给16萌萌哒的小学妹弟研一上运营管理om5-2quality management

1、11.Process Capability and Statistical Quality Control生产能力和统计质量控制 ninth editionProcess Variation工艺变化 Process Capability加工能力 Process Control Procedures过程控制程序 Variable data可变数据 Attribute data属性数据 Acceptance Sampling验收抽样 Operating Characteristic Curve操作特性曲线 OBJECTIVES目标 Basic Forms of Variation基本形式的变化 A

2、ssignable variation is caused by factors that can be clearly identified and possibly managed可传承的变化是由于可被明确界定且能够管理的因子引起Common variation is inherent in the production process常见的变异存在于生产过程Example: A poorly trained employee that creates variation in finished product output.例如:一个缺乏训练的员工,在成品输出方面创造了奇迹。Exampl

3、e: A molding process that always leaves “burrs” or flaws on a molded item.例如：一个成型工艺,在塑造项目中总是存在“毛刺”或缺陷。 Taguchis View of Variation变化的塔古奇观点IncrementalCost of Variability增量成本的可变性 HighZeroLowerSpecTargetSpecUpperSpecTraditional ViewIncrementalCost of VariabilityHighZeroLowerSpecTargetSpecUpperSpecTaguch

4、is ViewTraditional view is that quality within the LS and US is good and that the cost of quality outside this range is constant, where Taguchi views costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs.传统观点认为：在LS和US范围内质量是好的，质量成本将超出

5、恒定范围；而田口的观点认为费用将随着变异性的增加而增加，所以努力达到零缺陷,这将真正地降低质量成本。Process Capability加工能力 Process limits过程限制 Specification limits规格界限 How do the limits relate to one another?如何使限制彼此相关? Process Capability Index, Cpk过程能力指数， CpkShifts in Process Mean转变过程的含意Capability Index shows how well parts being produced fit into d

6、esign limit specifications.能力指数显示了好的部件是适合设计规格限定的。 As a production process produces items small shifts in equipment or systems can cause differences in production performance from differing samples.作为产生物品的生产过程，设备或系统的小变化会引起不同样品生产性能的差异。 A simple ratio:一个简单的比例: Specification Width规格宽度 Actual “Process Wi

7、dth”真实的“工艺宽度 ”Generally, the bigger the better.一般来说,越大越好 Process Capability A Standard Measure of How Good a Process Is.过程能力用于衡量过程有多好Basic Forms of Statistical Sampling for Quality Control统计抽样质量控制的基本形式Acceptance Sampling is sampling to accept or reject the immediate lot of product at hand抽样验收是一种抽样方法

8、，用来接受或拒绝当前在手边的许多产品Statistical Process Control is sampling to determine if the process is within acceptable limits统计过程控制一种抽样方法，用来确定那些过程是否在可接受的限度内Acceptance Sampling验收抽样 Purposes目的Determine quality level确定质量水平 Ensure quality is within predetermined level确保质量在预定的水平 Advantages优势 Economy经济性Less handling

9、damage减少操作损失 Fewer inspectors减少检查员 Upgrading of the inspection job检查工作升级Applicability to destructive testing破坏性试验的适用性Entire lot rejection (motivation for improvement)完全排斥（改进动力）Disadvantages劣势Risks of accepting “bad” lots and rejecting “good” lots接受“次品的” 风险很大，同时错过很多 “正品”Added planning and documentati

10、on添加规划和文档Sample provides less information than 100-percent inspection抽样比100%检验提供更少的信息Acceptance Sampling: Single Sampling Plan验收抽样:单一的抽样方案 A simple goal一个简单的目标 Determine (1) how many units, n, to sample from a lot, and (2) the maximum number of defective items, c, that can be found in the sample bef

11、ore the lot is rejected决策(1)确定有多少单元, n值,样品来自那里(2)最多的次品,c, 在许多退回的样品中查找出来的Risk风险Acceptable Quality Level (AQL)可接受的质量水平(AQL)Max. acceptable percentage of defectives defined by producer生产者决定缺陷的最大可接受比例。The a (Producers risk) a(生产者的风险) The probability of rejecting a good lot拒绝良好选择的概率Lot Tolerance Percent

