SPC 抽样教程PPT学习教案

1、会计学1 SPC 抽样教程抽样教程PPT课件课件 第1页/共79页 Misconceptions of SPC Lets check our understanding by looking at the most common control chart, X-chart.通过回顾基本的均值控制图，检阅我们对SPC的了解 LSL USL Putting USL & LSL on X- chart helps ensure that parts are meeting Cpk requirements. Myth No. 1 It is alright to shrink USL & LSL

2、down to, say, 70% or 80%, to establish UCL and LCL. Myth No. 2 第2页/共79页 More myths and misconceptions on the X-chart.对均值控制图的误解 LSL USL Fortunately, parts still meet customer spec. although process is out of control Myth No. 3 Process in control: therefore parts meet customer spec. as well as Cpk req

3、uirements Myth No. 4 Misconceptions of SPC 第3页/共79页 LSL USL More myths and misconceptions of the X-chart.对均值控制图的误解 How did we establish the sampling plan? - Gut feel? - Passed-down figures? - Statistical calculation? - Technical judgement? 5 pcs/2 hr Myth No. 6 Misconceptions of SPC Myth No. 5 A2R W

4、e know A2R = 3s. But which s? sx, sx, swithin, soverall? 第4页/共79页 Raw Material, Components& Sub- Assemblies原材料，零件及半成品原材料，零件及半成品 Process Product Observation观察观察:Data Collection数据数据 收集收集 Evaluation评估评估:Data Analysis数据分数据分 析析 Diagnosis诊断诊断:Fault Discovery错误错误 发现发现 Decision决策决策:Formulate Action阐阐 明行动明行动

5、 Implementation推行推行:Take Action采取行动采取行动 Uncontrollable Inputs不可控的不可控的 输入输入 Controllable Inputs可控的可控的 输入输入 第5页/共79页 Statistical Process Control The process control model shifts focus to the home front, i.e. the manufacturing process, taking a preventive instead of reactive mode.制程控制模型具有前瞻性，如，制造制程，是采取

6、预防措施而非直接解决问题 It also has something which the old concept of product control lacked - statistics. This allows use of samples to understand the entire process.较早时期产品控制缺乏统计这一让我们明白整个制程的概念 The new emphasis had to have a name - Statistical Process Control (SPC).新的产品控制观念强调了SPC We owe the application of sta

7、tistics as a tool for manufacturing to Dr Walter A. Shewhart.统计在制造中的应用应归功于修哈特博士 第6页/共79页 第7页/共79页 defective raw material使用有缺陷的原材料 A process operating in the presence of assignable causes of variation is said to be “out-of-control”异因引 起的变异的制程处于不受控. 第8页/共79页 in statistical control.换句话说，使 得制程处于统计控制 第9页

8、/共79页 第10页/共79页 第11页/共79页 Measures how well a stable distribution (process in control) meets customer requirements by the proportion of products within or out of customer specs衡量一 个稳定的制程如何满足客户的 需要是看它的产品在客户规格 范围内的分布情况来确定. 第12页/共79页 控制极限控制极限 derived based on variability of the process来源于制程的变异 usually

9、apply to sample statistics such as subgroup average or range, rather than individual values通常 应用于抽样统计，如子组平均 或极差，而非个别值 第13页/共79页 meeting customer specs. or Cpk requirements 足客户规格或Cpk要求. 第14页/共79页 变量 属性 缺陷 有缺陷的 第15页/共79页 第16页/共79页 Shewhart variables control charts for subgroups work because of two imp

10、ortant principles修哈特控制图应用于子组，因为以下2个重要原理: Central Limit Theorem中心极限定律中心极限定律 Normal Distribution正态分布正态分布 Shewhart found that when the averages of subgroups from a constant-cause system are plotted in the form of a histogram, the normal distribution appears修哈特发现当把常量系统的子组平均值作成一个直方图时，就出现了常态分布. 第17页/共79页

11、2010Subgroup0 74.015 74.005 73.995 73.985 Sample Mean X=74.00 3.0SL=74.01 -3.0SL=73.99 0.05 0.04 0.03 0.02 0.01 0.00 Sample Range R=0.02235 3.0SL=0.04726 -3.0SL=0.000 X-bar-R Charts X-chart measures variability between samples均值图测 量2个样本间的差 异 R-chart measures variability within samples极差图测 量样本内的差异 第1

12、8页/共79页 R3 R4 3RRDLCL RLineCenter 3RRDUCL s s XX2 X XX2 3RAXLCL XLineCenter 3RAXUCL s s 第19页/共79页 nA2A3d2c4B3B4D3D4 21.8802.6591.1280.797903.26703.267 31.0231.9541.6930.886202.56802.575 40.7291.6282.0590.921302.26602.282 50.5771.4272.3260.940002.08902.115 60.4831.2872.5340.95150.0301.97002.004 70.41

