Lean与六西格玛培训第11课：Statistical Process Control统计过程控制

6 Sigma Control,May 2015,Kenny,Operational ExcellencePanyu / China,Control,ObjectiveThe objective of the control is to: Sustain the result Prevent the potential risks,Delivery of Control Phase,2. Documents the changes/good practices that sustain the gain,1. Control Plan,3. Monitor and control the X then Y can be sustained,5. Problem solved and achieved business results. Celebration!,4. Prevent the potential risks,SPC,May 2015,Kenny,Operational ExcellencePanyu / China,Statistical Process Control统计过程控制,Control charts can be used to monitor Xs and quickly detect a change in the process due to special cause variation.控制图可以用来监控Xs，可以快速的检测出因为特殊原因导致的流程变异       Very helpful when your Xs cannot be mistake proofed or easily controlled within the required tolerance range.当你的Xs不能采用防错的方法或者较难控制在所要求的公差范围内时，控制图就会非常有帮助,Five Main Uses of Control Charts控制图的五大用途,To reduce scrap and rework and for improving productivity.可以减少报废与返工，并提高生产力。 Defect prevention. In control means less chance of nonconforming units produced.缺陷预防。在控制之中就意味着更少的机会制造出不合格品。 Prevents unnecessary process adjustments by distinguishing between common cause variation and special or assignable cause variation. 通过区分自然原因产生变异和特殊原因产生的变异，来防止不必要的流程调整。 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.提供诊断信息。使得一个有经验的操作员可以通过看控制图的数据模型就能确定流程目前的状态，接下来操作员可以采取必要的行动来改进流程的表现。Provides information about important process parameters over time. 为重要的流程参数提供信息。,Statistical Process Control: Learning Objectives统计过程控制：学习目标,Describe the two types of Control Charts描述两种类型的控制图Describe and use Variable and Attribute Control Charts描述和使用数值变量和属性变量控制图Select the appropriate control chart for a given process based on data type根据所给流程的数据类型选择合适的控制图Define the control limits and its difference with respect to specification limits.确定控制界限，了解控制界限与规格界限的差异Explain the decision errors in SPC.解释在SPC中的判定错误Explain the rules to determine whether a process is out of control解释判定一个流程是否失控的规则,Key Concepts:  Common Cause and Special Cause重要概念：自然原因与特殊原因,Common Causes 自然原因,Special Causes 特殊原因,Common causes are those causes that are inherently part of the process (or system) hour after hour, day after day, and affect everyone working in the process.  Common cause variation is the variation that results from the consistent operation of the process as designed.  It is also called random variation, noise, noncontrollable variation, within group variation, or inherent variation.自然原因是流程（系统）中一直存在的，每一个小时，每一天，作用于流程中的每一个人。自然原因的变异是在流程中进行持续一致的规定操作而产生的。我们也称它为随机变异，噪音，不可控变异，组内变异或者固有变异。,Those causes that are not part of the process (or system) all of the time, or do not affect everyone, but arise because of specific circumstances and result in a shift in the output.   Special causes can be directly accounted for and potentially removed.  Special cause variation is also called assignable cause, nonrandom variation, controllable variation, or between group variation. 这些原因在任何时候都不是流程的一部分，也不会影响到每一个人，是由于出现了特殊情况而导致了输出的偏移。我们可以对特殊原因直接作出解释并将之消除。特殊原因变异也被称为可归属原因，非随机变异，可控变异，或组间变异。,Between Subgroups组间Different people不同人Different customers不同客户Different regions不同地区Different machines不同设备Different suppliers不同供应商Etc等等.,Within Subgroups组内Absence of special causes无特殊原因 Noise variation噪音变异,Common Cause,This man wants to reach his work place by 6.55 a.m.  But he is unable to do so exactly at 6.55 a.m. everyday.  Sometimes he reaches earlier (but almost never before 6.50 a.m.).  