统计过程控制简介

统计过程控制简介统计过程控制简介我们是否应该采取行动？Should we take action?每天我们都被数据淹没,而且不得不作出决定Every day we are flooded by data and we are forced to make decisions工厂产量下降Plants Output Decreases By 4%美国贸易赤字增加亿 US Trade Deficit Rises By$40Billion 某公司获利比上季度降低亿Company Xs Earnings Are Off$240Million From Previous Quarter 我们需要解释数据的方法 We Need Ways to Interpret Data今天采集什么样的数据？What Type Of Data Is Collected Today?制造业 Manufacturing:_非制造业 Non-Manufacturing _如何分析数据？How Is It Analyzed?制造业 Manufacturing :_非制造业 Non-Manufacturing _得知数据好坏后该当如何？What Happens If It Is Bad/Good?制造业 Manufacturing :_非制造业 Non-Manufacturing _ _客户需求下限Lower“Customer”Requirement这一方法THIS METHOD告诉你关于客户的需求Tells you where you are in regards to customers needs不告诉你怎么满足用户需求及下一步怎么办 It will NOT tell you how you got there or what to do next客户需求上限Upper“Customer”Requirement 我们管理数据的方式过去(历史来讲)的方式 The Way We Manage Data Historically不用管它,不会坏的Leave It Alone.It Aint Broke痛苦,受累Pain&Suffering痛苦,受累Pain&Suffering这一方法导致何种管理行为？This method causes what type of management behavior?客户需求下限Lower“Customer”Requirement客户需求上限Upper“Customer”Requirement 我们管理数据的方式历史来讲的方式 The Way We Manage Data Historically不用管它,不会坏的Leave It Alone.It Aint Broke痛苦,受累Pain&Suffering痛苦,受累Pain&Suffering23Scrap Level(%)废品率11996Celebration Time工厂废品率为年度最低的The factory scrap level is at a year low of 2%经理给工厂颁奖Manager presents an award to the plant 在餐厅进行庆祝：每人都可分享免费皮萨饼和饮料 Ceremony in the cafeteria:pizza and refreshments for all!“每人都应为他们的成就骄傲每人都应为他们的成就骄傲”“Everyone should be proud of what theyve accomplished”.Everyone should be proud of what theyve accomplished”.Derived from Understanding Variation:The Key To Managing Chaos,Donald J.Wheeler,SPC Press.1993.年月 APRIL 1996J F M A 2311996经理希望能将发出去的奖收回来Manager wants to take back award废品率连续三个月持续增长Three consecutive months of scrap increases.经理希望能将发出去的奖收回来Manager wishes he could take back the award经理考虑要采取行动了 Manager is thinking about taking actionScrap Level(%)废品率年月 JUNE 1996Derived from Understanding Variation:The Key To Managing Chaos,Donald J.Wheeler,SPC Press.1993.J F M A M J2311996No more“Nice Guy”不再充好人了废品率上升到 Scrap rises to a value of 2.6%经理决定采取行动 Manager decides to take action召开一个“特别会议”来寻求一个永久性的解决方案A“special meeting”is called to solve this problem once and for all.经理在长篇大论次品率多么重要后离开了雇员们不知道该干什么另外，他们有其他更重要的评估标准于是，他们什么也没做 After a sound lecture on the importance of scrap,the manager leaves.Employees arent sure what to do.Besides,they have other metrics which have more importance.So they do nothing.Scrap Level(%)废品率年月NOVEMBER 1996Derived from Understanding Variation:The Key To Managing Chaos,Donald J.Wheeler,SPC Press.1993.J F M A M J J A S O N经理看到从去年开始废品率持续下降 Manager has seen reduced scrap levels since the end of last year 教训教训：“严格的管理会出成效！严格的管理会出成效！”The Learning:“A tough management style gets results!”“A tough management style gets results!”Manager concludes:“Tough Love Makes Things Happen”23119961997Scrap Level(%)废品率1997年6月 JUNE 1997Derived from Understanding Variation:The Key To Managing Chaos,Donald J.Wheeler,SPC Press.1993.J F M A M J J A S O N D J F M A M JDerived from Understanding Variation:The Key To Managing Chaos,Donald J.Wheeler,SPC Press.1993.