什么是CP和CPK.doc

什么是CP和CPK
CP(或Cpk)是英文Process Capability index缩写，汉语译作工序能力指数，也有译作工艺能力指数, 过程能力指数。
　　工序能力指数，是指工序在一定时间里，处于控制状态(稳定状态)下的实际加工能力。它是工序固有的能力，或者说它是工序保证质量的能力。
　　这里所指的工序，是指操作者、机器、原材料、工艺方法和生产环境等五个基本质量因素综合作用的过程，也就是产品质量的生产过程。产品质量就是工序中的各个质量因素所起作用的综合表现。
　　对于任何生产过程，产品质量总是分散地存在着。若工序能力越高，则产品质量特性值的分散就会越小；若工序能力越低，则产品质量特性值的分散就会越大。那么，应当用一个什么样的量，来描述生产过程所造成的总分散呢?通常，都用6σ(即μ＋3σ)来表示工序能力：工序能力＝6σ
　　若用符号P来表示工序能力，则：P＝6σ 　　式中：σ是处于稳定状态下的工序的标准偏差
　　工序能力是表示生产过程客观存在着分散的一个参数。但是这个参数能否满足产品的技术要求，仅从它本身还难以看出。因此，还需要另一个参数来反映工序能力满足产品技术要求(公差、规格等质量标准)的程度。这个参数就叫做工序能力指数。它是技术要求和工序能力的比值，即
工序能力指数=技术要求／工序能力
　　当分布中心与公差中心重合时，工序能力指数记为Cp。当分布中心与公差中心有偏离时，工序能力指数记为Cpk。运用工序能力指数，可以帮助我们掌握生产过程的质量水平。
工序能力指数的判断
　　工序的质量水平按Cp值可划分为五个等级。按其等级的高低，在管理上可以作出相应的判断和处置(见表1)。该表中的分级、判断和处置对于Cpk也同样适用。
表1工序能力指数的分级判断和处置参考表
Cp值
级别
判断
双侧公差范(T)
处 置
Cp>1.67
特级
能力过高
T＞10σ
(1)可将公差缩小到约土4σ的范围 (2)允许较大的外来波动，以提高效率 (3)改用精度差些的设备，以降低成本 (4)简略检验
1.67≥Cp＞1.33
一级
能力充分
T＝8σ—10σ
若加工件不是关键零件，允许一定程度的外来波动
(2)简化检验 (3)用控制图进行控制
1.33≥Cp>1.0
二级
能力尚可
T＝6σ—8σ
(1)用控制图控制，防止外来波动 (2)对产品抽样检验，注意抽样方式和间隔
(3)Cp—1.0时，应检查设备等方面的显示器
1.0≥Cp>0.67
三级
能力不足
T＝4σ—6σ
(1)分析极差R过大的原因，并采取措施(2)若不影响产品最终质量和装配工作，可考虑放大公差范围 (3)对产品全数检查，或进行分级筛选
0.67>Cp
四级
能力严重不足
T＜4σ
(1)必须追查各方面原因，对工艺进行改革 (2)对产品进行全数检查
Ppk, Cpk, Cmk 三者的区别及计算
1、首先我们先说明Pp、Cp两者的定义及公式
Cp（Capability Indies of Process）：稳定过程的能力指数，定义为容差宽度除以过程能力，不考虑过程有无偏移，一般表达式为：
 Pp（Performance Indies of Process）：过程性能指数，定义为不考虑过程有无偏移时，容差范围除以过程性能，一般表达式为：
   （该指数仅用来与Cp及Cpk对比，或/和Cp、Cpk一起去度量和确认一段时间内改进的优先次序）
CPU：稳定过程的上限能力指数，定义为容差范围上限除以实际过程分布宽度上限， 
CPL：稳定过程的下限能力指数，定义为容差范围下限除以实际过程分布宽度下限，
 2、现在我们来阐述Cpk、Ppk的含义
Cpk：这是考虑到过程中心的能力（修正）指数，定义为CPU与CPL的最小值。它等于过程均值与最近的规范界限之间的差除以过程总分布宽度的一半。
 Ppk：这是考虑到过程中心的性能（修正）指数，定义为： 或 的最小值。
 其实，公式中的K是定义分布中心μ与公差中心M的偏离度，μ与M的偏离为ε=| M-μ| ，
3、公式中标准差的不同含义
①在Cp、Cpk中，计算的是稳定过程的能力，稳定过程中过程变差仅由普通原因引起，公式中的标准差可以通过控制图中的样本平均极差 估计得出：
因此，Cp、Cpk一般与控制图一起使用，首先利用控制图判断过程是否受控，如果过程不受控，要采取措施改善过程，使过程处于受控状态。确保过程受控后，再计算Cp、Cpk。
②由于普通和特殊两种原因所造成的变差，可以用样本标准差S来估计，过程性能指数的计算使用该标准差。
 4、几个指数的比较与说明
① 无偏离的Cp表示过程加工的均匀性（稳定性），即“质量能力”，Cp越大，这质量特性的分布越“苗条”，质量能力越强；而有偏离的Cpk表示过程中心μ与公差中心M的偏离情况，Cpk越大，二者的偏离越小，也即过程中心对公差中心越“瞄准”。使过程的“质量能力”与“管理能力”二者综合的结果。Cp与Cpk的着重点不同，需要同时加以考虑。
② Pp和Ppk的关系参照上面。
③ 关于Cpk与Ppk的关系，这里引用QS9000中PPAP手册中的一句话：“当可能得到历史的数据或有足够的初始数据来绘制控制图时（至少100个个体样本），可以在过程稳定时计算Cpk。对于输出满足规格要求且呈可预测图形的长期不稳定过程，应该使用Ppk。”
④ 另外，我曾经看到一位网友的帖子，在这里也一起提供给大家（没有征得原作者本人同意，在这里向原作者表示歉意和感谢），上面是这样写的：
“所谓PPK，是进入大批量生产前，对小批生产的能力评价，一般要求≥1.67；而CPK，是进入大批量生产后，为保证批量生产下的产品的品质状况不至于下降，且为保证与小批生产具有同样的控制能力，所进行的生产能力的评价，一般要求≥1.33；一般来说，CPK需要借助PPK的控制界限来作控制。… …
One is in QS9000. Ppk in QS9000 means Preliminary Process Capability Index. It should be calculated before Mass Production and based on limited product quantity. Normally, it should be more than 1.67 because it's a short term process capability which doesn't consider the long term variation. But, in QS9000 3rd edition, there's no Compulsory Requirement that the Ppk must be more than 1.67. In QS9000 3rd edition, it states like Ppk/Cpk >=1.33.