Sometimes he reaches later (but almost never after 7.00 a.m.). WHY ?,6.55 a.m. +/-  5  minutes.,Common Cause Continued,Of Certain Factors WhichAffect the time he takes He cannot controlVary randomly e.g. The traffic he encounters under normal course of travelThe variation that occurs due to these kind of factors is called inherent variation or common cause variation.,Common Cause Continued,InherentVariability(Common Cause Variation),Aimed  value,Minimum deviation,Maximum deviation,Special cause,Special cause,TODAY HE IS LATE! WHY ?,PROBABLY BECAUSE :He  overslept.He missed the Bus.The Bus Driver was new & took some other routeHe stayed over at a friends far away,These causes are characteristic of a specific circumstance and do not occur in the normal scheme of actions.Variation due to these types of reasons is called assignable or special cause variation,Sources of Variation,14,Graphical Display of Variability,Common CauseVariability,Special Cause Variability,Special Cause Variability,Special Cause Variability,Special Cause Variability,Target Value,Control Charts 控制图,The control chart is a process analysis technique.  It is used to quickly detect the occurrence of assignable causes or process shifts so that a successful investigation of the process and proper corrective action may be taken.  This proactive approach assists in keeping the process on target with minimum variation.控制图是一种流程分析技术。用来快速的检测处特殊原因或发生的流程变化，以便于成功对流程进行研究并采取恰当的改进行动。这种主动的方法帮助我们保持流程与目标之间最小的差距,Average,表现Performance,时间Time,UCL控制上限,LCL控制下限,Control Charts show the distribution over time控制图显示了随着时间变化的分布,Components of a Control Chart控制图的组成部分,Center Line中心线,UCL控制上限,LCL控制下线,SAMPLE NUMBER样本数,Region of Nonrandom Variation非随机变异区域,Region of Nonrandom Variation非随机变异区域,Inherent Process + Measurement Variation固有的工艺值+测量的变异,+3s,-3s,X-BarX平均值,To interpret these charts, we use the control limits and look for identifiable patterns that indicate non-randomness in process behavior.我们通过控制界限和寻找可认别的非随机变化的模式这两方面来解释控制图,Sample,18,Out of control,Typical Control Chart 典型的控制图,Statistical Basics统计学基础,General Model for Centre Line and Upper and Lower control limits for variables chart 变量图形的中心线和上下控制界限的常规模型,这里,样本的均值,样本的标准偏差,控制界限与中心线之间的距离（通常为3 ）,Control Limits (If we select k=3),m,UCL,LCL,a/2 or 0.00135,a/2,Distribution of Sample Means,If you selecting +/- 3 s.You expect 1 of every 370 points to be beyond control limits when process is in control. +/- 3 s 就意味着 我们期望每370个点中，只有1个允许超出控制范围之外,Normal distribution in control chart,In control or not?,Sample,23,Five Rules五条规则,The Process is “Out of Control” if.如果满足以下任一规则，那么流程就是失控的 A point is outside the control limits.一个点在控制界限之外      2 out of 3 consecutive points > 2 s away from the mean on the same side.    3个连续点中有2个在离均值同侧2 s 的范围之外      4 out of 5 consecutive points > 1 s away from the mean on the same side.    5个连续点中有4个在离均值同侧1 s 的范围之外     9 consecutive points are on one side of the mean.    9个连续点都在均值的同一侧6 consecutive points are consistently increasing or decreasing.    6个连续点都在上升或下降,Process Out of Control流程失控,Process Out of Control流程失控,Process Out of Control流程失控,Process Out of Control流程失控,Control Charts Decisions and Actions控制图的决定与行动,What, if any, action should be taken?如果需要的话，要采取什么行动？Identify rule violations indicating assignable causes of variation.    确定显示出现特殊原因变异的规则  Identify the assignable cause(s) as to source(s).确定特殊原因及其根源 Remove and prevent recurrence.消除根源并防止再次发生  Adjust/correct for assignable cause if it can not be removed and prevented.    