12、Defective (LTPD)废品率的接受度(LTPD) Percentage of defectives that defines consumers rejection point废品率决定消费者拒绝接受的限度 The (Consumers risk) （顾客的风险）The probability of accepting a bad lot接受一个次品的概率 Operating Characteristic Curve操作特性曲线 n = 99c = 4AQLLTPD01123456789101112Percent defectiv

13、eProbability of acceptance =.10(consumers risk)a = .05 (producers risk)The OCC brings the concepts of producers risk, consumers risk, sample size, and maximum defects allowed together操作特性曲线带来的生产者风险、消费者的风险、样本大小和允许存在的最大次品数的概念The shape or slope of the curve is dependent on a particular combination of t

14、he four parameters曲线的形状或波动是依赖于四个参数的特定组合Example: Acceptance Sampling Problem例如:验收抽样问题 , a manufacturer of video interfaces, purchases printed wiring boards from an outside vender, Procard. Procard has set an acceptable quality level of 1%(AQL) and accepts a 5% (alpha) risk of rejecting lots at or bel

15、ow this level. considers lots with 3% (LTPD) defectives to be unacceptable and will assume a 10%(beat) risk of accepting a defective lot. ,一个视频接口的制造商,购买来自外部供应商Procard的打印配线板。Procard已经设定了一个1%可接受的质量水平(AQL)，同时他接受5%或者低于这个水平的被拒绝的风险(生产者风险)。 认为有3%(LTPD次品率接受度)次品是不可接受的,然而顾客将承担10%(（顾客的风险）)的次品 。 Develop a sampl

16、ing plan for and determine a rule to be followed by the receiving inspection personnel. 形成了一个抽样计划，同时确定了一个被接收检查人员验证的规则。 Example: Step 1. What is given and what is not?例如:第一步。什么是已知的和什么不是? In this problem, AQL is given to be 0.01 and LTDP is given to be 0.03. We are also given an alpha of 0.05 and a be

17、ta of 0.10.在这个问题中，已知可接受的大质量标准是0.01 ，次品率接收度是0.03。我们已知是0.05 ，是0.10。What you need to determine is your sampling plan is “c” and “n.”根据你的样本规划，你需要计算出“c” 和 “n.”Example: Step 2. Determine “c”例如:第二步。计算 cFirst divide LTPD by AQL.第一步，用LTPD 比AQL得出nThen find the value for “c” by selecting the value in the “n(AQ

18、L)”column that is equal to or just greater than the ratio above. 然后根据n值列（与它相等或比它更大的比率）选择对应的ccLTPD/AQLn AQLcLTPD/AQLn AQL044.8900.05253.5492.613110.9460.35563.2063.28626.5090.81872.9573.98134.8901.36682.7684.69544.0571.97092.6185.426So, c = 6.Example: Step 3. Determine Sample Size例如：步聚三，确定样本容量c = 6,

19、from Tablen (AQL) = 3.286, from TableAQL = .01, given in problemSampling Plan:Take a random sample of 329 units from a lot. 取一个含有329个个体的随机样本 .Reject the lot if more than 6 units are defective.如果次品率超过就拒绝接受。Now given the information below, compute the sample size in units to generate your sampling pla

20、n现以已知下面的信息，来计算样本容量，然后制定你的样本规划n(AQL/AQL) = 3.286/.01 = 328.6, or 329 (always round up)12. Capability of Process工艺能力ninth editionProcess CapabilityThis is a “one-sided” Capability Index这是一个“片面”能力指数Concentration on the side which is closest to the specification - closest to being “bad”集中最接近的一方达到次品规格。工序

21、能力指数(1)概念：工序能力指数是衡量工序能力对产品规格要求满足程度的数量值，记为Cp。通常以规格范围T与工序能力B的比值来表示。即： T=规格上限TU - 规格下限TL。 (2)工序能力与工序能力指数的区别：工序能力是工序具有的实际加工能力，工序能力强并不等于对规格要求的满足程度高。 而工序能力指数是指工序能力对规格要求满足的程 度，工 序能力指数越大，说明工序能力的贮备越充足，质量保证能力越强，潜力越大，不合格品率 越低，一定的工序能力指数将与一定的不合格品率相对应。 计量值双侧规格界限 双侧规格界限是指既具有规格上限(TU)要求，又有规格下限(TL)要求的情况 (1)无偏规格中心Tm与分

