这是黑带如何完成一个项目的实例教程

这是黑带如何完成一个项目的实例教程，指导黑带如何更好的完成项目。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

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$175K

b3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---------------------------------------------------------------------------------------------------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---------------------------------------------------------------------------------------------------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---------------------------------------------------------------------------------------------------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《6Sigma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)。潮《6Si纳gma项目日运作实例》起->《测量膛阶段》->矛如何进行项欢目描述撒-----败-----粪-----剥-----择-----拥-----盈-----资-----猾-----璃-----扁-----搞-----缠-----桃-----嘉-----吐-----匙-----爪-----始-----址----涉如何进行项稠目描述:鞋1，目标陈冶述劝2，Met袋ric图抓3，月节省宣额饮如何绘制工绕艺流程图:召集小组:成流程图绘制镇是集体努力际的结果嫩小组包括：湾流程负责人谅：项目结果哄的负责人厚工程部门-犯工艺，产品甚，设计及设漫备赛生产部门-抚操作员，各另班次主管，毫培训员，操索作班长，维扮修技师搭流程图所需吃信息抽脑力风暴丸观察/经历办操作手册铺工程标准，浅工作指示吸六大方面（浊人，机，方治法，测量，录材料，环境片）乖确定工艺范咳围:桶范围至观重淋要增越窄越好！恐大量工艺步亦骤可能表明民项目定义不库佳或问题鸭源于几个项缘目狼问题藏于问攻题中梢若问题可以惕由粗略分析窃解决，管理舅层会去做吹绘制可执行震的工艺图认你能确认缺废陷来源吗？觉我们能有意攻识地改变输译入指标变量兵吗？障有意识的改冶变输入指标序变量能直接甲影响输出结钳果吗？屡工艺流程图兰（PFD）驰:额6Sig拨ma工艺超流程图的要留素：叙所有工艺步淋骤包括隐形钻工厂许数据采集点宏所有设备/植工具壳各步骤表明狭增值性（V片A）和非增乌值性（NV废A）盒控制标准文境件痛用标准符号馋绘制工艺流妙程：熔在Micr掏osoft举Offi樱ceTM总等软件中可颗找到眯工艺流程图兰-程序:终绘制工艺记春载的工艺步蜘骤叼包括所有检群查点，测量促指标和传运稻步骤甜确认所有数纹据采集点玩标示各工序雷标准控制文鸭件渴各步骤标明笨为增值性（坏VA）或非闯增值性（N意VA）宗确认各工艺闪步骤的X重和Y之标明可能消浅除的NVA黎步骤彩加入并标明扑“隐形工厂死”工段队标明为VA锡或NVA，跳标明可能消漂除的步骤黑标明须指定昏控制文件的周步骤策加入DUP鹊，RTY，妻COPQ，灵循环周期等承估计值匠标明须进行险量具和工艺型能力研究的久步骤晃通过直接或蚀秘密观察确蝶认准确性抢文件记录/欣确认:燃文件记录的杜工艺流程绘首先绘制记弊录下来的工华艺航加入并标明看隐形工厂步音骤殖当所有步骤磨展示出来后劣，流程图就页属于实际工对艺炸确认偿流程图的准带确性至关重翠要壤项目组必须导花时间观察院工艺材秘密进行。病观察导致行膝为改变璃确认实际工挖艺设置与记腿录的设置相梢同辆跨班跨机器贤观察工艺薄如何绘制工姜艺流程细图喘:麻工艺流程细软图：送6Sig猎ma工艺甘流程图要素坛：曾工艺或产品驾是输出指标盲Y和输入指忧标X局标准上下限锋和标准控制怒文件江所用设备/仓工具也绘制工艺流做程细图台工艺流程细绩图必须依工席艺流程图而箭画。更改其雾一应在另一铺个中反映出替来。完应使用最新好的控制文件梨标明所有隐情形工厂步骤言的输入输出席指标艰工艺流程细浸图程序：解1，从流程凑图中列出工驰艺步骤妨2，加入下夺列内容枯输出指标还输出指标标绘准，若存在西输入指标追输入指标标榨准，若存在隙工艺能力或辰量具能力指排标块所用设备警3，标明隐孤形工厂步骤父4，标明各怨步骤属于增慎值性（VA挑）或非增值勉性（NVA猎）筹5，标明各装步骤属于可永控性的（C构）或噪音性和的（N）猾6，确认各抬设备的输入与指标设置虚7，确认流袖程图准确性咐8，必要时志更改及更新区流程齿标准限和工易艺能力：协工艺及产品皂标准收加入X的工鬼艺设置棉加入Y的储标准限老标明未记录宣的Y和可控黑的X珍测量系统苏加入量具重掘复性及复验游性数据臭标明须做测弟量系统分析绒的量具骂工艺能力趣展示RTY哨，DPU，沉CPK等的橡估计值馒标明哪些工懒艺步骤数据花陈旧或不完充整而需做工欧艺能力分析餐更改及更新锤：僚更改博记住：6轧Sigma挥的目标之倡一是找出：债Y=F（X饭）埋随着对工艺开的深入了解燕，更新工艺旷图以反映新撤的信息猫更新穷项目最终成及果之一是现防有的工艺的榆流程图舟更新工艺图除以反映任何叹工艺改变债加入测量系籍统分析及工理艺能力分析姿结果更精简制造与虎5S:理精简制造例给似于日本的浊5S悠精简制造与尤5S:鱼骨图:锐鱼骨图汪一种系统确猪认所有可能炕导致问题(奸后果)产生婆的原因方法嘱。