SPC Introduction I

1、Jen2014-01-15SPC IntroductionSPC Introductionknowledgeknowledge ofof basicbasic statisticalstatistical conceptsconceptsSPCSPC导论导论基本基本统计统计概念知识概念知识六点原则六点原则1.1. 知识要转换成行动，只收集资料及知识要转换成行动，只收集资料及绘图是不够的。绘图是不够的。2.2. MSMS必须确认是受控、稳定及不是重必须确认是受控、稳定及不是重要变异来源。要变异来源。3.3. 变异的研究及统计讯号及工具的应变异的研究及统计讯号及工具的应用范围，不限於工厂生产。用范

2、围，不限於工厂生产。4.4. SPCSPC每个字都是重点。不用统计没每个字都是重点。不用统计没S S。只对产品，不对过程没。只对产品，不对过程没P P。都不是。都不是SPCSPC。六点原则六点原则5. 实做，才可以真知。每个人都必须实做，才可以真知。每个人都必须实际进行个案。实际进行个案。6. 持续深入研究，以满足客户需求。持续深入研究，以满足客户需求。尤其是统计学。尤其是统计学。个案设计个案设计 RP01RP01 PPAPPPAP样品分组习题样品分组习题The need for process control Detection-tolerates waste侦测 Prevention-av

3、oids waste预防Process control system model with feedback FigureFigure I.1I.1 FourFour elementselements ofof thethe system(system(四要素）四要素）TheThe processprocess（过程）（过程）InformationInformation aboutabout performanceperformance（过程绩效资讯）（过程绩效资讯） 过程本身、过程的内在变异性过程本身、过程的内在变异性 选定过程特性、设定目标值、监控实际值、差异比较、是否选定过程特性、设定目

4、标值、监控实际值、差异比较、是否需要行动需要行动ActionAction onon thethe processprocess（针对过程的行动）（针对过程的行动）ActionAction onon thethe outputoutput（针对产出的行动）（针对产出的行动） 隔离、分检、重工、修理、报废隔离、分检、重工、修理、报废 过程不稳定、不够能力时，不得已还是要做。过程不稳定、不够能力时，不得已还是要做。制程控制系统制程控制系统 有反馈的过程控制系统模型有反馈的过程控制系统模型 过程的呼声 人 设备 材料 方法 产品或 环境 服务 输入 过程/系统 输出 顾客的呼声我们工作的方式/资源的融

5、合统计方法顾客识别不断变化的需求和期望54.554.454.854.354.254.755.254.754.154.055.254.554.354.854.154.954.254.954.854.753.954.753.854.554.354.654.555.454.453.854.554.454.854.354.254.755.254.754.154.055.254.554.354.854.154.954.254.954.854.753.954.753.854.554.354.654.555.454.453.854.554.254.654.654.755.454.454.854.954.25

6、4.854.855.254.254.354.353.954.454.354.353.954.753.854.554.354.654.555.454.453.854.554.454.854.354.254.755.254.754.154.054.154.454.554.354.254.755.254.754.854.054.854.555.254.854.154.954.254.954.354.754.454.753.954.554.354.654.555.453.853.854.954.254.554.654.755.454.454.854.654.254.354.854.854.254.35

7、4.353.954.455.254.3抽样抽样推论推论样本样本样本统计量样本统计量母体参数母体参数母体母体62.7762.4662.3462.3562.3462.4662.4862.2362.3962.4562.3662.4662.4962.7562.2062.4562.7062.5062.4962.3362.3662.4762.6362.5362.6762.3462.4462.5062.5462.3362.6062.6862.4662.6462.3762.5062.5162.3762.4562.4562.3462.5762.3662.5562.4462.4462.4462.5462.6862

8、.5062.6262.5462.6362.6062.4762.5162.4662.2562.6062.4062.3662.2662.2362.2762.5762.3862.4862.5662.5962.4462.7262.4362.4462.4562.3862.2062.5462.5062.5662.3762.4662.5462.3562.4162.4262.7862.6462.3462.3762.4962.4962.6362.4662.3662.4662.5362.2462.4162.3662.470510152025303562.2762.3462.4262.4962.5662.6362.

