCentralLimitTheoremis感谢阅读validforthisuniformdataVariableNMeanStDevn=1(Individuals)10000-0.003310.57918谢谢阅读n=2(Means)100000.002590.40613谢谢阅读n=5(Means)10000-0.001130.25953谢谢阅读n=30(Means)10000-0.002370.10559精品文档放心下载相关性及简单线性回归:Regression&CorrelationIntroductionUsedforquantitativevariables(X’sandY’s)谢谢阅读Forreview:WhatisthefocusofSixSigma?感谢阅读Q.Whatdoesthisequationrepresent?谢谢阅读A.Amathematicalmodelofaprocess谢谢阅读PurposeofRegression:topredictYfromasettingofx谢谢阅读Examples:Distance=f(acceleration,initialvelocity,time)谢谢阅读Productyield=f(concentrationsofreactants)谢谢阅读Hardness=f(alloy,annealtemperature)谢谢阅读)(xfY=Remember,thefocusofSixSigmaisto精品文档放心下载determinethedefiningequationofthe感谢阅读process.Itistoidentifytheimportantinput精品文档放心下载variables,determinetherelationshiptothe感谢阅读outputs,determinetheoptimumvaluesofthe精品文档放心下载criticalinputsandthencontroltheinputsat感谢阅读theoptimumsettings.Todothis,theBlackBeltmustknowthe感谢阅读relationshipbetweentheinputsandthe精品文档放心下载outputs.Thismodulediscusseslinear感谢阅读modelingtechniquesforidentifyingthe谢谢阅读relationshipbetweencontinuousvariable精品文档放心下载inputsandcontinuousvariableoutputs.精品文档放心下载ASimpleLinearModelLinearequationsrequirecontinuousinput感谢阅读andoutputvariables.Oneotherassumptionis感谢阅读thattheindependentvariable(input)isknown感谢阅读andfixedandthatallofthevariationisinthe精品文档放心下载dependentvariable(output).Thisisnot精品文档放心下载usuallythecase,butoftentheinputsare精品文档放心下载settingsondialsorgaugesorsoftwarethat精品文档放心下载seemsfixedandinvariable.Manytimesthe精品文档放心下载variationintheoutputisafunctionofthe精品文档放心下载inabilityoftheinputcontrollertoholdthe谢谢阅读inputatthesamevalue.CollectingData(y&x)–AFewThoughts感谢阅读Pg8?March01,BreakthroughManagementGroup.Unpublishedproprietaryworkavaila精品文档放心下载bleonlyunderlicense.Allrightsreserved.March16,2001感谢阅读Makesuretheprocesssettingscoverthelikelyproduction谢谢阅读range(butnottoofar).Toogreatarangepointsoutsidethenormalrangemay精品文档放心下载havetoogreataneffectonthemodel.精品文档放心下载ToosmallarangeErrortermmaydominatethefit.精品文档放心下载Takeseveralreplicatesateachinputsetting(x).感谢阅读Replicaterunshelpincreasethemodelaccuracy.感谢阅读Randomizerunswheneverpractical.谢谢阅读Runorderisoftensignificantfactor.精品文档放心下载Theoutput(y)atdifferentinputs(x抯)isnotalways精品文档放心下载independentofprevioussettings.精品文档放心下载Agoodspreadinthedataisrequiredfora精品文档放心下载goodmodel.Considertwoexamples:谢谢阅读Allofthedataiscollectedatthenormal感谢阅读processsettings.Inthiscase,regressionwill谢谢阅读trytofitalinearmodeltoacombinationof精品文档放心下载randomprocessvariationandrandom精品文档放心下载measurementvariation.Theresultswillbeof感谢阅读novalue.Thesecondcaseiswhenmostofthedata谢谢阅读isclusteredaroundthestandardsettings谢谢阅读exceptforacoupleofpointsattheextreme谢谢阅读ranges.Inthiscase,theextremepoints精品文档放心下载controlthefitofthemodel.Ifoneofthe感谢阅读extremepointsisaflyer,thenthemodelwill感谢阅读beinerrorduetotheflyer.TheidealcaseisfortheBlackBeltto精品文档放心下载collectarangeofdatathroughouttheprocess精品文档放心下载space.置信区间:ConfidenceIntervalsApopulationisthesetofallmeasurementsofinteresttotheexperimenter精品文档放心下载Asampleisasubsetofmeasurementsselectedfromthepopulation感谢阅读Aninferenceisastatementaboutapopulationparameterbasedon感谢阅读informationcontainedinasample感谢阅读TwotypesofinferenceEstimationApollhasbeendevisedtodeterminethepublic’sreactiontoa精品文档放心下载newpoliticalscandal.Thepurposeistoestimatethereaction感谢阅读ofallAmericansbypollingarepresentativesample精品文档放心下载HypothesistestingAvaccineforLymediseasehasbeendevelopedbuttherate精品文档放心下载ofnegativesideeffectsis1.45%.Anewvaccinehasbeen谢谢阅读developedanditisdesiredtoknowiftherateofnegativeside精品文档放心下载effectsislowerthan1.45%.Theotherbranchofstatisticsis感谢阅读descriptive.Itspurposeismerelyto感谢阅读describeasetofmeasurements.