允构造鱼骨图室的方法：宗1.陈述厕问题，并置斤于右边的方徒框内槽2.朝方祝框画一水平占箭头。胳3.在箭恢头上下写上睁传统因素类伙型名称*或逢你怀疑是的宽类型名称。适用究直线连到箭爷头线上。关4.在各主圆要的类型范乡围内，集思肆广益并列出佛所有可能引本起问题发生璃的因子。垫5.进一步叛优化：对各低种详细列出蚀的因子再列赢出其输入变般量。品*6m--策man,捐machi名ne,m剩ethod狱,mea孟surem屯ent,腔mothe冤rnat古ure(阴envir嫩onmen哈t)余(6M:人叮员，机器，责测量方法，节原材料，环蛛境)席定性测量系雄统研究:绢定性型量具泽R&R畅-术语:霉检验员分数随（%）-在雅定性型R&杨R检验过程像中，检验员顺前后一致的拣比例堡定性数据-油-定性（合每格/不合格症）数据，可诵用来做记录庭和分析狐定性型测量底系统--把坛每个部件与闭标准进行比缴较，从而决鼠定部件是否贷符合标准的猎测量系统。飘消费者偏见共--员工倾轰向把合格产前品判为废品裕有效筛选分肆数（%）-寿-在定性型绞R&R检验塔过程中，所鞠有员工本身勤前后一致且劝相互之间也辈一致的比例船。浴标准值--班由一个高准券确度量具所溜测的平均值纷生产者偏差糊--员工倾截向于把不合爆格（有缺陷蜜的）产品判记为合格泳筛选--用宫检验方法对回产品进行1叉00%的评有估献筛选有效性离--定性量刊具系统区别欠合格与不合妻格的能力浮使用定性型纪量具R&繁R的目的怒:乖工艺评估贺评估你的检穷查标准或工霉作质量标准具与客户要求傻的一致性淘确定所有班典次，机器等脸的检查人员投是否使用相怨同标准来决犹定合格与不范合格兵量化检查人具员准确重复抛其检验结果歌的能力刷确定检查人省员与“已知闭标准”的一仅致性及倾向筋于消费者偏绳差还是生产键者偏差聋工艺改进君发现是否需等要培训，缺载少工序或缺甩乏标准胖定性型量具名R&R籍的方法:山准备父从工艺中挑拼选30个部驰件，50%翅合格，50渔%次品凳可能的话，锹挑选近乎于脾合格和不合章格样本僚挑选检查人鞠员--受过星完全培训的闲和有资格的倦实施俗要求每一个帮检查人员随尸机地检查部燕件，决定合布格与不合格絮并重复此检衰查凯评估赵将结果载入跨文件袜如果必要，奥采取适当的他措施调整测株量工艺凉重做R&R叹试验，核实抬调整后的有捷效性逗定性型量具断R&R稼--结论:非检查员分数券如果大多数梯员工都是1止00%，则腹培训作用极的为有限雷筛选有效分扛数况如果员工本壁身前后一致这但是相互间什不一致，则尼重新培训可攀帮助减少错灿误。奔标准化分数隙如果员工时荡常与标准不连一致，则需陷要改变测量银系统（或局在部标准）悦工艺能力分集析:布为何测量工吗艺能力?稠使我们根据铲数据分配资清源！（这剖可不常见！资）爱缺陷率得以普量化命确认可以改然进机会盘分析工艺能锤力可使组织斧预测其所有范产品和服务简的真实质量爱水平坦确认工艺发爆生问题的本谈质-居中程东度或分散度维工艺能力研宰究程连续数据痛离散数据鸟1.确认标迅准限1.沟确认标准限蝶2.收集数狡据2.收涛集数据衬3.确定短株期偏差3绿.决定：短纸期还是长期贱？斯4.计算工汉艺能力指标钻：（通常婚是长期）计a.短期：法4.计算予工艺能力指颤标：币ⅠZU,底ZLa.府长期：晃ⅡCP撤ⅠPPM丢ⅢCPK咬ⅡSi娱gma水平怀ZLT陪ⅣSig煮ma水平Z爬STⅢ们PPK之b.长期：意b.短期森：池ⅠSig介ma水平Z魄LTⅠ对Sigma调水平ZST挨ⅡPPK另ⅡCP纹K带工艺能力计完算实例雅一位技师负多责医院设备姐的蒸汽杀菌辫过程。其中施一个关键参斗数是控制“陶暴露”阶段染的温度。基设备室温度暮和在最小饱价和蒸汽浓度移的周期时间猎决定杀菌程劳度在整个设功备室维持前肾后一致的温摩度范围很重摇要。峰第一步：确来认标准栋这一阶段常邀被忽视。锦我们如何设韵定标准？登设计部门-帆设计蓝图揪设计部门如父何得到各项歇要求？举工艺部门-泄标准由工艺仗以前能够做屋到的或开始牺使用时的能睁力定杆这想法有错捕吗？诊客户法我们总是对家客户说可以孙吗？薪对上例而言云：睛设备室目标仙温度是12千50C±1扔.50C越第二步：采灵集数据-合奏理编组赢应采集数据尽获得“短期伐”性能，如遭可能，“长温期”性能那通过固定时模间区间采集桨一系列快照开型数据源应按合理编颠组采集快照拾数据懂什么是合理陈编组？扛从流程连续倾不断产生的谜零件或产品斗中合理取样测以期捕获最估小工艺偏差仅的方法骂组内偏差反跨映一般偏差嫂平均标准差采（用一种均掠方差方法平捏均）是对工见艺应有能力锹的良好估计饺第二步：采分样-例子变例子：技师符在暴露周期狱从控温探针债读数中选取俩五个数据，锻并从连续七批个杀菌运转辆周期采集数芬据，数据列刃在Cham悦berTe浇mp2.m使tw文件的疼杆Cham呢bTemp绪栏中斯第三步：确克定短期偏差么多数现有数千据居于长期挨和短期之间围为了估计真矛实短期数据萍：援小心设计工淋艺能力研究耀方法适确保编组策描略合理基某些工艺无面法研究短期肆数据迫如低产量和吉长循环周期忧工艺混采样昂贵或放难以取样的厘工艺横第三步：短羞期还是长期哥？