将数据置于统计流程控制图中Putting The Data In A SPC Chart23119961997Scrap Level(%)废品率J F M A M J J A S O N D J F M A M JUCLLCL统计流程控制图显示不同的解释,可为什么呢?SPC Tells A Different Story.But Why?23119961997Scrap Level(%)废品率J F M A M J J A S O N D J F M A M JUCLLCL“人们已知的最佳方式之一是如不能使用控制图分析数据会：增加成本,浪费的努力和降低士气;-Donald J.Wheeler 博士“Failure to use control charts to analyze data is one of the best ways known to mankind to:increase costs waste effort andlower morale.”-Dr.Donald J.Wheeler统计流程控制图显示不同的解释,可为什么呢?SPC Tells A Different Story,But Why?S=统计技术:检查偏差 Statistical techniques used to examine process variationC=控制过程通过积极管理 Controlling the process through active managementP=过程,任何过程 Process,ANY Process现在我们管理数据的方法-SPCThe Way We Manage Data-Today SPC显示过程偏差随时间变化的图形控制图方法Control Charts Method它从哪里来的?Where Did It Come From?19世纪20 年代-西部电器 的 Walter Shewhart博士:1920s-Western Electric/Dr.Walter Shewhart惯于确认受控的&未受控的偏差 Used to identify Controlled&Uncontrolled Variation 受控制的:普通原因或固有偏差Controlled:Common Cause or Inherent Variation未控制的:特殊起因或可指定的偏差Uncontrolled:Special Cause or Assignable Variation在背景噪声中试图发现由特殊原因造成的偏差Tries to find the special cause variation in all of the background noise使用控制图作为主要工具Uses Control Charts as main toolFive Main Uses of Control Charts 控制图的5个主要用途To reduce scrap and rework and for improving productivity.为了减少废品和返工及提高生产力Defect prevention.In control means less chance of nonconforming units produced.预防缺陷Prevents unnecessary process adjustments by distinguishing between common cause variation and special or assignable cause variation.预防不必要的过程调整 Provides diagnostic information so that an experienced operator can determine the state of the process by looking at patterns within the data.The operator can then make the necessary changes to improve the process performance.提供过程诊断信息Provides information about important process parameters over time.提供过程重要参数随时间推移的信息 差异类型-“普遍 VS 特别”Types of Variation“Common vs.Special”普遍原因 COMMON CAUSE呈现在每个过程中 Is present in every process 自然的 Natural 随机的 Random可能被去除和或变小,但在过程上要求一个根本变化Can be removed and/or lessened but requires a fundamental change in the process稳定的,可重复的过程偏差来源.存在于每一个操作/过程由过程本身造成的(由我们做事的方式决定的)一般来说,通过管理可以控制特殊原因 SPECIAL CAUSE不可预见的Unpredictable与普通偏差比较大 Typically large in comparison to Common Cause variation可以由基本的过程控制和监视去除或变小 Can be removed/lessened by basic process control and monitoring 偏差类型“普遍 VS 特别 Types of Variation“Common vs.Special”时不时地存在于大多数操作/过程,并且持续地存在于某些过程.由一个或一系列的干扰造成的.一般来说,通过操作者可以控制(至少可以发觉).我们认为如果过程中有我们认为如果过程中有特别原因偏差特别原因偏差,它们就是它们就是失控和不稳定的失控和不稳定的.A process exhibiting Special Cause variation is said to be Out-of-Control and Unstable练习Exercise当它与你的项目有关系时,确认某种“普通原因”和“特别原因”偏差可能的形式As it relates to your project,identify some possible forms of“common cause”and“special cause”variation普遍原因Common Cause特殊原因Special Cause Minitab 控制图 Control ChartsMinitab 控制图练习Control Charts Exercise我们用一些随机的数据Lets use some Random data从您的生意中，我们使用一些代表性的数值和正态偏差创造25 行任意正常数据，Create 25 rows of random normal data using some representative values for Mean and Std Dev from your business绘制单独图 Plot an Individuals chart注意监视时间和价值被绘制在Y 轴 Note that monitoring over time and the value is plotted in the Y axis随时间变化的数据 DATA PLOTTED OVER TIMEMONITORED CHARACTERISTICUCLCenter LineLCLUCL=Upper Control Limit /LCL=Lower Control LimitPlotted Data主要部分-控制图Key Component -Control Charts Definitions 定义In Control 受控No special cause variation present 在波动中没有特殊原因引入All variation is random所有的波动都是随机的Out of Control失控At least one special cause is present至少有一个特殊原因引入Some variation is non-random 一些波动不是随机的关于测试我们建议The tests we suggest:-MINITAB 测试Minitab tests:全部测试All Tests(测试1-8Test 01 through 08)-样品规则Pattern rule:如果你看到一个样品，过程已经失控If you see a pattern,the process is out of control 1 Sigma2 Sigma3 Sigma1 Sigma2 Sigma3 Sigma60-75%90-98%99-99.9%of Data PointsUCLLCL时间时间 TIMETIME我们测量的项目 The Item We Are Measuring标准偏差的规则Rules of Standard Deviation数据应该在哪?