感谢阅读Inferentialstatisticsisusedtoguesswhat谢谢阅读Godknowsaboutapopulationfromasample.谢谢阅读Withininferentialstatistics,therearetwo感谢阅读types:estimationandhypothesistesting.感谢阅读Estimationistryingtoguessthepopulation精品文档放心下载statisticsfromasample.Hypothesistesting感谢阅读concernsevaluatingasamplestatisticand感谢阅读comparingittosomehypotheticalvalue.精品文档放心下载EstimatesandtheCLTWhatisthebestestimateofthepopulationmeanusingsampledata?谢谢阅读Thesamplemean!Howgoodofanestimateisthesamplemean?谢谢阅读Whatfactorsinfluencetheaccuracyoftheestimateofthemean精品文档放心下载fromsampledata?Recallthat:Thevariationinthedistributionofsamplemeansisafunctionofthe感谢阅读varianceofthePopulationandthesamplesize!感谢阅读nPopX/σσ=WhatAboutSmallSamples?Ifthepopulationstandarddeviationisknown(italmostneveris)use谢谢阅读thepreviousformulaforsmallsamples,too感谢阅读Ifthepopulationsigmaisunknown(itusuallyis):精品文档放心下载Theestimateforstandarddeviation(s)isused精品文档放心下载Thet-distributionisusedinsteadofthenormal(Z)distribution精品文档放心下载Q:Whatisat-distribution?Thet-distributionisafamilyofbell-shaped(normal-like)谢谢阅读distributionsthataredependentonsamplesize感谢阅读Thesmallerthesamplesizen,thewiderandflatterthe精品文档放心下载distributionnstXμnstXnn1,2/1,2/+≤≤ααThet-distributionisthegeneralcasefor精品文档放心下载anysamplewherethepopulationstandard感谢阅读deviationisunknown.However,withlarge精品文档放心下载samples,thet-andz-distributionsarenearly精品文档放心下载identical,soeithercanbeused.谢谢阅读YoucanverifythisinMinitabby谢谢阅读generatingalargesampleofnormaldataand感谢阅读thenanalyzingitwithboththez-andt-感谢阅读distributionroutines.ProportionsandBinomialExperiments谢谢阅读Pg35.April01,BreakthroughManagementGroup.Unpublishedproprietaryworkavail精品文档放心下载ableonlyunderlicense.Allrightsreserved.April3,2001感谢阅读Proportiondataisusuallytheresultofabinomial-type谢谢阅读experimentBinomialexperiments(orBernoullitrials)arethosethat精品文档放心下载haveonlyoneoftwooutcomes,eithera“success”ora感谢阅读“failure”Theprobabilityofthistypeofexperimentisdescribedbya谢谢阅读binomialdistribution,acomplicateddistribution谢谢阅读Inmanycasesthenormaldistributioncanbeusedto感谢阅读approximatethebinomialdistribution感谢阅读Whennxp>5andnx(1-p)>5μ=nxpandσ2=nxpx(1-p)Binomialdistributionsarediscussedin谢谢阅读almosteverystatisticstextbook.Calculations谢谢阅读withthemisnotnecessarilydifficult,butitis感谢阅读tediousifitmustbedonemanually.Minitab精品文档放心下载hasroutines,however,thatgreatlysimplifies谢谢阅读thecalculations.Ifthebinomialapproximationappliesand谢谢阅读thedatacanbeestimatedwithanormal感谢阅读distributionotherstatisticaltestsandcontrol感谢阅读chartscanbeusedthatwouldnotbeavailable谢谢阅读otherwise.Trytoconstructyourexperimentssuch精品文档放心下载thatthebinomialapproximationisvalid.精品文档放心下载Ageneralruleofthumb:forthenormal谢谢阅读approximationtoapply,haveasamplesizeof谢谢阅读atleast30andlargeenoughtoguaranteesat感谢阅读least5successes.假设测试:IntroductiontoHypothesisTesting谢谢阅读ABrightIdeaNotes:Pg511Nov2000?April01,BreakthroughManagementGroup.Unpublishedproprietaryw精品文档放心下载orkavailableonlyunderlicense.Allrightsreserved.谢谢阅读Alightbulbcompanyistryingtoproduceabrighterlightbulbforthe谢谢阅读sameenergy.Itishopedthatachangeinthefilamentcoating谢谢阅读processwillproduceabrighterlight.