母一个指导思掉想：如果允即许80%的死输入指标匆在其自然范培围内浮动，肠数据就是长赤期的询短期及长期膜：组内及组养间气平均标准差沸与总标准差田对各组方差痰取平均值可箱得到组内标译准差的平均侵值戴总标准差由状所有数据算专出，不计编着组鄙平均标准差俘不计组间偏终差，而总标洞准差计入组广间偏差绵平均标准差舟是对组内标弃准差的最佳波估计遮长期和短期汤指导思想廊短期梦数据在有限艇的周期或间网隔采集烘数据在有限银的机器和员农工中采集喷差不多总是心连续变量仿长期壳数据在很多猛的周期，间冒隔，机器和旱员工中采集蝶可以是离散申或连续数据伯离散数据几婶乎都是长期寨性的棵第四步：罗计算ZU和冲ZL:乎Z-分数熊提供统计数陕据以便用共脊同语言交流请提供一个与年标准上下限兵相关的工艺荣性能指标缩第四步：足计算CP虎例子狂工艺平均值财为325番标准差为1织5索标准上限为翅380，下膀限为270围CP是多少串？穴若平均值为啦355而燃标准差不变虹CP又是多材少？狼Cp与工艺宪应有能力恩Cp是工艺区应有能力的答良好指标营工艺应有能唐力--一个惨工艺观察到夜的最好的短弯期性能戴机会--工绕艺长期性能辣与工艺应有枣能力间的差删距赶Sigma及项目--致艇力与把长期斗性能与工艺灾应有能力的近差距缩短洽定量测量系赞统研究:邀定性型量具哗R&R乖--模型暑测量系统弦μ哥总和=业μ程工艺+数Δμ册测量系统班偏离度：情观察值=实县际真实值+挂测量偏移朴通过“校准紫计划”渡Δ那测量偏移怜来评估真伶实值测量职值创（准确度）凯测量系统跃σ嫁2总合=坑σ巩2工艺+农σ蜓2测量系统绣偏离度：晴观察的偏差用=工艺的偏纹差+测量的锡偏差丈通过“校准狸计划”些来评估真期实值测量根值极（准确度）唯测量系统的颗指标:梅量具R&R锅结果->量菌具偏差（σ皇measu割remen石tsys晌tem）该真实值精弱确度（量具球偏差）膀观察值收测量系统的伞精确度（P妥）：储精确度包括笛重复性和复赏制性结测量系统的慢指标-PT饰:梯精确度与公炸差之比--绞P/T脊代表量具偏素差占公差的追部分涂此部分通常惑用百分数来加表示遇最好的情形染P/T<1孕0%--可糟接受的P/棋T<30%警测量系统的速测量方法-个-P/TV旱:咏精确度与总飞偏差之比票代表量具偏管差占据总偏诊差的部分方此部分通常珍用百分率来淡表示爹最好情形<飘10%量维具可接受条逐件<30%摆测量系统的屯指标--分堤辨指数:踏分辨指数是哀测量系统从哗工艺数据中框可辨认的不勺同读数的数乔量肢分辨指数是骗一个分辨率宏指标谨分辨指数是腹重复性和复记制性的函数化最好情形：岭>4，可麦接受的：3岩-4猾P/T和朽P/TV椒的用处:筝P/T（旦%公差）节最常用于测心量系统的精势确度评估呆将量具的精周确度与公差狼要求进行对蜂比形如果量具用页来对生产样悦品进行分类晓P/T富还可以语P/SV（苗%R&R）谎--6S桑igma杜首选凳测量量具与杏量具研究偏杨差相比其性剪能如何泳最适合进行筝工艺改进的削评估降使用时应小唇心。量具研旱究偏差并不闪一定代表真省实的工艺偏掘差兰P/TV（蚁%R&R）遵--6S路igma挤首选弦测量量具与估工艺偏差相款比其性能如塔何密使用时应小薪心。量具研史究偏差并不揭一定代表真杜实的工艺偏勉差她当量具样本奥中的偏差代跨表真实工艺钳偏差时，P庆/TV等于遗P/SV晚定量型量具民R&R得--使用方烧法说明:捧1，校准量马具或确认最悟近校准仍然腿有效原2，收集1不0个代表工五艺偏差全部弃范围的样本拴3，从每日怠使用这种测库量方法的员插工中选出检职验员深4，运用影Clac>朋Make添Patte崭rned蚕Data>尼准备量具至研究数据表碍5，让员工斯测量所有无吴标识，随机给次序的样本巧6，分别让现另外其他员桶工测量所有员无标识，随慰机次序的样寺本坑7，重复第桐五步及第六衫步循环三次窄。也尽量打或乱员工次序隆8，用M同inita妄b作下列妈两个分析铅Stat>志Quali住tyTo娃ols>G括ageR蜂&RSt亚udy(C范rosse边d)谈Stat>晋Quali测tyTo释ols>G亲ageR族unCh枣art忠9，对测量定系统能力研气究结果进行握分析芳10，确定桨适当的后续须措施造定量型量具治R&R晌--Min漆itab坦实例:谅一个黑带想哑对冶金工艺沉使用的温度展表进行量具糊研究，他严类格按前面一绞页的方法进谱行实验，并筑将数据输进猎了R&Re慕xampl贪e.xls委中。炕运用Min省itab分桨析数据并评修估量具能力号Stat>府Quali董tyTo好ols>G拢ageR予&RSt子udy(C诚rosse该d)...舒Minit污ab量具谜R&R研究桃--选项乏输入该工艺葱公差和偏差归，如果你想茫要Mini爹tab帮你猫计算P/T恢和P/毅TV的话。厌Minit君ab默认膝计算P/S旨V备量具R&R首结果--A奸NOVA表无P值是变化笔源在统计上烘对总偏差影索响是否不显脸著的概率淘在这个例子茫中，部件和兄员工均为显编著的偏差源悦另外，你能扫用Mini配tab的计替算器计算总衰的平方和吗沃？这个值代钥表什么意思考？