“Where should the data lie?”Minitab 测试TestsTest#1Test#2过程控制测试标准Process Control Tests我们建议使用。全部测试We suggest using.all tests.在控制下还是失控？In Control or Out of Control?如果在控制以外,打破了什么规则或表现出什么条件?If out of Control,which rule(s)is broken or condition(s)is present?在控制下还是失控？In Control or Out of Control?如果在控制以外,打破了什么规则或表现出什么条件?If out of Control,which rule(s)is broken or condition(s)is present?在控制下还是失控？In Control or Out of Control?如果在控制以外,打破了什么规则或表现出什么条件?If out of Control,which rule(s)is broken or condition(s)is present?失控意味什么?What does Out-of-Control mean?查出控制的缺陷Detecting Lack of Control如果您确定您的过程是“失控”你应该做什么？What should you do if you determine that your process is“Out of Control?”查出控制的缺陷 Detecting Lack of Control因此,根据现在你所知道的,如果你的过程在控制下，在控制上限和下限之间百分之多少数据点将会下降?Therefore,based on what you know so far,what percent of data points should fall between the upper control limit(UCL)and lower control limit(LCL)if your process is in-control?UCLLCLTIMETIME控制极限 VS 规格限制 Control Limits vs.Specification Limits如果点落在上限之外或控制下限之下，是否意味着我们为顾客做了一个缺陷产品?If a point falls beyond the upper or lower controlcontrol limit does this mean we are making a defect for the customer?控制极限 VS 规格限制 Control Limits vs.Specification Limits UCLLCLTIMETIME控制极限对规格限制 Control Limits vs.Specification Limits过程控制极限是由过程能力决定的 Process Control Limits are calculated based on data from the process itself他们根据+/-3s(99.73%我们期望过程偏差落在这些极限之间)They are based on+/-3s (99.73%of the process variation is expected to fall between these limits)产品规格极限规范极限是由客户的要求决定的,不是在控制图上发现的Product Specification Limits ARE NOTARE NOT found on the control chart很重要一点是要了解程序控制与顾客要求如何吻合.Understanding how the process matches up against customer requirements IS IS important to know确定过程执行如何满足顾客期望,需要进行过程能力研究。To determine how the process performs to Customer Expectations,a Process Capability StudyProcess Capability Study is required.n把规格限制放在在控制图上Putting specification limitsspecification limits on a Control Chartn 把控制上限和控制下限当做规格限制 Treating UCL and as a specification limit2个控制图的大错误TWO BIG CONTROL CHART ERRORS控制极限对规格限制 Control Limits vs.Specification Limits当你把任意上下限作为监视工具时，他就不再是个控制图.LCL When you do either of these the control chart becomes just an inspection tool-its no longer a control chart.控制上限和控制下限并不直接与客户缺陷有联系!UCL/LCL are not directly tied to customer defects!如何收集数据How to Collect Data合理分组 Rational subgroups n通过合理分组，使各组只包括普遍原因 collect data so that subgroups contain only common cause variation.The same as in capability analysis.n通过合理分组，使各组尽可能包括更多信息 Choose rational subgroups to gain as much information as possible about the process.过程偏移 To detect process shifts:n每组尽可能在相同时间获取测量结果 each subgroup should consist of measurements taken at approximately the same time.n选择样本时尽可能获取组内各样本间最大的波动可能性 Choose a sample so that it maximizes the likelihood of detecting variability between the samples抽样Samplingn样本大小 Sample size 过程容量越大，对于关键CTQ特性的测量就越容易越简单。The higher the process volume and the easier and cheaper the measurements of the CTQ characteristic,the more likely you are to select an X and R chart(typically 3-5 data points per sample)over an Individual and Moving Range chart(I and MR).n抽样频率 Frequency of sampling考虑到每时、每天、每班、每月、每年、每批次等等。