13、91.1822.7040.95940.1181.8820.0761.924 80.3731.0992.8470.96500.1851.8150.1361.864 90.3371.0322.9700.96930.2391.7610.1841.816 100.3080.9753.0780.97270.2841.7160.2231.777 110.2850.9273.1730.97540.3211.6790.2561.744 120.2660.8863.2580.97760.3541.6460.2831.717 130.2490.8503.3360.97940.3821.6180.3071.693

14、140.2350.8173.4070.98100.4061.5940.3281.672 150.2230.7893.4720.98230.4281.5720.3471.653 160.2120.7633.5320.98350.4481.5520.3631.637 170.2030.7393.5880.98450.4661.5340.3781.622 180.1940.7183.6400.98540.4821.5180.3911.608 190.1870.6983.6890.98620.4971.5030.4031.597 200.1800.6803.7350.09690.5101.4900.4

15、151.585 210.1730.6633.7780.98760.5231.4770.4251.575 220.1670.6473.8190.98820.5341.4660.4341.566 230.1620.6333.8580.98870.5451.4550.4431.557 240.1570.6193.8950.98920.5551.4450.4511.548 250.1530.6063.9310.98960.5651.4350.4591.541 For sample size n 10, R loses its efficiency in estimating process sigma

16、 and R-chart may not be appropriate. 样本数大于10时，极差不 能用于估算制程标准差， 极差图不适用 Shewhart Constants 修哈特常数修哈特常数 第20页/共79页 How do we begin to set up an X-R chart from scratch? 如何建立均值极差控制图？ 第21页/共79页 第22页/共79页 Mixture混合性 Periodicity周期性 第23页/共79页 Secondar y Indicators Primary Indicator 第24页/共79页 Lower Control Limit

17、 Upper Control Limit Center Line Sample Number or Time Sample Quality Characteristic Upper Warning Limit Lower Warning Limit So what do you do if a point is above the Warning Limit?点在 警告线以上如何办？ 第25页/共79页 The rational subgroup concept requires that parts are pulled consecutively from the process when

18、 forming a subgroup修哈特 的合理子组概念要求组成子组的 样本必须连续地从制程抽取. Rational Subgroups合理子组合理子组 第26页/共79页 Rational Subgroups合理子组合理子组 第27页/共79页 between samples可以最大化异因在 不同样本内出现的机会. Good for detecting process shifts能 很好地探测制程偏移 Rational Subgroups合理子组合理子组 第28页/共79页 S3 S4 3SSBLCL SLineCenter 3SSBUCL s s _ XX3 X XX3 3SAXLC

19、L XLineCenter 3SAXUCL 第29页/共79页 nA2A3d2c4B3B4D3D4 21.8802.6591.1280.797903.26703.267 31.0231.9541.6930.886202.56802.575 40.7291.6282.0590.921302.26602.282 50.5771.4272.3260.940002.08902.115 60.4831.2872.5340.95150.0301.97002.004 70.4191.1822.7040.95940.1181.8820.0761.924 80.3731.0992.8470.96500.1851

20、.8150.1361.864 90.3371.0322.9700.96930.2391.7610.1841.816 100.3080.9753.0780.97270.2841.7160.2231.777 110.2850.9273.1730.97540.3211.6790.2561.744 120.2660.8863.2580.97760.3541.6460.2831.717 130.2490.8503.3360.97940.3821.6180.3071.693 140.2350.8173.4070.98100.4061.5940.3281.672 150.2230.7893.4720.982

21、30.4281.5720.3471.653 160.2120.7633.5320.98350.4481.5520.3631.637 170.2030.7393.5880.98450.4661.5340.3781.622 180.1940.7183.6400.98540.4821.5180.3911.608 190.1870.6983.6890.98620.4971.5030.4031.597 200.1800.6803.7350.09690.5101.4900.4151.585 210.1730.6633.7780.98760.5231.4770.4251.575 220.1670.6473.

22、8190.98820.5341.4660.4341.566 230.1620.6333.8580.98870.5451.4550.4431.557 240.1570.6193.8950.98920.5551.4450.4511.548 250.1530.6063.9310.98960.5651.4350.4591.541 1n2c 3 1B 1n2c 3 1B 3n4 1n4 c nc 3 A 4 4 4 3 4 4 3 For n 25 第30页/共79页 np c p u Constant常数 Lot Size Variable变数 Lot Size Defects (Poisson Di

23、stribution 泊松分布) Defectives (Binomial Distribution 二项分布) 第31页/共79页 20100 0.5 0.4 0.3 0.2 0.1 0.0 Sam ple Num ber Proportion p C h art 1 P=0.2140 3.0SL=0.3880 -3.0SL=0.04000 第32页/共79页 k21 k21 .n n n x.xx p p k n n n p1p k 1i i 2 p k = number of subgroups, should be between 20 to 25 before constructin