蚀《6Si乏gma项目某运作实例》妨->《分析氏阶段》->材失效模式及肃后果分析扛-----译-----决-----虎-----煎-----光-----超-----蚁-----椒-----榆---呼-----兰-----米-----强-----炕-----免-----杂-----谅-----垃-----伯-----扶-仁失效模式及才后果分析:辉市Failu弃reMo县desa湾ndEf薄fects蚀Anal炼ysis器(FMEA贵)矿Backg孕round卡:拍Failu挡reMo殊desa建ndEf薄fects冲Anal策ysis门(FMEA酸)套旬Firs钉tdev抓elope兵din个the1想950’s队Appr植opria事tedb摸yNAS臂Ain闲the1播960’s埋for粱thes侵pace湖progr涌am宴摆Fo德rdMo长torC夜ompan戒ywas弦the盲first章Nort警hAme蹦rican劫comp咐anyt僚owid璃ely月imple塌ment曲theu构seof铸FMEA杂s安Types普ofF政MEA爸狮Syst灶em–渔Top-l窝evel,若earl怪ysta德gean单alysi旨sof赛compl羡exsy凉stems不育Desi怒gn–幻Syste充ms,s六ubsys愈tems,块part船s&c罗ompon饮ents区early确ind粱esign拢stage轻更Proc道ess–蚊Focu授seso贼npro正cess量flow,琴sequ钞ence,荷equi裂pment锯,too攻ling,鞋gauge盘s,in欢puts,漫outp愤uts,屠setp厚oints铸,etc盆Who?歉When?爹鲁Why?茫Warm介upex如ercis音e:绿Youh羡ave6锄0sec草onds体todo攀cumen超t:败What浓woul起dyou部want罩tok赠nowa再bout铃a“de罩fect”痰?举Fort缓hepr谨ocess舅:揭FMEA井impro扇vest柴here陆liabi绳lity附ofth现epro剥cess锡AnFM长EAid穴entif趴iesp餐roble叼msbe竹fore方they偷occur钞FMEA绳serve宏sas努arec占ordo究fimp牲rovem腹ent&凡know爸ledge汪Fort复hefu茎ture:兄FMEA妙helps籍eval商uate慕ther稼isko律fpro膨cess骂chang烂es浪FMEA谢ident烤ifies旗area侍sfor碑othe此rstu臂dies行–胁multi暖-vari瘦,ANO运VA,D愁OE芳6sPr跟ocess铁FMEA数--T屋ermin殖ology陕FMEA:私Asy拔stema殊tica闲nalys旱isof紧apr闭ocess今used踢toi煌denti级fypo列tenti凑al症failu放resa荡ndto梅prev钞entt割heir疏occur板rence却Poten五tial拿Failu锅remo枣de:T希hema苹nner占inwh概icht堡hepr桌ocess催coul爆d型poten共tiall组yfai伏lto海meet磨thep催roces碗sreq术uirem宾ents.劣Poten西tial土Failu邻reEf绕fect:瞒The眨resul银tsof同the桑failu肃remo梦deon挑the艺custo政mer.新Seve恐rity:古Ana聚ssess不ment结ofth顷eser妥iousn康esso嫌faf墨ailur油emod杀e.好Sever瞧itya阁pplie隆sto需thee竖ffect涝sonl吵y.丽Cause谣:How郑the臂failu腾reco迫uldo慧ccur,伟desc猛ribed奇int另erms愉ofso幸methi鼓ng膛that沸canb途ecor鞭recte压dor暑contr径olled来.召Occur稿rence撕:The凯like们lihoo仔dtha渣tas肉pecif升icfa剃ilure榆mode超isp惜rojec穿ted咽tooc举cur.刃Dete菜ction尘:The烘effe蹄ctive丰ness需ofcu肾rrent浇proc宏essc且ontro昌lsto撇iden靠tify干thef弯ailur子emod藏e(or朋the锤failu洪reef墙fect)甘prio生rto铸occur眼ring,贩prio小rto论relea蓝seto虫prod介uctio趋n,or浑prio樱rto有shipm驳entt府othe报cust皇omer.裙RPN-趴-Ris岛kPri延ority次Numb症er:T摊hepr炉oduct洲ofS订everi拿ty,O新ccurr哥ence吵&Det业ectio慰n穷FMEA瓦Examp扯les拴Plati俭ngEx氧ample休Anae韵rospa求cepl林ating级comp丸anyw狡assh张ippin们gpro猜duct朋toit称s厌custo刃mers渗with狱nicke纠lpla房ting睁that支wast违ooth山in.P弯arts喊were浸faili睁ng漂corro论sion自testi勇ngat卷the货custo逝mer.缓Shipp避ingE候xampl跳e鼻Thes咬hippi蛛ngde绕partm茄ento旦fan疏elect袭ronic篮scom乓pany气isun华able栋to唇ship笑anas街sembl灭ywit柱hout贞itsc饼lams民hell住prote掘ctive筐pack可aging高.Thi伞s换cause四socc夏asion忧alla心tesh撇ipmen潮tsto距the瓦custo差mer.主Inth调efol吗lowin巨gexa缝mples酿,as备ingle惕line伴from蛙the脸FMEA衡isus厘edas行an邪illus片trati洁onfo屡reac高hof哀thea抱bove宵examp工les.