过程质量水平越高，所需样本越小。Consider hourly,daily,shifts,monthly,annually,lots,and so on.The better your process is performing,the less frequently you will need to sample.当前产业标准趋向于小批量多频率的抽样。Current industry standard tends to favor smaller,more frequent samples.如果采取消除特别起因行动(稳定过程)并且能力被证明,100%监视可能被取消(但是要知道客户的特殊检查计划)建立和维护控制限Setting Up and Maintaining Control Limitsn用20-25个样本计算控制限,每个样本大小为3-5。Calculate the control limits with 20-25 samples(e.g.,for the X and R chart that would mean 20-25 samples of size 3-5).n如果受控进入最后一步。If process is in control,go to the last step.n如果不受控，找出特殊原因 If process is not in control,try to identify special cause.n消除特殊原因，重新收集数据，重新计算控制限，直到过程受控Remove special cause,recollect data,recalculate control limits,until you find the process is in control.n在未来的监测中不要随意的改变控制限，除非过程有永久和渴望的改变。For future monitoring,do not change the limits unless a permanent,desired change has been made to the process.两种数据类型控制图 Two General Kinds of Data属性控制图 ATTRIBUTE 使用离散,可计的数据 Pass/Fail,Good/Bad,Go/No-Go Information 合格/不合格,好/坏,通过/不通过等信息Can Be Many Characteristics Per Chart 一张图可以同时描述许多特性 Less Expensive,But Less Information 需要较少的资源，所含信息量亦较少Ex:1,2,3,4 etcGood/BadMachine 1,2,3.变量控制图 VARIABLES-使用连续,可测量的数据 Continuous,Measured DataCycle Time,Lengths,Diameters,Drops,etc 周期,长度,直径,体积,等等Generally One Characteristic Per Chart 通常每张图描述一种特性 More Expensive,But More Information 需要更多的资源,但所含信息量更多 Ex:Weight=10.2 LbsThickness=11.211 inches(1)螺钉扭矩在每个装配线传输的左前角离开 Bolt torque on the front left corner of every transmission coming off the assembly line(2)每个螺钉离开装配线传输的平均扭矩Average bolt torque of every bolt for each transmission coming off the assembly line(3)每个发动机所缺的螺钉数#of missing bolts per engine(4)每个销售合同的排字数#of typos per sales contract(5)每月生产缺陷发动机的数目 Number of engines with defects in monthly production(6)每月生产缺陷发动机的的百分比数%of defective engines in monthly production(7)根据应收帐款,收回它的时间 Per accounts receivable,amount of time it takes to close it(8)每100个发动机的缺陷数 Number of engines with defects per 100 built练习：什么类型的数据？Exercise:What Type of Data?属性型变量连续型变量数据类型？连续变量 VS 属性变量数据分组还是单个数据?缺陷数 VS 缺陷比例?GROUPS(Averages)(n1)INDIVIDUALVALUES(n=1)X-Bar RX-Bar SIndividualsMoving Range缺陷数缺陷比例Is The Probability Of A Defect Low?If You Know How ManyAre Bad,Do You Know How Many Are Good?Poisson DistributionBinomial DistributionIndividualsMoving RangeNOYESYES样本大小一定？YESNOc Chartu Chart样本大小一定？np ChartNOYESp Chart如何选择控制图 Choosing the Correct Control Chart NOTE:X-Bar S is appropriate for subgroup sizes(n)of 10控制图的主要类型 Major Types of Control Charts变量图 Variables ChartsI-MR(个体individuals)X-Bar(平均average)特性图 Attribute ChartsNP (有缺陷的数字Number defective)P (有缺陷的比率Proportion defective)C (过失数量Number of defects)U (每个单位的过失数量Number of defects/unit)练习:选择什么类型的控制图?Exercise:What Type of Control Chart?(1)螺钉扭矩在每个装配线传输的左前角离开 Bolt torque on the front left corner of every transmission coming off the assembly line(2)每个螺钉离开装配线传输的平均扭矩Average bolt torque of every bolt for each transmission coming off the assembly line(3)每个发动机所缺的螺钉数#of missing bolts per engine(4)每个销售合同的排字数#of typos per sales contract(5)每月生产缺陷发动机的数目 Number of engines with defects in monthly production(6)每月生产缺陷发动机的的百分比数%of defective engines in monthly production(7)根据应收帐款,收回它的时间 Per accounts receivable,amount of time it takes to close it(8)每100个发动机的缺陷数 Number of engines with defects per 100 builtVariable Control Charts连续数据控制图X-bar R Chart平均值和极差图(Xbar-R 图)属性型变量连续型变量数据类型？