    Another one is in 6-Sigma. Ppk in 6-Sigma means Process Performance Index. It's a long term process capability covered the long term process variation and based on more product quantity. Generally, in 6-Sigma, the Ppk value is less than Cpk value.
Ppk：Overall performance capability of a process, see Cpk.  过程的整体表现能力。
Cp：A widely used capability index for process capability studies. It may range in value from zero to infinity with a larger value indicating a more capable process. Six Sigma represents Cp of 2.0. 在流程能力分析方面被广泛应用的能力指数，在数值方面它可能是从零到显示更强有力流程的无穷大之间的某个点。六个西格玛代表的是Cp=2.0。
Cpk：A process capability index combining Cp and k (difference between the process mean and the specification mean) to determine whether the process will produce units within tolerance. Cpk is always less than or equal to Cp.一个将Cp和k（表示流程平均值与上下限区间平均值之间的差异）结合起来的流程能力指数，它用来确定流程是否将在容忍度范围内生产产品，Cpk通常要么比Cp值小，要么与Cp值相同。”

如何正确计算设备的Cpk非常重要。在选择不同供应商设备产品时，Cpk为用户用于比较设备性能的参数，Cpk还是生产线设置、设备查错、成品率管理使用的统计学工具。
Sort your Sigmas out!
The theory behind the all-important Sigma or Cpk rating for machines on the factory floor can be confusing. A Statistical Process Control (SPC) tool can calculate the answer, but what if the machine consistently falls short of its manufacturer's claims? Even some machine vendors cannot necessarily agree on when a machine has reached the Holy Grail of 6-Sigma repeatability. Most uncertainties center on how to interpret the data and how to apply appropriate upper and lower limits of variability. The key lies with the standard deviation of the process, which, fortunately, everyone can agree on.
Greater Accuracy, Maximum Repeatability
Industrial processes have always demanded the utmost repeatability, to maximize yield within accepted quality limits. Take electronic surface mount assembly: as fine-pitch packages including 0201 passives and CSPs enter mainstream production, assembly processes must deliver that repeatability with significantly higher accuracy. As manufacturing success becomes more delicately poised, this issue will become relevant to a growing audience, including product designers, machine purchasers, quality managers, and process engineers focused on continuous improvement.
This article will explain and demystify the secrets locked up in the charmingly simple - yet obstinately inscrutable - expression buried some where down a machine's specification sheet.  You may have seen it written like this:
Repeatability = 6-Sigma @ ± 25  m
This shows that the machine has an extremely high probability (6-sigma) that, each time it repeats, it will be within 25  m of the nominal, ideal position.