饥图形技术分劈析:返Graph樱ical输Metho携ds虫Proce膊ssVa斜riati喊on饮Noise甲vari劈ation涂from晶disc探rete吐input补s彩Diffe添rent钥opera硬tors,亭mach容ines,链setu繁ps啄Diffe涨rent桌days,菊shif景ts呢Diffe勺rent常batch掀es,m挥ixtur迎es,r盾awma课teria牛ls乏Noise乎vari曲ation脚from想cont湾inuou巾sinp差uts护Ambie唯ntte或mpera魔ture,震humi多dity,怀pres线sure蚕Wear,宣drif药t,er恒osion解,che讽mical元depl雹etion差),..夹.,,模(21邀kPr亦ocess刃xx废xfy峡=),良...,球,(2歌1k葛Noise孝nn只nf+买Inten伯tiona迷lUnw晓anted缓The候equat绝ionj顶ustm俭eans稳that描anyo禁utput殃is弱deter繁mined稿byt第hein艘tenti睛onal败proce剩ssse正tting乐s洗andt圾heun左wante茂dnoi粱seva拐riati茫on.礼Commo西nCla擦ssifi蹄catio蛛nof稠Noise凤Vari剃ables郑Posit翠ional姻(wit衔hinp险artv席ariat盖ion)才猜Vari拐ation围with简ina化singl受epro昼ducti乳onun浪it鞭Thick错ness叹varia聚tion疗acros涨sap贫lated半part东厨Vari段ation易acro右ssa养unit今conta扇ining馅many均part购s孕Varia俯tion欠acros散sas肠emico暗nduct乌orwa睡ferw色ithm芝anyd奥ie新爹Vari雨ation公byp抱ositi疑onin敏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achpersonintheclassistotossasinglediesixteentimesandrecordthedata.CalculatethemeanandstandarddeviationofeachsampleofsixteenRecordthemeansandstandarddeviationsfromeachpersonintheclassinaMinitabworksheetUseMinitab’sGraphicalSummaryroutineforanalysisStat>BasicStatistics>DisplayDescriptiveStatistics…Alternately,asampleofsixteenthrowsofthedicecanbesimulatedinMinitabasfollows:Select:Calc>RandomData>Integer…fromthemainmenuGenerate16rowsofdatainC1:Min=1,Max=6AnalyzetheSampleDataWhatisthemeanofthesampleaverages?Mean≈3.5Whatisthestandarddeviationofthesampleaverages?Sigma≈0.4Isthedistributionnormal?Whatisthep-value?Whatistherelationshipbetweentheaverageofthesamplemeansandthepopulationaverage?Whatistherelationshipbetweenthesigmaoftheaveragesandthesigmaoftheindividuals?TheCentralLimitTheoremFormalDefinition:Ifrandomsamplesofnmeasurementsarerepeatedlydrawnfromapopulationwithafinitemeanμμμμandastandarddeviationσσσσ,then,whennislarge,therelativefrequencyhistogramforthesamplemeans(calculatedfromtherepeatedsamples)willbeapproximatelynormalwithameanμμμμandastandarddeviationequaltothepopulationstandarddeviation,σσσσ,dividedbythesquarerootofn.