如果其根本原因无法消除或防止，那么调整/纠正特殊原因If no assignable causes of variation are present, assess if the amount of common cause variation is too much    如果没有特殊原因变异发生，那么评估自然原因变异的数量是否过多,Possible Decisions -可能的决定 -Take no action不采取行动Take action to adjust centering采取行动，调整中心线Take action to reduce variability采取先动，减少变异,Types of Errors in Control Charts控制图的几类错误,3s level Control Limits3个标准偏差水平控制界限 Created by Shewhart to minimize two types of mistakes由哈华特发明，用来最大程度减少两类错误 Placed empirically because they minimize the two types of mistakes这个是根据大量经验而定的,因为它们可以使这两种错误最少化.Are not probability limits不是概率界限Two types of Mistakes:两类错误 Calling a special cause of variation a common cause of variation (Missing a chance to identify a change in the process)把特殊原因变异当成了自然原因变异（错过了识别出流程变化的机会Calling a common cause of variation a special cause of variation  (Interfering with a stable process, wasting resources looking for special causes of variation that do not exist.)把自然原因变异当成了特殊原因变异 （干扰了一个稳定的流程，把资源浪费在去寻在不存在的特殊原因变异上）,Two Types of Control Chart两种类型的控制图,Uses Measured Values利用测量值Cycle Time, Lengths, Diameters, Drops, etc.周期时间，长度，直径，等Generally One Characteristic Per Chart一般每个特征值一幅控制图More Expensive, But More Information高成本，但更多的信息,Pass/Fail,  Good/Bad,  Go/No-Go  Information成功/失败，好/坏，去/不去等信息Can Be Many Characteristics Per Chart每张图里可以包括多个特征值Less Expensive, But Less Information低成本，但更少的信息,VARIABLE CHART for Continuous Data针对连续数据的变量图,ATTRIBUTE CHART for Discrete Data针对离散数据的属性图,Selecting the Appropriate Control Chart选择合适的控制图,Reference:  Most Common Control Charts参考：最常见的控制图, 2008 Capgemini All rights reserved,Continuous,Discrete,I-MR,Xbar - R,Chart Type,Good where individuals data is most logically the “rational subgroup”.Shewhart zone rules can be applied to individuals regardless of data distribution.,Pros,Cons,Falsely suggests that few data are required - best when > 30 pointsControl limits tend to be wide due to relatively small sample sizesDoes not detect most process changes as fast as charts for averages using subgroups.,p chartu chart,p chart for binomial distributionsu chart for Poisson distributionsSample size must be constant for u chartsCenterline is constant,Control limits can be variable and are a function of sample sizeNeed sample size > 50 for the p chart,Good when have high volume, sample size is 3-5,<10 allows="" process="" mean="" and="" variability="" between="" subgroups="" over="" time="" to="" be="" viewed="" assessed="" together="" detects="" changes="" quicker="" than="" i-mr="" must="" properly="" select="" rational="" reference:="" most="" common="" control="" charts="" xbar="" -="" .="">30个数据因为样本量太小，控制界限会存在变大的趋势不能像用子组均值的图表那样快的将主要的流程变化检测出来,p chartu chart,p chart 用于二项分布 u chart 用于泊松分布u chart 的样本大小必须一致中心线是固定不变的,受到样本大小的影响，控制界限是可变化的p chart 的样本大小必须> 50,适用于当大量生产时，样本大小在3至5之间，<10可以同时观测和评估流程均值和组间变异比I-MR图更快的发现变化,必须恰当的选择合理的子组,Sample size: 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).样本大小：流程产量越高，特征值的测量方式越容易，成本越低，那么你越应该选择X和R图（通常每个样本3-5个数据点），而不是单值移动极差图（I-MR）Frequency of sampling:  Consider hourly, daily, shifts, monthly, annually, lots, and so on.  The better your process is performing, the less frequently you will need to sample.抽样频率：可以考虑每小时，每天，每班，每月，每年，每批次抽样。你的流程表现的越好，抽样频率就可以越低Current industry standard tends to favor smaller, more frequent samples.目前制造业的抽样标准倾向于样本小，而抽样频率高,Sampling抽样,Process Out of Control流程失控,Control Chart Roadmap控制图的步骤,Select the appropriate variable control选择适当的变量控制 Select the data collection point选择数据收集点 Select Type of Control Chart 选择控制图表的类型 Establish basis for subgrouping建立子群基础 Determine sample size and frequency确定样本的大小和频率。 Determine measurement method/criteria确定测量的方法/标准 Determine gage capability确定测量量器的能力 Perform initial capability study to establish control limits进行最初的能力分析以建立控制界限 Set up forms for charting data 建立制图数据的形式 Prepare procedures 准备流程程序 Train personnel 人员培训,Example,Supp1Supp2598.0601.6599.8600.4600.0598.4599.8600.0600.0596.8600.0602.8598.8600.8598.2603.6599.4604.2599.6602.4599.4598.4599.4599.6600.0603.4598.8600.6599.2598.4599.4598.2599.6602.0599.0599.4599.2599.4600.6600.8,现在要研究2家供应商稳定交货的能力, 特抽取了他们各100次的交货时间,五种货物,各20个sample(如左图).