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1、SPC进阶培训,课程一 Module 1,课程二 : 内容 Module 2 : Agenda,统计技术重温 Statistics Review 新统计技术概念New Statistical Concept 直方图 Histograms 正态分布 Normal Distributions 控制限及规格限 Control Limits and Specification Limits 流程能力 Process Capability 流程稳定及能力 Process Stability and Capability,统计技术重温 Statistics Review,中心趋向 - 平均 Central
2、 tendency - Average 典形数值的位置 The location of the typical value 流程设定 Process setting,统计技术重温 Statistics Review,分布 Spread 极差，标准差 Range, standard deviation (sigma) 数据相距多远，数据的变量程度 How spread apart are the data; the amount of variation in the data,统计技术重温 Statistics Review,新统计技术概念 New Statistical Concept,数据
3、的分布 Distribution of the data 某一数值出现多少次 how often certain data values occur 数值在分布上的集中程度 the concentration of data values across the spread 数据分布的形状 the shape of the data,very short,medium,tall,very tall,short,练习 - 孔径 Exercise - Hole Diameters,大量数据! A bunch of data! 60个孔径数值,每行十个量度数值,按次序排列 60 hole diame
4、ters - 10 measurements per column, listed in sequence,直方图 Histogram,18 16 14 12 10 8 6 4 2 0,孔径 Hole Diameters,直方图 - 钟状曲线 Histogram - Bell-Shaped Curve,小样本数 Small Sample Size,较大样本数 Slightly Larger Sample Size,多加数据会将图形变成钟状 Adding more data to the sample rounds out the shape like a bell!,大样本数 Large Si
5、ze,整体 The Whole Population,正态分布 Normal Distribution,钟状曲线=正态分布 Bell curve = normal distribution 用于 Use it to: 预测 predict. 计算事情发生的可能性(概率) calculate probabilities of things happening. 如何制作? How? 将钟状曲线分开为不同部分,如切饼. By dividing the bell curve into parts - like slicing a pie!,正态分布 Normal Distribution,所有钟状图
6、可分作六份. All bell-shaped pies have 6 slices. 各份有多大? How big are the slices? 每一份都是一样准差宽! Each slice is one standard deviation wide! 6标准差 = 整份的99.7%. Thats 6 standard deviations = 99.7% of the pie. 两边各有小“尾巴” = 0.3% We left a few crumbs at each edge = .3%.,其中: = 3.14159 e = 2.71828,概率密度函数：,那一部分最大? Which
7、are the biggest slices?,正态分布 Normal Distribution,使用标准差决定控制上限及下限,如钟状曲线. To determine UCL & LCL, use standard deviation (s) - just like the bell curve!,+3s,-3s,-3s,+3s,如何将这些应用在控制图? How does this relate to control charts?,设定控制限 Setting Control Limits,将钟状曲线转90度 Flip the bell curve on its side,设定控制限 Sett
8、ing Control Limits,这是什么意思? What does it all mean?,控制限 - 控制上,下限 Control Limits - UCL, LCL,若流程受到控制: If your process is in control: 99.7%的数据将会在控制上限及下限之间. 99.7 % of the data points will be between the UCL and LCL. 数据没有特定的图样,随机的. Data points will show no pattern = random. 大部分数据会趋向平均值. Most data points wi
9、ll be close to the average. 数据应有一半在平均值以上及一半在以下. Data points be 50/50 above and below average.,标准差如何影响 控制上限及下限 How Standard Deviation Affects UCL & LCL,将图1至图4与正确的标准差连线 那一个标准差会在控制图上定出最宽的控制限,规格限 Specification Limits,客户,供应商或内部工程要求 Customer, supplier or internal engineering requirements 包括 : Include : 目标
10、或中间值(最理想的) target or nominal value (the ideal!) 在目标值两旁可接受的变异 allowable variation on either side of the target value 规格上限 = 目标值 + 可接爱的变异 USL = target + allowable variation 规格下限 = 目标值 - 可接受的变异 LSL = target - allowable variation,例子- 酸浓度 Example - Acid Concentration,规格是130克/升+/-30克升 Specification is 130
11、 grams/liter +/- 30 grams/liter 规格上限=目标值+可接受的变量 USL = target + allowable variation 130 + 30 = 160 规格下限=目标值-可接受的变异 LSL = target - allowable variation 130 - 30 = 100 可接受变异的总值=规格上限=规格下限 Total allowable variation = USL - LSL 160 - 100 = 60,我们可以量度能力吗? Can We Measure Capability?,Cp 必须大于1 Cp Should Be Grea
12、ter Than 1,显示实际变异少于可接受变异 Indicates actual variation is less than allowable variation.,Cp - 量度流程分布 Cp - Measures Process Spread,比较可接受变异(T)及实际变异(A) Compare allowable variation (T) to actual variation (A). T = USL LSL：给定的技术要求 T ( 公差) A = 6 ：工序自身实际存在的能力( 质量水平) 6 Cp = T/ 6 ,Cp - 总结 Cp - Conclusions,数值越大越
13、好! The bigger the number, the better! Cp的缺点-只能显示流程分布,但不能显示是否符合规格 Deficiency of Cp - It shows only the spread of process, but not the compliance to specification. 例子：两流程的Cp一样。 Example: Two processes with same Cp.,Ca 准确度 Capability of accuracy,想一想: 如果T 的中心( 公差中心 ), 与6 之中心不重合時, CP会是一种怎样的值, 不重合时CP如何考虑呢?
14、-Cp值是不会发生变化的？Why？,偏移量 =X-,如何去表征这种情况呢？,Cpk - 量度流程能力 Cpk - Measures Process Capability,比较流程中间值设定及目标. Compares setting of process center (average) to target. Cpk = min(USL-X, X-LSL) 3,Cpk,Cpk良好 Good Cpk,Cpk差 Poor Cpk,基本定律: Cpk要求最少1.33 General rule - aim for Cpk of 1.33 minimum,流程能力不足的两种情况 Two Ways a Pr
15、ocess Is NOT Capable,1. 实际流程变异(A : 6 )超出右接受变异的总值(B :规格) Actual process variation (A : six sigma) exceeds total allowable variation (B : spec),流程能力不足的两种情况 Two Ways a Process Is NOT Capable,2. 如流程表现不足处于规格的中间位置,并其中一边的控制限超越规格限. If process is not centered properly and one of the control limits exceeds th
16、e spec limit.,LSL,USL,LCL,UCL,Target,Average,若流程能力不足如何办? What if a process isnt capable?,流程需要改善 The process needs improvement! 首先,采取改善行动,减少变异,然后,按目标值将流程表现调至中间值. First, take action to reduce the variation. Then, center the process over the target.,你需要做什么? What should you do?,你需要做什么? What should you do?,你需要做什么? What should you do?,稳定的流程 Stable Process 一致的 Consistent 可预测的 Predictable 没有特别原因 No speci