(Note:Theapproximationbecomesmorepreciseasnincreases.)CentralLimitTheorem–ExerciseFromaMinitabanalysisoftheuniformlydistributeddata:Foranexercise,verifythattheCentralLimitTheoremisvalidforthisuniformdataVariableNMeanStDevn=1(Individuals)10000-0.003310.57918n=2(Means)100000.002590.40613n=5(Means)10000-0.001130.25953n=30(Means)10000-0.002370.10559相关性及简单线性回归:Regression&CorrelationIntroductionUsedforquantitativevariables(X’sandY’s)Forreview:WhatisthefocusofSixSigma?Q.Whatdoesthisequationrepresent?A.AmathematicalmodelofaprocessPurposeofRegression:topredictYfromasettingofxExamples:Distance=f(acceleration,initialvelocity,time)Productyield=f(concentrationsofreactants)Hardness=f(alloy,annealtemperature))(xfY=Remember,thefocusofSixSigmaistodeterminethedefiningequationoftheprocess.Itistoidentifytheimportantinputvariables,determinetherelationshiptotheoutputs,determinetheoptimumvaluesofthecriticalinputsandthencontroltheinputsattheoptimumsettings.Todothis,theBlackBeltmustknowtherelationshipbetweentheinputsandtheoutputs.Thismodulediscusseslinearmodelingtechniquesforidentifyingtherelationshipbetweencontinuousvariableinputsandcontinuousvariableoutputs.ASimpleLinearModelLinearequationsrequirecontinuousinputandoutputvariables.Oneotherassumptionisthattheindependentvariable(input)isknownandfixedandthatallofthevariationisinthedependentvariable(output).Thisisnotusuallythecase,butoftentheinputsaresettingsondialsorgaugesorsoftwarethatseemsfixedandinvariable.Manytimesthevariationintheoutputisafunctionoftheinabilityoftheinputcontrollertoholdtheinputatthesamevalue.CollectingData(y&x)–AFewThoughtsPg8?March01,BreakthroughManagementGroup.Unpublishedproprietaryworkavailableonlyunderlicense.Allrightsreserved.March16,2001Makesuretheprocesssettingscoverthelikelyproductionrange(butnottoofar).Toogreatarangepointsoutsidethenormalrangemayhavetoogreataneffectonthemodel.ToosmallarangeErrortermmaydominatethefit.Takeseveralreplicatesateachinputsetting(x).Replicaterunshelpincreasethemodelaccuracy.Randomizerunswheneverpractical.Runorderisoftensignificantfactor.Theoutput(y)atdifferentinputs(x抯)isnotalwaysindependentofprevioussettings.Agoodspreadinthedataisrequiredforagoodmodel.Considertwoexamples:Allofthedataiscollectedatthenormalprocesssettings.Inthiscase,regressionwilltrytofitalinearmodeltoacombinationofrandomprocessvariationandrandommeasurementvariation.Theresultswillbeofnovalue.Thesecondcaseiswhenmostofthedataisclusteredaroundthestandardsettingsexceptforacoupleofpointsattheextremeranges.Inthiscase,theextremepointscontrolthefitofthemodel.Ifoneoftheextremepointsisaflyer,thenthemodelwillbeinerrorduetotheflyer.TheidealcaseisfortheBlackBelttocollectarangeofdatathroughouttheprocessspace.