请绘制出他们的SPC图来进行研究.,在这里,我们可以采用 Xbar R Chart.为什么?,Example,Delivery,Example,根据图形, 你对供应商1和供应商2,有何意见和看法?,Setting and Changing Limits 建立和改变控制界限,Develop initial control limits through a short term capability study.通过短期过程能力分析建立最初的控制界限 Remove all outliers from the data. 除去所有的数据的奇异点 Do not recalculate control limits unless process has significantly improved or based on a predetermined revision period. 不要重新计算控制界限除非流程在预先确定的修正阶段有明显的改进 Control chart limits are not constantly updated with new data.控制图的上下界限不可以随着新数据的增加而不断改变。 The goal is to improve the process over time to narrow  the control limits. 目标是改进流程，随之缩小控制界限 When do you widen the limits?什么时候要扩展界限？,Control Limits vs. Specification Limits控制界限 vs.规格界限,Question:问：      Are Control Limits the same as Specification Limits?控制界限与规格界限是一样的吗？Answer:答：     No!不一样！Control Limits reflect the expected variation in the data and are based on the distribution of the x data points. Comparing the data to the control limits will give us information about the consistency of the process over time.  控制界限反映的是预期的数据变化，它是根据X数据的分布建立起来的。通过对比数据与控制界限，我们可以得到流程随着时间推移，其一致性的信息 Specification Limits are established based upon customer or regulatory requirements.  Comparing the process to the specification limits provided information on the adequacy of the process. 规格界限是根据客户或法规的要求建立起来的。通过比较流程与规格界限，我们可以了解到流程的适当程度 A process may be in control, but the product or service may still not meet customer needs.  Being in control only means that the process is not displaying special cause variation.一个流程可能是受控的（稳定的），但是产品或服务可能仍然不能满足客户的需求。受控仅仅表示流程目前不存在特殊原因变异,Control Limits vs. Specification Limits控制界限 vs.规格界限,控制上下限,(客户的)规格上下限,真正意义,控制限由流程自身决定，而规范限由客户决定,Control Limits vs. Specification Limits控制界限 vs.规格界限,Capable of Meeting Specification能够满足规格要求,Out of control不受控,Upper Control Limit控制上限,Lower Control Limit控制下线,In control 受控,Centerline (process average or average variability)中心线 (流程平均值或平均变异）,控制上限  Upper Control Limit,控制下线  Lower Control Limit,Reference - Attribute Control Charts参考 - 属性控制图,May 2015,Kenny,Operational ExcellencePanyu / China,Selecting the Appropriate Control Chart选择合适的控制图,Attribute Data,Important Definitions重要的概念,A  Defect 一个缺陷点A single characteristic that does not meet requirements某个不符合要求的特征点          A  Defective一个缺陷品A unit that contains one or more DEFECTS包含了一个或多个缺陷点的某个产品,Attribute Charts Can Consider Either Case depending On The Chart Type Chosen通过选择合适的图表类型，属性控制图可适用于这两种情况的任何一种,Scratch,unfixed,slanted,Classification of Attribute Chart Types属性控制图分类,c,u,np,p,ConstantLot / Unit Size恒定的样本大小,VariableLot / Unit Size可变的样本大小,Defects缺陷数,Poisson柏松分布,Binomial二项分布,Defective缺陷品数,Defect缺陷 A single characteristic that does not meet requirements某个不符合要求的特征点Defective缺陷品 A unit that contains one or more DEFECTS包含了一个或多个缺陷点的某个产品,C-Chart Attribute Control Charts  C-Chart属性控制图,Chart for defects per unit (subgroup) 用于每个样本缺陷数的图表Based on Poisson distribution 以柏松分布为依据High probability of finding defect of some type.  Large samples are needed if defect probabilities are low找到某种缺陷存在高的概率。如果概率低的话需要大的样本 Lower probability of a defect of a given type对于某一指定的缺陷类型概率会较低Works best on complex unit of product 对于复杂的产品最有效 Constant subgroup/lot size 恒定的样本大小,Example C Chart,工程师希望通过SPC来控制defects rate，每两小时从1000个产品种取20个样本，然后按照各种不良种类记录下不良数。如下图。用CChart绘制出总不良的控制图以及按照不良种类绘制出各个控制图。,Results,Comment ?,Summary of Attribute Charts 属性图综述