9、762.78单单峰峰对对称称平均数的意义平均数的意义 所有观察值的总合，除以所有观察值的个数。平均数在数线上代表资料的平衡点。平均数平均数求下列数据的平均数平均数(62.53+62.47+62.68+62.55+62.38+62.79+62.41) / 7= 62.544編號1234567量測值62.5362.4762.6862.5562.3862.7962.41中位数中位数将观察值由大而小排列，位于中央的数值即为中位数，若观察值为偶数，中位数为中央两个数值的平均。求下列数据的中位数中位数为62.53編號1234567量測值62.5362.4762.6862.5562.3862.7962.41

10、排序1234567量測值62.3862.4162.4762.5362.5562.6862.79众数众数量测值中出现次数最多的数值。求下列数值的众数众数为62.4762.2962.3862.4162.4762.4762.4762.4962.5362.5562.6662.6862.6862.7062.79量測值极差极差将量测值中的最大值减去量测值中的最小值，所得到的数值即为极差。极差 = 62.79 - 62.38 = 0.41編號1234567量測值62.5362.4762.6862.5562.3862.7962.41样本标准偏差公式为距离重心所在位置的距离，平方之後的平均数样本与母体公式不一样

11、求下列数值的样本标准偏差平均数= 62.552样本标准偏差編號1234量測值62.5362.4762.6862.55求下列数据的平均数、中位数、众数、求下列数据的平均数、中位数、众数、极差与标准偏差。极差与标准偏差。平均数平均数= 171.98 / 21 = 8.189= 171.98 / 21 = 8.189中位数中位数 首先将数据排序首先将数据排序8.248.188.208.228.128.278.158.238.188.208.218.118.268.148.228.168.198.208.118.258.14中位数= 8.20 众数= 8.20极差= 8.27 - 8.11 = 0.1

12、6标准偏差= 0.04848.118.118.128.148.148.158.168.188.188.198.208.208.208.218.228.228.238.248.258.268.27DistributionDistribution分配分配 Pieces vary from each other. But they form a pattern that, if stable, can be described as a distribution.有大有小才有分配 Distribution can differ in location, spread and shape.位置、分布宽

13、度、形状 Figure I.2 upper side 每件产品的尺寸与别的都不同 范围 范围 范围 范围但它们形成一个模型，若稳定，可以描述为一个分布 范围 范围 范围分布可以通过以下因素来加以区分 位置 分布宽度 形状 或这些因素的组合态分配曲线以钟形呈现，在正中央部份为其顶峰，该点是机率分配的平均数，中位数及众数所在。态分配以其平均数为中心，左右对称且向左右延伸，渐趋向X轴靠近。0510152025303562.2762.3462.4262.4962.5662.6362.762.78010020030040050060070080062.1462.1762.262.2362.2562.28

14、62.3162.3462.3762.462.4262.4562.4862.5162.5462.5762.5962.6262.6562.6862.7162.7362.7662.7962.82 f(x)xaa-5-4-3-2-1012345N(0, 1)N(0, 0.09)N(0, 0.25)xf(x) 0-5-4-3-2-1012345N(-2, 0.25)N(2, 0.25)N(0, 0.25)xf(x)=0=2=-2首先将区间上下限予以标准化，设若要求(a , b )区间内的机率，则先将数值a与b予以标准化。所谓标准化，即是将欲求的数值换算为与平均值的距离为几个标准偏差已知平均值为10.24

15、，标准偏差为1.28，请将区间( 1112 )化成正态分配的标准化数值表示。 f(z)0N(0,1)0.54P 02054.zf(z)0.54P=0.2946N(0,1)0zf (z)zP=0.5P=0.1368-0.35 0f (z)P=0.3413P=0.1915-0.501z首先计算首先计算226226克于正态分配中的位置克于正态分配中的位置Z=( 226 - 224.8 )/0.72Z=( 226 - 224.8 )/0.72Z=1.67Z=1.67P(z=1.667)=0.9525P(z=1.667)=0.9525成品总重小于成品总重小于226226公克的比例为公克的比例为95.25

16、%95.25%计算225克于正态分配中的位置Z=( 225 - 224.8 )/0.72Z=0.27P(z=0.27)=0.6064P(0.27=z=1.67)=0.9525-0.6064=0.3461成品总重介于225公克与226公克之间的比例为34.61%首先计算138.45mm于正态分配中的位置Z=( 138.45 - 138.49 )/0.033Z=-1.21P(z=-1.21)=1- P(z=1.21)=1-0.8869=0.1131成品总长度小于138.45mm的比例为11.31%计算计算138.55mm138.55mm于正态分配中的位置于正态分配中的位置Z=( 138.55 -