22、布中心 重合 计算公式： 工序不合格品率p 的估计： 直接根据规格上、下限TU、TL 以及工序分布的数字特征，估 计 和S 进行计算 根据工序能力指数Cp计算。 由式: 因此有 例1P1P2TLTUTmf（x）T例1根据某工序加工零件的测试数据计算得出， =6.5,S=0.0055，规格要求为 。试求该工序的工序能力指数及不良品率。解： 计算公式： 绝对偏移量 ： (图中曲线1) 偏移系数 ： 工序能力指数： 或： 当k，即eT/2时， 规定Cpk=0 (图中，曲线2) 不合格品率估计： 采用“用Cp和k值估计不合格品率”例2f（x）有偏时工序能力指数与不合格品率e12eTLTUP1P2Tmx

23、T(2)有偏规格中心Tm与分布 中心 不重合计量值双侧规格界限例2测试一批零件外径尺寸的平均值 =19.0101，S=0.0143，规格要求为 ，试计算工序能力指数并估计不合格品率。 解：由题意： 计算Cpk 或由Cp=0.816，k=0.145查表得不良品率估计约为2.1%2.3% (1)仅给出规格上限TU 计算公式： 当TU 时，p50%，则规定Cp0 不合格品率估计： 例 某零件质量要求加工后不得大于71g，测试部分数 据后得 70.2g，S0.24g，试计算工序能力指数 Cp及不合格品率p。 解： 计量值单侧规格界限f（x）TUx计量值单侧规格界限(2)仅给出规格下限TL 计算公式：

24、当 TL 时，p50%，则规定Cp0 不合格率估计： 例3 要求零件淬火后的硬度HRC71，实测数据后计算 得 HRC73；S1，试计算工序能力指数Cp及不 良品率p。 解：f（x）TLx-TL计数值计件值 计算公式 以不合格品率上限pU作为规格要求： (1)取k个样本，每个样本的样本容量分别为n1，n2，nk，每个样本中 的不合格品 数为d1，d2，dk。 (2)计算平均不合格品率及平均样本量 (3)计算工序能力指数Cp例1 某产品规格要求pU0.1，现取5个样本，n1n2n5100, 各样本中不合格品数为：d17，d25，d36，d42，d54，求工序能力指数Cp。 解： 计数值计点值 计

25、算公式 :规格要求是单位产品平均缺陷(或疵点数)上限或不合格品率 很小时的样本中不合格品数上限CU (1)取k个样本，每个样本的样本容量分别为n1,n2，nk， 每个样本的疵点数(或不 合格品数)为C1，C2，Ck。 (2)计算平均疵点数(或平均不合格品数) (3 )计算工序能力指数Cp 例2:设某产品规格要求单位产品平均缺陷上限CU2，取容量为10的样本5个，各样本中产品的缺陷数分别为C17；C25；C36；C4 2； C54，求工序能力指数Cp。 解：工序能力的评价与处置 工序能力指数Cp客观地、定量地反映了工序能力对规格要求的适应程度，因此它是工序能 力评价的基础。根据工序能力指数的大小

26、一般可将加工分为五类： 1 Cp1.67 特级加工 2 1.67Cp1.33 一级加工 3 1.33 Cp1 二级加工 4 1Cp0.67 三级加工 5 Cp0.67 四级加工 Example: Step 3. Determine Sample Size例如：第三步，确定样本容量c = 6, from Tablen (AQL) = 3.286, from TableAQL = .01, given in problemSampling Plan:Take a random sample of 329 units from a lot.取一个含有329个个体的随机样本 . Reject the

27、lot if more than 6 units are defective.如果次品率超过就拒绝接受Now given the information below, compute the sample size in units to generate your sampling plan现以已知下面的信息，来计算样本容量，然后制定你的样本规划n(AQL/AQL) = 3.286/.01 = 328.6, or 329 (always round up)The Cereal Box Example麦片盒的例子 We are the maker of this cereal. Consume

