6sigma实例教程.doc

6 SIGMA 项目运作实例项目运作实例 INDEX 6 6 SigmaSigma 项目运作实例项目运作实例 定义阶段定义阶段 如何定义一个项目 我们在定义阶段做什么 如何进行项目问题陈述 如何作项目财务节省预测 如何绘制宏观图 项目的目标陈述要点 财务评估表样本 确定 Team Members 成员 测量阶段测量阶段 如何进行项目描述 如何绘制工艺流程图 如何绘制工艺流程细图 精简制造与 5S 如何绘制鱼骨图 定性测量系统研究 工艺能力分析 定量测量系统研究 分析阶段分析阶段 失效模式及后果分析 图形技术分析 中心限理论 相关性及简单线性回归 置信区间 假设测试 均值测试 标准偏差测试 比例测试 偶然性检验 样品尺寸选择 一元方差分析 改进阶段改进阶段 2K 因子实验（基本） 2K 因子实验（中心点） DOE 简介 部分因子实验 全因子实验 随机分区设计 控制阶段控制阶段 项目如何结束 控制方法 EVOP-FLEX 多变量回归 定性 SPC 因变量表面回归方法 变量 SPC-1 变量 SPC-2 6 Sigma 项目运作实例项目运作实例-定义阶段定义阶段-如何项目定义一个项目如何项目定义一个项目 如何定义一个项目？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 a2. Pareto 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 CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-定义阶段定义阶段-我们在定义阶段做什么我们在定义阶段做什么 我们在定义阶段需要做什么？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 CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-定义阶段定义阶段-如何进行项目问题陈述如何进行项目问题陈述 如何进行问题陈述？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？ CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-定义阶段定义阶段-如何作项目财务节省预测如何作项目财务节省预测 项目财务节省预测金额由冠军提供项目财务节省预测金额由冠军提供 6 Sigma 项目运作实例项目运作实例-定义阶段定义阶段-如何绘制宏观图如何绘制宏观图 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 6 Sigma 项目运作实例项目运作实例-定义阶段定义阶段-项目的目标陈述要点项目的目标陈述要点 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 CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-定义阶段定义阶段-财务评估表样本财务评估表样本 财务评估表样本财务评估表样本: CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-定义阶段定义阶段-确定确定 Team Members 成员成员 确定确定 Team Members 成员成员: 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)。 CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-测量阶段测量阶段-如何进行项目描述如何进行项目描述 如何进行项目描述如何进行项目描述: 1.目标陈述 2.Metric 图 3.月节省额 6 Sigma 项目运作实例项目运作实例-测量阶段测量阶段-如何绘制工艺流程图如何绘制工艺流程图 如何绘制工艺流程图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 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）: 6 Sigma 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 Microsoft OfficeTM 等软件中可找到 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 CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-测量阶段测量阶段-如何绘制工艺流程细图如何绘制工艺流程细图 如何绘制工艺流程细图如何绘制工艺流程细图: 工艺流程细图： 6 Sigma 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。 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） 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：6 Sigma 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 CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-测量阶段测量阶段-精简制造与精简制造与 5S 精简制造与精简制造与 5S: 精简制造例似于日本的 5S 6 Sigma 项目运作实例项目运作实例-测量阶段测量阶段-如何绘制鱼骨图如何绘制鱼骨图 精简制造与精简制造与 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。 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。 5.进一步优化：对各种详细列出的因子再列出其输入变量。 *6m-man, machine ,method, measurement, material, mother nature (environment) (6M:人员，机器，方法，测量，原材料，环境) CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-测量阶段测量阶段-定性测量系统研究定性测量系统研究 定性测量系统研究定性测量系统研究: 定性型量具 R the alternate hypothesis is that the data is not normal. For interpretation, a low p-value means that the data is not normal. Exercise Variance Vs. Target A drug company has reformulated an anti-histamine product. The company is concerned that the variability in the potency of the new product may not be the same as the old product. Plenty historical data tells us that the standard deviation of the old drug is 0.15. Thirty samples of the new drug were tested and the data is in column C4 of VarExamples.mtw Is the variability potency of the new drug different from the old drug? Use = 0.01. Use the single-variance hypothesis testing recipe to conduct the appropriate hypothesis test and answer the question CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-分析阶段分析阶段-比例测试比例测试 比例测试比例测试: Testing Proportion In Six Sigma, the target for the mean is often the specification mean. This is to answer the question, 乬 Is my process centered, yet?乭 Other times, the target is the old process baseline. Then the question is, 乬 Have I made a significant change, yet?乭 The 2-mean comparisons have many uses: comparing machines, processes, factories, process settings, testers, etc. The paired t-test is a special case of the 2-sample test when each data point in the first distribution has an exact counterpart in the second distribution. These tests are often before/after tests. For example, if a Black Belt or Green Belt wants to test the effectiveness of a new chicken feed, he might measure the chickens before the diet change and after. The data are then analyzed as paired observations, because the final weight of the chickens, irrespective of the diet, is most certainly dependent on the weight before the change. ANOVA Model Mathematical Model for ANOVA ij j ij y += Where: y ij = a single response from Treatment j = overall mean j = the contribution from Treatment j ij = random error 0 0 0 = j a one least : H s : H different is one least : H . : H j a j =2 1 0 Mathematical Hypothesis Conventional Translation This mathematical model is the basis for ANOVA. The importance of this will be made clearer during discussion of DOE. ANOVA Introduction Example: A fertilizer company wants to compare fields treated with four new, spring wheat fertilizers to fields with no fertilizer. Ten different fields were sampled for each treatment and the average bushels/acre was computed. Problem: Were any of the fertilizers different from each other and the unfertilized control group? Many times, there are more than two groups of means. ANOVA solves the problem of more than two means. Multiple t-tests Adequate? An experimenter could run 2-sample t-tests against every combination of means 1 vs. 2, 1 vs. 3, 1 vs. 4, 1 vs. 5 2 vs. 3, 2 vs. 4, 2 vs. 5 3 vs. 4, 3 vs. 5 4 vs. 5 Why would this not be a good idea? Obviously, it is tedious and cumbersome What about alpha risk? Each t-test has a risk of false rejection () 4 . 0 10 95 . 0 1 = =total Remember, the probability of being successful in a multi-step process is the product of the individual step probabilities. Each of the 10 combinations of tests would need to be correct in order for the entire analysis is correct, that is, 0.95 x 0.95 x x.095 for each of the ten processes. The total alpha risk is one minus the probability of being correct, or in this case 0.4. That is approximately 40% of the time in a five-treatment analysis like this, we would incorrectly identify a difference that does not in truth exist. Solution Analysis of Variance ANOVA is really an extension (generalization) of the 2-sample t-test ANOVA is a method of detecting difference between multiple means of samples Why is it called Analysis of Variance? ANOVA is the mathematics behind the intuitive evaluation ANOVA compares/analyzes variances Variance within a group Variance between groups ANOVA is also the basis for analyzing DOE, which will be covered in Week 3. Minitab ANOVA Results Case 1 One-way ANOVA: TmtA, TmtB, TmtC, TmtD, TmtCntrl1 Analysis of Variance Source DF SS MS F P Factor 4 24.65720 6.16430 643.60 0.000 Error 45 0.43100 0.00958 Total 49 25.08820 Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -+-+-+- TmtA 10 6.5500 0.0850 (*) TmtB 10 6.9500 0.0850 (*) TmtC 10 5.9900 0.1101 (*) TmtD 10 7.5200 0.1033 (*) TmtCntrl 10 5.5200 0.1033 (*) -+-+-+-Pooled StDev = 0.0979 6.00 6.60 7.20 Level NNMeanStDev TmtA106.55000.0850 (*) TmtB106.95000.0850 (*) TmtC105.99000.1101 (*) TmtD107.52000.1033 (*) TmtCntrl105.52000.1033 (*) What do you think this means? Minitab ANOVA Results Case 2 One-way ANOVA: Tmt1, Tmt2, Tmt3, Tmt4, TmtCntrl2 Analysis of Variance Source DF SS MS F P Factor 4 31.51 7.88 3.89 0.009 Error 45 91.25 2.03 Total 49 122.76 Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -+-+-+-+- Tmt1 10 6.250 1.457 (-*-) Tmt2 10 7.260 1.561 (-*-) Tmt3 10 6.240 0.729 (-*-) Tmt4 10 7.710 1.412 (-*-) TmtCntrl 10 5.490 1.748 (-*-) -+-+-+-+-Pooled StDev = 1.424 4.8 6.0 7.2 8.4 Level NMeanStDev Tmt 1106.2501.457(-*-) Tmt 2107.2601.561(-*-) Tmt 3106.2400.729(-*-) Tmt 4107.7101.412(-*-) TmtCntrl105.4901.748 What do you think this means? Analysis of Variance General Recipe 1.State the practical problem 2.State the null hypothesis 3.State the alternate hypothesis 4.Do the model assumptions hold? 5.Construct the Analysis of Variance Table 6.Do the assumptions for the errors hold (residual analysis)? 7.Interpret the p-value (or the F-statistic) for the factor effect (p 分析阶段分析阶段-偶然性检验偶然性检验 偶然性检验偶然性检验: Contingency Tables measuring only one characteristic in each sampling unit Examples: Blood pressure reading on a patient, number of crashes at an intersection in a month Bivariate or Multivariate Measurements taken on 2 or more characteristics per sampling unit. Examples: Surveys that correlate answers to demographic data, a study of voting habits by education level. Contingency tables are concerned with bivariate or multivariate data. A Contingency Table Example The board of regents at a university would like to determine if two variables are independent: employee classification (staff, faculty, administrator) and whether a single union should be the sole collective bargaining agent for employee benefits. A random sample of 200 employees is taken from employee records and each employee is classified according to both variables. The data are in Excel worksheet CTables.xls and on the following slide Minitab Output Expected counts are printed below observed counts Favor NotFavor Undecide Total 1 30 1515 60 24.00 27.00 9.00 2 40 5010100 40.00 45.00 15.00 3 10 25540 16.00 18.00 6.00 Total 80 90 30 200 FavorNotFavorUndecideTotal0027.009.00 