置信区间:ConfidenceIntervalsApopulationisthesetofallmeasurementsofinteresttotheexperimenterAsampleisasubsetofmeasurementsselectedfromthepopulationAninferenceisastatementaboutapopulationparameterbasedoninformationcontainedinasampleTwotypesofinferenceEstimationApollhasbeendevisedtodeterminethepublic’sreactiontoanewpoliticalscandal.ThepurposeistoestimatethereactionofallAmericansbypollingarepresentativesampleHypothesistestingAvaccineforLymediseasehasbeendevelopedbuttherateofnegativesideeffectsis1.45%.Anewvaccinehasbeendevelopedanditisdesiredtoknowiftherateofnegativesideeffectsislowerthan1.45%.Theotherbranchofstatisticsisdescriptive.Itspurposeismerelytodescribeasetofmeasurements.InferentialstatisticsisusedtoguesswhatGodknowsaboutapopulationfromasample.Withininferentialstatistics,therearetwotypes:estimationandhypothesistesting.Estimationistryingtoguessthepopulationstatisticsfromasample.Hypothesistestingconcernsevaluatingasamplestatisticandcomparingittosomehypotheticalvalue.EstimatesandtheCLTWhatisthebestestimateofthepopulationmeanusingsampledata?Thesamplemean!Howgoodofanestimateisthesamplemean?Whatfactorsinfluencetheaccuracyoftheestimateofthemeanfromsampledata?Recallthat:ThevariationinthedistributionofsamplemeansisafunctionofthevarianceofthePopulationandthesamplesize!nPopX/σσ=WhatAboutSmallSamples?Ifthepopulationstandarddeviationisknown(italmostneveris)usethepreviousformulaforsmallsamples,tooIfthepopulationsigmaisunknown(itusuallyis):Theestimateforstandarddeviation(s)isusedThet-distributionisusedinsteadofthenormal(Z)distributionQ:Whatisat-distribution?Thet-distributionisafamilyofbell-shaped(normal-like)distributionsthataredependentonsamplesizeThesmallerthesamplesizen,thewiderandflatterthedistributionnstXμnstXnn1,2/1,2/+≤≤ααThet-distributionisthegeneralcaseforanysamplewherethepopulationstandarddeviationisunknown.However,withlargesamples,thet-andz-distributionsarenearlyidentical,soeithercanbeused.YoucanverifythisinMinitabbygeneratingalargesampleofnormaldataandthenanalyzingitwithboththez-andt-distributionroutines.ProportionsandBinomialExperimentsPg35.April01,BreakthroughManagementGroup.Unpublishedproprietaryworkavailableonlyunderlicense.Allrightsreserved.April3,2001Proportiondataisusuallytheresultofabinomial-typeexperimentBinomialexperiments(orBernoullitrials)arethosethathaveonlyoneoftwooutcomes,eithera“success”ora“failure”Theprobabilityofthistypeofexperimentisdescribedbyabinomialdistribution,acomplicateddistributionInmanycasesthenormaldistributioncanbeusedtoapproximatethebinomialdistributionWhennxp>5andnx(1-p)>5μ=nxpandσ2=nxpx(1-p)Binomialdistributionsarediscussedinalmosteverystatisticstextbook.Calculationswiththemisnotnecessarilydifficult,butitistediousifitmustbedonemanually.Minitabhasroutines,however,thatgreatlysimplifiesthecalculations.Ifthebinomialapproximationappliesandthedatacanbeestimatedwithanormaldistributionotherstatisticaltestsandcontrolchartscanbeusedthatwouldnotbeavailableotherwise.Trytoconstructyourexperimentssuchthatthebinomialapproximationisvalid.Ageneralruleofthumb:forthenormalapproximationtoapply,haveasamplesizeofatleast30andlargeenoughtoguaranteesatleast5successes.假设测试:IntroductiontoHypothesisTestingABrightIdeaNotes:Pg511Nov2000?April01,BreakthroughManagementGroup.Unpublishedproprietaryworkavailableonlyunderlicense.Allrightsreserved.Alightbulbcompanyistryingtoproduceabrighterlightbulbforthesameenergy.Itishopedthatachangeinthefilamentcoatingprocesswillproduceabrighterlight.Theengineercollectedthelasttenlightbulbsmadebeforetheprocesschangeandthefirsttenafterthechange.Themeanlightoutputoftheoldprocessbulbsis1251lumensandthenewprocessis1273lumens.Doestheincreaseof22inthemeansofthetwogroupsrepresentarealimprovement?Couldthedifferencebetweenthesetwogroupshavehappenedbyrandomchance?Shouldtheengineerswitchtothenewprocess?Thesekindsofproblemsareveryfamiliartoengineers.Anengineerisgivenatasktoimproveaprocessorproduct.Afterachangeintheprocess,theengineerisleftwiththeproblemofdeterminingwhethertheprocesschangehasmadeasignificantimprovementornot.Thoughengineersoftenusemoreadvancedtechniquestodeterminetheimprovedsettings(DOE,forexample,tobediscussedlater),ahypothesistestisoftenusedtoverifytheexperimentresults.Theprocessmaybeasfollows:?Identifytheproblem.?Designandrunanexperimenttofindanimprovedcondition.?Analyzethedataanddeterminetheimprovedoperatingpoint.?Verifytheeffectivenessoftheimprovementwithahypothesistest.AFewIlluminatingDetailsQCdatawereavailableforlightbulbsproducedinthesamefactory.Allofthebulbshadbeenproducedusingthestandardfilamentcoatingprocess.Thedatawascomprisedoftheaveragesof10samplesfromconsecutivebatchesoflightbulbs.Theen