28、r Reports has just published an article that shows that we frequently have less than 15 ounces of cereal in a box.我们是麦片制造商。消费者报告刚刚发表了一篇文章,显示出在我们的麦片包装盒里经常少装低于15盎司的麦片。 Lets assume that the government says that we must be within 5 percent of the weight advertised on the box. 政府说我们必须确保盒内麦片重量在盒子上的广告上所说的5

29、%的波动范围内波动。 Upper Tolerance Limit = 16 + .05(16) = 16.8 ounces（上线）Lower Tolerance Limit = 16 .05(16) = 15.2 ounces（下线）We go out and buy 1,000 boxes of cereal and find that they weight an average of 15.875 ounces with a standard deviation of .529 ounces.我们出去买1000盒麦片粥，然后发现他们平均重15.875盎司，标准差.529盎司。 Cerea

30、l Box Process Capability麦片盒工艺能力Specification or Tolerance Limits规格或接受范围Upper Spec = 16.8 ozLower Spec = 15.2 ozObserved WeightMean = 15.875 ozStd Dev = .529 ozWhat does a Cpk of .4253 mean?.4253 Cpk 的意思是什么？An index that shows how well the units being produced fit within the specification limits. 一个索

31、引表明了产生的部件符合规格程度。 This is a process that will produce a relatively high number of defects.这是一个生产相对较多次品数的工艺。Many companies look for a Cpk of 1.3 or better 6-Sigma company wants 2.0!许多公司追求Cpk达到1.3，而公司想要达到2.0。Types of Statistical Sampling统计抽样的类型Attribute (Go or no-go information)属性Defectives refers to t

32、he acceptability of product across a range of characteristics.次品数指的是产品的可接受性超过特定范围Defects refers to the number of defects per unit which may be higher than the number of defectives.不合格数是指单位次品数量可能高于次品率。 p-chart applicationp-chart应用 Variable (Continuous)连续变量Usually measured by the mean and the standard

33、 deviation.通常用均值和标准差衡量。 X-bar and R chart applicationsx标杆和R图的应用 Statistical Process Control (SPC) Charts统计过程控制(SPC)图表UCLLCLSamples over time 1 2 3 4 5 6UCLLCLSamples over time 1 2 3 4 5 6UCLLCLSamples over time 1 2 3 4 5 6Normal Behavior正常行为Possible problem, investigate探讨可能存在的问题,Possible problem, in

34、vestigateControl Limits are based on the Normal Curve基于正常曲线的控制限制x0123-3-2-1zmStandard deviation units or “z” units. Control LimitsWe establish the Upper Control Limits (UCL) and the Lower Control Limits (LCL) with plus or minus 3 standard deviations from some x-bar or mean value. Based on this we ca

35、n expect 99.7% of our sample observations to fall within these limits.我们从一些x标杆或者平均值中加上或者减去三倍标准差，以建立上控制限(UCL)和下控制限(LCL）。基于此,我们可以期待99.7%观察样品达到这些限制。 xLCLUCL99.7%Example of Constructing a p-Chart:构建一个p-Chart图Required Data数据要求Sample No.样本编号No. ofSamples样本数量Number of defects found in each sample在每一个样本中发现的

36、次品数Statistical Process Control Formulas:统计过程控制公式: Attribute Measurements (p-Chart)属性测量(p-Chart) Given:Compute control limits: 1. Calculate the sample proportions, p (these are what can be plotted on the p-chart) for each sample计算样品的比例,p(这些东西可以绘制在p-chart)为每一个样品 Example of Constructing a p-chart: Step

37、 12. Calculate the average of the sample proportions计算样品的平均比例 3. Calculate the standard deviation of the sample proportion计算样本比例标准差Example of Constructing a p-chart: Steps 2&34. Calculate the control limits计算控制限 UCL = 0.0924LCL = -0.0204 (or 0)Example of Constructing a p-chart: Step 4Example of Cons

38、tructing a p-Chart: Step 5UCLLCL5. Plot the individual sample proportions, the average of the proportions, and the control limits绘制个别样品比例,平均水平比例,控制范围Example of x-bar and R Charts: Required DataExample of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean of means, and mean of ranges.在x标杆的和R图表的例子中:步骤计算样本均值、样本容量、均值的均值和均值范围Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Val