24、g control limits.建立控制线之前，子组数建立控制线之前，子组数 应选择在应选择在20到到25之间之间 Xk = number of defective units in subgroup k which has a total sample size of nk units 第33页/共79页 n p1p 3pLCL pLineCenter n p1p 3pUCL 第34页/共79页 n这说名在p& n 一定的条件下， 二项分布接近正态分布: p 1/2 and n 10 implying np 5 For other values of p, the general guid

25、eline is to have np 10 to get a satisfactory approximation of the normal to the binomial.如果P不等 于1/2，通则是使np10,这样就可 以使二项分布得到满意的正态型 第35页/共79页 n p1p 3p LimitsControl i n p1p 3p LimitsControl 第36页/共79页 别的样本的大小有明显的变化 nThere is a point which is near the control limits.有一点接近控制线 第37页/共79页 p1pn3pn pn p1pn3pn

26、LCL LineCenter UCL 第38页/共79页 Sample Size for p and np Charts Sample Size is determined based on the 2 criteria样本 大小基于2个标准来决定: 1.Assumption to approximate Binomial Distribution to a Normal Distribution假定二项分布近似正态分布 2.To ensure that the LCL is greater than zero.确保下 控制线大于0 p 5 , p p1 9Maximumn For p 0.5

27、 For p = other values p 10 , p p1 9Maximumn 第39页/共79页 20100 20 10 0 Sample Number Sample Count c C hart C=9.650 3.0SL=18.97 -3.0SL=0.3307 第40页/共79页 c m c c 2 c m 1ii c s c3cLCL cLineCenter c3cUCL 第41页/共79页 u u aaa ccc u u k k 2 . . 21 21 s i i i a c u Where ci is the count of the number of defects i

28、n number of inspection units, ai这里ci 是数量为ai的检查单元的缺陷数 第42页/共79页 u3uLCL uLineCenter u3uUCL 第43页/共79页 Sampling Plans for X Chart 均值图抽样计划 Sampling frequency?抽样频率 Sample size?样本大小 Width of control limits?控制线宽度 第44页/共79页 Should we take smaller samples at short intervals? Or larger samples at longer interv

29、als?可以在较短时 间内抽取小样本吗， 或在较长 时间间隔内抽取较大样本吗 Current industry practice tends to favour smaller, more frequent samples目前业界的共识是频繁 地抽去小样本 Designing an X-R Chart 第45页/共79页 results with sound practical judgement最后根据计算结果和 惯例来决定 Designing an X-R Chart 第46页/共79页 3 s s 3 s s 99.73% Lower Control Limit Center Line

30、Upper Control Limit What does each area of 0.135% mean?每一个这样 的区域代表什么？ 0.135% 0.135% 第47页/共79页 Lower Control Limit Upper Control Limit Center Line Sample Number or Time 0.135% 0.135% Is process really out of control? Or is the point outside due to random variation? 第48页/共79页 第49页/共79页 0.135% 0.135% L

31、ower Control Limit Upper Control Limit Center Line Sample Number or Time 0.135% 0.135% Is process really in control? Or is the point inside due to random variation of the shifted process? Shifted Process 第50页/共79页 sampling frequency平均运转周期用来 帮助决定抽样大小和频率 1 0 ARL )1 ( 1 1 ARL 第51页/共79页 Designing an X-R

32、 Chart 3 s s 3 s s 99.73% Lower Control Limit Center Line Upper Control Limit 0.135% 0.135% 第52页/共79页 Designing an X-R Chart 3 s s 3 s s 99.73% Lower Control Limit Center Line Upper Control Limit 0.135% 0.135% 第53页/共79页 Designing an X-R Chart 第54页/共79页 Designing an X-R Chart 第55页/共79页 nn = f , , D D

33、 , s s Designing an X-R Chart 第56页/共79页 Designing an X-R Chart 第57页/共79页 Designing an X-R Chart 2 2 k ZZ n This chart is for = 0.27% only. k, 1 1 第58页/共79页 Designing an X-R Chart 2 2 k ZZ n 第59页/共79页 Example 1: Designing an X-R Chart Your management has the following concerns with regards to impleme

34、nting control charts at the shopfloor在推行控制 图时，管理层很关心下列问题: 1.False Alarm:错误报警 Not more than 1 false alarm for every 500 hrs of production 每500小时的生产不超过1个错误报警. 2.Exposure:暴露 Not more than 3 hrs exposure if process has shifted如果制程 偏移，不超过3小时暴露. 3.Allowable Shift允许偏移: From historical data, Ppk 2.2. Min customer requirement, Ppk 1.6 Design an appropriate Xbar-R chart to meet the above constraints.设计一个均值极差图满足上列条件要求 第60页/共79页 After some time, the factory decides to switch to 14 hrs of production per day.一段时间后，工厂决定每天14小时生产 Tolerable false alarm:极限错误报警 Average 1 false alarm per month (30 days)每月平均1个错误报警