连续变量 VS 属性变量数据分组还是单个数据?缺陷数 VS 缺陷比例?GROUPS(Averages)(n1)INDIVIDUALVALUES(n=1)X-Bar RX-Bar SIndividualsMoving Range缺陷数缺陷比例Is The Probability Of A Defect Low?If You Know How ManyAre Bad,Do You Know How Many Are Good?Poisson DistributionBinomial DistributionIndividualsMoving RangeNOYESYES样本大小一定？YESNOc Chartu Chart样本大小一定？np ChartNOYESp Chart如何选择控制图 Choosing the Correct Control Chart NOTE:X-Bar S is appropriate for subgroup sizes(n)of 10有效的连续数据控制图包括.A Valid Variable Control Chart Has Data in time or production sequence 以时间或生产顺序排序的数据to show stability,time-to-time variation 表示稳定性，随时间的波动A measure of central tendency 对居中趋势的测量to portray behavior of process center 描述过程的居中A measure of variability 对离散程度的测量Control limits 控制极限to allow separating common cause from assignable cause 可用来区分通常原因和特殊原因(可归因原因)X-Bar-R charts(Xbar-R图)X Bar Chart:a plot of the sample means over time.Xbar图：反映样本平均值随时间的变化R Chart:a plot of the range(difference between highest and lowest values)of a sample over time.R图：反映样本的极差(样本中最大值和最小值的差)随时间的变化Xbar-R图实例 Minitab File:Xbar_r.mtw contains measured data for a main shaft O.D.see column 1(C1)=NC_Lathe.The data is in subgroups of size 3.Minitab文件:Xbar_r.mtw 包含主轴的测量数据，数据见C1栏(NC_Lathe).数据子样为3.The O.D.specifications are.060+/-.003.产品的规范是.060+/-.003.=1.Check stability with a run chart.用趋势图检验过程的稳定性2.Check for normality.检验过程是否是正态分布3.Using Minitab,create an Xbar and R Chart what are your observations?用Minitab画出Xbar-R图，你得出什么观察结论?4.Do the given specifications(specs)“relate”to the Control Limits on the Xbar Chart?If so,how?给出的产品规范与Xbar图的控制极限相关吗？如果是的话，如何相关？5.How does Process Control“relate”to Process Capability?过程控制如何与过程能力相关？MINITAB FILE:Xbar_r.mtw MINITAB文件:Xbar_r.mtwXbar-R图实例 1.Double Click“C1.”双击“C1.”2.Type in a 3 for Subgroup size.子样大小为3.3.Click“OK.”点击“OK.”Note that 3.0 SL denotes a 3 sigma limit=Control Limit注意3.0 SL 表示控制极限=3sigma水平 Do not confuse this with specification limits.不要将控制极限与规范极限混淆Xbar-R图实例 The control limits are for averages,not individual values.控制极限是根据平均值计算得出的 Most specifications are for individual values.大多数规范是关于个体数值的USLUCLLCLLSLXbar-R图实例 Variable Control Charts：I&MR Chart连续数据控制图：I-MR图离散型变量连续型变量数据类型？连续变量 VS 属性变量数据分组还是单个数据?缺陷数 VS 缺陷比例?GROUPS(Averages)(n1)INDIVIDUALVALUES(n=1)X-Bar RX-Bar SIndividualsMoving Range缺陷数缺陷比例Is The Probability Of A Defect Low?If You Know How ManyAre Bad,Do You Know How Many Are Good?Poisson DistributionBinomial DistributionIndividualsMoving RangeNOYESYES样本大小一定？YESNOc Chartu Chart样本大小一定？np ChartNOYESp Chart如何选择控制图 Choosing the Correct Control Chart NOTE:X-Bar S is appropriate for subgroup sizes(n)of 10I-MR图More useful in low volume,intermittent operations 在数据量较少，间歇性操作时更有用Similar to X bar&R Charts,Except 除以下几点外，与Xbar-R图相似Single Values,Not Subgroups 单个数值，不是子样平均值Range Values Must Be Artificially Constructed 极差值需要人工计算Somewhat“Noisier”Because Of Loss Of“Damping”由于使用个体数值，与Xbar-R图比较更易受干扰 IM Charts IM图Individuals Chart:a plot of the individual values over time.个体图(I图)：反映个体数值随时间的变化Moving Range Chart:a plot of the moving range(for two samples|Xi-Xi-1|)over time.