240501010040.0045.0015.00 3102554016.0018.006.00 Or FavorNotFavorUndecideTotal0027.009.00 240501010040.0045.0015.00 3102554016.0018.006.00 Total809030200 90=27+45+18 200 = 60+100+40 30=9+15+6? Chi-Sq = 1.500 + 5.333 + 4.000 + 0.000 + 0.556 + 1.667 + 2.250 + 2.722 + 0.167 = 18.194 DF = 4, P-Value = 0.001 Does this look familiar? ? P-value分析阶段分析阶段-样品尺寸选择样品尺寸选择 样品尺寸选择样品尺寸选择: Why Sample Size Is Important: A Class Exercise in Minitab Start Minitab - Select Calc Random Data Normal Generate two data sets Sample1 = 0, = 1, n=10 Sample 2 = 0.5, = 1, n=10 Conduct a 2-sided, 2-sample t-test on the data. What do you conclude? Repeat with n = 25, n=50, n=75 Hi = 80 minutes ?Temp: Lo = 127.5 degrees; Hi = 132.5 degrees First Step: Code the variables from raw values to +1 抯, 0 抯 and -1 抯. We will call coded variables X1, X2 etc. and refer to natural variables as N1, N2etc. The general coding formulae for X1 is: Or N N low high high low 1 112 1 N12 X1=+ (NN ) / ) ()/ Center Nat Range X1 2 =N1(Nat ()/ Point) CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-控制阶段控制阶段-变量变量 SPC-1 变量变量 SPC-1 Points to Ponder (cont.) SPC stands for Statistical Process Control. Too often these techniques are applied to outputs (product characteristics) instead of inputs (process characteristics). Often monitoring of outputs is a necessary first step, but input control is the goal. Measurement systems are critical to proper data analysis Measurement variation must be understood and in statistical control before application of SPC. Measurement variation must be a small fraction of the total process variation in the process data. Do not implement an SPC program on instruments without first performing a Measurement Systems Analysis (MSA)! A large fraction of the control charts are actually applied to the monitoring of outputs instead of the controlling of inputs. Often this comes from enthusiasm for SPC without doing the difficult work of finding y=f(x) first. Until the critical outputs have been identified, output monitoring may be the only option. Also, the application of SPC techniques on outputs does increase the understanding of time series data. The election example later in this module is an example of charting an output to help draw conclusions about the time ordering of data. Prevention vs. Detection In the past, manufacturing depended on inspection to screen out nonconforming product This process produces rework and scrap, in other words, waste or lots of MUDA. Inspection does not increase quality, it only affects customer annoyance. DETECTION TOLERATES WASTE Strategies for prevention are required in todays markets First, mistake-proof the process If mistake-proofing is impractical or impossible, then control the inputs to prevent nonconforming outputs PREVENTION AVOIDS WASTE One of the problems with charting outputs is the slow response time. The product is already out of statistical predictability before the data show the change or deviation. Deviation in an input may be caught prior to making any bad product if SPC is instituted on the inputs. Remember, the goal of Lean Manufacturing and Six Sigma is the reduction of waste, not the detection of waste. SPC Is a Feedback System Parts of the process control (feedback) system: The process the way the 5ms (man, machines, materials, methods, and mother nature) work together to produce the output Information about performance the ideal information to be gathered is about the inputs (Xs), although some benefit is obtained from monitoring the outputs (Ys). SPC is the vehicle for communicating information about changes in Xs or Ys. Action on the process (Xs) actions on the input should be taken to prevent output variation. The effect of the action should be monitored and further action taken if necessary. Action on the product (Ys) least economical method. Required sometimes when the output does not consistently meet customer requirements. Required sometimes to verify effectiveness of action on the process. CLICK TO INDEX 6 Sigma 项目运作实例项目运作实例-控制阶段控制阶段-变量变量 SPC-2 变量变量 SPC-2 Interpreting Control Charts Control charts are powerful tools for detecting special cause variation. If a special cause is found: 1.If the out of control condition is part of a trend, mark the beginning and end of the trend 2.Analyze the process to determine the cause of the OOC condition 3.Correct the condition and prevent it from recurring 4.Recalculate the control limits omitting the OOC values from the calculations 5.Re-evaluate the chart according to the new limits Control limits are only recalculated when the causes for the OOC conditions have been identified and corrected Control charts should be plotted for only one purpose: to generate actions to contro