17、138.49 )/0.033Z=( 138.55 - 138.49 )/0.033Z=1.82Z=1.82P(z=1.82)=0.9656P(z=1.82)=0.9656P(-1.21=z=1.82)=0.9656-0.1131=0.8525P(-1.21=z=2.40)=1-0.9918=0.0082P(z=2.40)=1-0.9918=0.0082P(z=-2.56)=1- P(z=2.56)=1-P(z=-2.56)=1- P(z=2.56)=1-0.9948=0.00520.9948=0.00520.0082+0.0052=0.01340.0082+0.0052=0.0134不良率为不

18、良率为1.34%1.34%Ppk=1 Ppk=2 中心值距离上下规格线，1*3 标准偏差时Ppk=1 中心值距离上下规格线，2*3 标准偏差时Ppk=2 中心值偏向哪一边？距离多少？Ppk=? 中心值距离上下规格线，各多少？其中小值是多少？Ppk=? Common causes refer to the many causes of variation that consistently acting on the process. common causes within a process produce a stable(稳定） and repeatable（可重复） distribut

19、ion over time. If only common causes of variation are present and do not change, the output of a process is predictable（可预测）. Special causes (often called assignable causes) refer to any factors causing variation that only affect some of the process output. They are often intermittent（间歇） and unpred

20、ictable（不可预测）. If special causes of variation are present, the process output will not be stable over time（不稳定）. 特殊原因并不只是特殊差，可以特殊好。 Local actions局部行动Are usually required to eliminate special causes of variationCan usually be taken by people close to the processCan correct typically about 15% of proc

21、ess problems Actions on the system系统行动Are usually required to reduce the variation due to common causesAlmost always require management action for correction(People directly connected with the operation will be in a better position to identify them and pass them to management for action.)Are need to

22、 correct about 85% of process problems Connections between actions and causes Confusion about the type of action to take Close teamwork between management and those persons directly connected with the operation Corrections or reaction plan Corrective action or preventive actionDetectedpotential 过动儿（

23、过严控制、干预或是过度调整） 植物人 The decisions about actions affecting the process require balancing the risk of taking action when action is not necessary (over control or tempering) versus failing to take action when action is necessary (under control). These risks should be handled in the context of the two so

24、urces of variationspecial causes and common causes. Mistake 1. Ascribe a variation or a mistake to a special cause, when in fact the cause belong to the system (common causes) Mistake 2. Ascribe a variation or a mistake to a system(common cause), when in fact the cause was special. Over adjustmentte

25、mpering is a common example of mistake No. 1. Never doing anything to try to find a special cause is a common example of mistake No. 2. 过程必须保证始终产生准确和精密的结果不精密 精密准确不准确 Statistical controlIn controlOut of controlCapabilityAcceptableCase 1Case 3Unacceptable Case 2Case 4Case 3 processThe customer is inse

26、nsitive to variation within specifications.The economics involved in acting upon the special cause exceed the benefit to any and all customers. Economically allowable special causes may include tool wear, tool regrind, cyclical (seasonal) variations, etc.The process is mature. That means the process

27、 has undergone several cycles of continual improvement. The special cause to be allowed has been shown to act in a consistent manner over a known period of time.A process control plan is in effect which assure conformance to specification of all process output and protection from other special cause

28、s or inconsistency in the allowed special cases.过程控制过程控制 受控 （消除了特殊原因） 时间 范围 不受控 （存在特殊原因） 过程能力过程能力 受控且有能力符合规范 （普通原因造成的变差已减少） 规范下限 规范上限 时间 范围 受控但没有能力符合规范 （普通原因造成的变差太大） Process capability能力 is determined by the variation that comes from common causes共同原因. It generally represents the best performance of

29、 the process itself.最佳性能 Process performance性能 is determined by the overall output of the process全部产出 . The data used to calculate process indices shall be gathered from processes that are in a state of statistical control.控制下 过程改进循环过程改进循环1、分析过程、分析过程 2、维护过程、维护过程 本过程应做什么？ 监控过程性能 会出现什么错误？ 查找变差的特殊原因并 本

30、过程正在做什么？ 采取措施。 达到统计控制状态？ 确定能力 计划 实施 计划 实施 措施 研究 措施 研究 计划 实施 3、改进过程、改进过程 措施 研究 改进过程从而更好地理解 共同原因变差 减少共同原因变差减少样本数或是抽样频率 在统计控制下的作业性定义：Sampling distribution and Control charts provide the operational definition of “in statistical control” One function of process control system is to provide a statistical signal when special causes of variation are present, and to avoid giving false s