移动极差图(MR图)：反映两个连续样本的移动极差随时间的变化 Individual Data个体数据Moving Range移动极差 55 N/A 56 ABS(55-56)=1 59 ABS(56-59)=3 55 ABS(59-55)=4605958575655Individuals个体43210Moving Range移动极差建立I-MR图Data from a shaft diameter turning operation are entered on the control chart form on the next page for 25 consecutive pieces of product,in production sequence.数据是按照生产次序排列的25个连续的转轴产品的直径The data is in Minitab File:Imr.mtw,column shaft_OD.Using Minitab,create the I-MR chart.数据在Minitab文件:Imr.mtw的shaft_OD.栏中，用Minitab画I-MR图Analyze your results.Are there out-of-control indications?List the indications,if any,by type and by plot point numbers.分析结果，过程是否有失控的征兆?根据征兆类型及其编号，列出失控征兆 What is happening in the process?过程出现了什么情况?I-MR图实例MINITAB FILE:Imr.mtwMINITAB文件:Imr.mtwI-MR图实例1.Double click on“Shaft_OD.”双击“Shaft_OD.”2.Click“Tests.”点击“Tests.”3.Click on“Perform all eight tests.”点击“Perform all eight tests.”I-MR图实例I-MR图实例 连续数据控制图小结Take AwaysVariable Control Charts Variable control charts can be used with continuous data to tell when a process is:连续数据控制图可以用来区分过程状态:experiencing only common cause variation and working at its intended best 过程只包含通常原因引起的偏差，处于受控状态 when the process is disturbed and needs corrective action 过程受到干扰，需要采取纠正行动控制图:time ordered plot of data 描绘数据随时间的变化reflect the expected range of variation of the data 反映所期望的数据波动的范围 identifies when a special cause appears to be influencing the data 识别何时特殊原因出现，影响数据分布 X-Bar&R charts are used for plotting means and ranges of subgroups over time.Xbar-R图用来描述子样的平均值和极差随时间的变化 I&MR charts are used for plotting individual values and moving ranges over time.I-MR图用来描述个体的数值和移动极差随时间的变化 Control limits are typically calculated as 3 standard deviations away from the mean of the process.控制极限一般是按过程中心值+/-3个标准偏差计算出来的 Control limits and specification limits are not the same.控制极限和规范极限是不一样的 Control limits are calculated from the sample data;they are internal to the process 控制极限是根据样本数据计算得出的;是过程的内部特征 Specification limits are determined by your performance standard;they are external to the process 规范极限是由执行的标准决定的;是过程的外部特征 Know when a process is out of control:Western Electric Rules.知道过程何时失控:Western Electric规则 Control charts are only as good as the actions that you take to keep the process under control.控制图和采取的纠正行动共同使过程保持受控 连续数据控制图小结Take AwaysVariable Control Charts Attribute Control Charts逻辑数据控制图属性型变量连续型变量数据类型？连续变量 VS 属性变量数据分组还是单个数据?缺陷数 VS 缺陷比例?GROUPS(Averages)(n1)INDIVIDUALVALUES(n=1)X-Bar RX-Bar SIndividualsMoving Range缺陷数缺陷比例Is The Probability Of A Defect Low?If You Know How ManyAre Bad,Do You Know How Many Are Good?Poisson DistributionBinomial DistributionIndividualsMoving RangeNOYESYES样本大小一定？YESNOc Chartu Chart样本大小一定？np ChartNOYESp Chart如何选择控制图 Choosing the Correct Control Chart NOTE:X-Bar S is appropriate for subgroup sizes(n)of 10重要定义 Important Definitions A Defect(缺陷)A single characteristic that does not meet requirements 不满足要求的单一特性A Defective(缺陷率)A unit that contains one or more DEFECTS 包含单个或多个缺陷的单位Attribute Charts Can Consider Either CaseDepending On The Chart Type Chosen根据所选择的控制图类型，逻辑数据控制图可以考虑两者之一的情形逻辑数据控制图的分类Classification of Attribute Chart Types cun ppConstantLot/Unit Size样本数不变VariableLot/Unit Size样本数变化Defects缺陷数Poisson泊松分布Binomial两项式分布Defective缺陷率Attribute Control Chart逻辑数据控制图C-Chart(C图)属性型变量连续型变量数据类型？连续变量 VS 属性变量数据分组还是单个数据?缺陷数 VS 缺陷比例?GROUPS(Averages)(n1)INDIVIDUALVALUES(n=1)X-Bar RX-Bar SIndividualsMoving Range缺陷数缺陷比例Is The Probability Of A Defect Low?If You Know How ManyAre Bad,Do You Know How Many Are Good?