感谢阅读Theengineercollectedthelasttenlightbulbsmadebeforethe感谢阅读processchangeandthefirsttenafterthechange.Themeanlight精品文档放心下载outputoftheoldprocessbulbsis1251lumensandthenewprocess精品文档放心下载is1273lumens.Doestheincreaseof22inthemeansofthetwogroupsrepresenta精品文档放心下载realimprovement?Couldthedifferencebetweenthesetwogroupshavehappenedby感谢阅读randomchance?Shouldtheengineerswitchtothenewprocess?感谢阅读Thesekindsofproblemsarevery精品文档放心下载familiartoengineers.Anengineeris谢谢阅读givenatasktoimproveaprocessor精品文档放心下载product.Afterachangeintheprocess,感谢阅读theengineerisleftwiththeproblemof感谢阅读determiningwhethertheprocesschange感谢阅读hasmadeasignificantimprovementor精品文档放心下载not.Thoughengineersoftenusemore精品文档放心下载advancedtechniquestodeterminethe谢谢阅读improvedsettings(DOE,forexample,to感谢阅读bediscussedlater),ahypothesistestis精品文档放心下载oftenusedtoverifytheexperiment感谢阅读results.Theprocessmaybeasfollows:?Identifytheproblem.?Designandrunanexperimentto谢谢阅读findanimprovedcondition.?Analyzethedataanddeterminethe感谢阅读improvedoperatingpoint.?Verifytheeffectivenessofthe精品文档放心下载improvementwithahypothesistest.谢谢阅读AFewIlluminatingDetailsQCdatawereavailableforlightbulbsproducedinthesamefactory.精品文档放心下载Allofthebulbshadbeenproducedusingthestandardfilament精品文档放心下载coatingprocess.Thedatawascomprisedoftheaveragesof10精品文档放心下载samplesfromconsecutivebatchesoflightbulbs.Theengineer精品文档放心下载calculatedthedifferencesbetweenconsecutivegroupsandrecorded谢谢阅读itinaMinitabworksheetincolumnQCData.感谢阅读Consideringthenewdata,thequestionnowbecomes:精品文档放心下载“Howoftenhasthemeanbrightnessofagroup谢谢阅读oflightbulbsbeen22lumensbrighterthanthe谢谢阅读groupproducedimmediatelybefore?”感谢阅读OpenMinitabworksheetFilament.mtwforthedata精品文档放心下载IntheMinitabdatasheet,column感谢阅读‘OldData’isthefirstsetof10fromthe精品文档放心下载oldprocess.‘NewData’isthesetofdatafromthenew感谢阅读process.‘PlantData’isthe210averagesof10谢谢阅读consecutivemeasurementsfromtheold谢谢阅读processinsampleorder.‘Diff’isthemagnitudeofthedifference精品文档放心下载betweenconsecutivegroups.WhatIsaHypothesisTest?Ahypothesistestissimplycomparingrealitytoan感谢阅读assumptionandasking,“Aretheythesame?”精品文档放心下载OrAhypothesistestistestingwhetherrealdatafitsamodel谢谢阅读OrAhypothesistestiscomparingastatistictoahypothesis感谢阅读均值测试:MeansTests1.Statethepracticalproblem2.Statethenullhypothesis3.Statethealternatehypothesis4.Testtheassumptionsofthedata*5.Calculatetheappropriateteststatistic(orcalculatep-value)6.Lookupthecriticalvaluefromtheappropriatedistribution(orsetalpha)7.Ifthecalculatedstatistic谢谢阅读meetsthedecisionrulecriteria(orifp-value<α)thenrejectH08.FormulatethestatisticalconclusionintoapracticalsolutionThisisthegeneralrecipeforhypothesis谢谢阅读testing.Thetestsdifferintheappropriate谢谢阅读statisticsandappropriatedistributions.精品文档放心下载Themeanstestsrecipeisthesameaswas精品文档放心下载whatlearnedforvariancetesting.谢谢阅读Example–OneMeanVs.TargetBackground–Acompanyauditsitsstockoftennisballsbytestingthebounce感谢阅读heightof10randomlyselectedballs.Theaveragebounceheightofthe谢谢阅读sampleis19.8in.Thehistoricaldataisμ=20.1andσ=0.5.Hasstorage精品文档放心下载degradedthebounceofthetennisballs?Useα=0.05.精品文档放心下载1.Statethepracticalproblem:精品文档放心下载Isthebounceheightofthestoredpopulationlessthanthehistorical谢谢阅读value?2.StatethenullhypothesisHo:μstored=20.13.Statethealternatehypothesis精品文档放心下载HA:μstored<20.14.Testassumptions:normalityofthedata谢谢阅读p-value=0-.432–Dataisnormal感谢阅读Ave