A great deal of analysis, including the work of the Motorola Six Sigma quality program, among others, has led to 6-Sigma becoming accepted throughout manufacturing businesses as the Gold Standard as far as repeatability is concerned. A machine or process capable of achieving 6-Sigma is surely beyond reproach. Not true: many do not understand how to correctly calculate the value for sigma based on the machine's performance. The selection of limits for the maximum acceptable variance from nominal is also critical. In practice, virtually any machine or process can achieve 6-Sigma if those limits are set wide enough.
This is an important subject to grasp. Understanding it will help you make meaningful comparisons between the claims of various equipment manufacturers when evaluating capital purchases, for example. You will also be able to set up lines and individual machines quickly and confidently, troubleshoot and address yield issues, and ensure continuous improvement in the emerging chip scale assembly era. And you will have a clearer view of the capabilities of a machine or process in action on the shop floor, and apply extra knowledge when analyzing the data you are collecting through a SPC tool such as QC-CALC, in order to regularly reassess equipment and process performance.
The aim of this article, therefore, is to provide a basic understanding of the subject, and empower all types of readers to make better decisions at almost every level of the enterprise.
Grasp it Graphically
Instead of diving into a statistical treatise, let's take a graphical view of the proposition.
All processes vary to one degree or another. A buyer needs to ask "is the process or machine accurate and repeatable? And, "How can I be sure?" Accuracy is determined by comparing the machine's movements against a highly accurate gage standard traceable to a standards organization.
Consider the possibilities of accuracy versus repeatability. Suppose we measure the X & Y offset error 10 times and plot the ten points on a target chart as seen in figure 1. Case 1 in this diagram shows a highly repeatable machine since all measurements are tightly clustered and "right on target". The average variation between each point, known as the standard deviation (written as sigma, or the Greek symbol σ), is small.
However, a small standard deviation does not guarantee an accurate machine. Case 2 shows a very repeatable machine that is not very accurate. This case is usually correctable by adjusting the machine at installation. It is the combination of Accuracy and Repeatability we strive to perfect.
A simple way of determining both accuracy and precision is to repeatedly measure the same thing many times. With screen printing machines the critical measurement is X & Y fiducial alignment. Theoretically, the X & Y offset measurements should be identical but practically we know the machine cannot move to the exact location every time due to the inherent variation. The larger the variation the larger the standard deviation.

After making many repeated measurements, the laws of nature take over. Plotting all your readings graphically will result in what is known as the normal distribution curve (the bell curve of figure 2 also called Gaussian). The normal distribution shows how the standard deviation relates to the machine's accuracy and repeatability. A consistent inaccuracy will displace the curve to the left or right of the nominal value, while a perfectly accurate machine will result in a curve centered on the nominal. Repeatability, on the other hand, is related to the gradient of the curve either side of the peak value; a steep, narrow curve implies high repeatability. If the machine were found to be repeatable but inaccurate, this would result in a narrow curve displaced to the left or right of the nominal. As a priority, machine users need to be sure of adequate repeatability. If this can be established, the cause of a consistent inaccuracy can be identified and remedied. The remainder of this section will describe how to gain an accurate understanding of repeatability by analyzing the normal distribution.
A number of laws apply to a normal distribution, including the following:
1. 68.26% of the measurements taken will lie within one standard deviation (or sigma) either side of average or mean
2. 99.73% of the measurements taken will lie within three standard deviations either side of average
3. 99.9999998% of the measurements taken will lie within six standard deviations either side of average

Consider the bell curve shown in figure 2. The process it depicts has three standard deviations between nominal and 25  m. Therefore, we can describe the process as follows:
Repeatability = 3-sigma at ±25  m
There are two important facts to understand right away:
" Do not be confused by the fact that there are six standard deviation intervals between the upper and lower limits, -25  m and +25  m: this is not a 6-sigma process. The laws governing the normal distribution say it is 3-sigma.
" The normal distribution curve continues to infinity, and therefore exists outside the ±25  m limits. It continues to 6-sigma, described by note 3 above, and even beyond. Simply by drawing extra sigma zones onto the graph, we can illustrate that the 3-sigma process at ±25  m achieves 6-sigma repeatability at ±50  m. It is the same process, with the same standard deviation, or variability.
Now consider what happens if we analyze a more repeatable process. Clearly, as the bulk of the measurements are clustered more closely around the target, the standard deviation becomes smaller, and the bell curve will become narrower.
For example, let's discuss a situation where the machine has a repeatability of 4-sigma at ±25 microns, and is centered at a nominal of 0.000 as shown in figure 3. This bell curve shows an additional sigma zone between nominal and the 25  m limit. Quite clearly, a higher percentage of the measurements lie within the specified upper and lower limits. The narrowing of the bell curve relative to the specification limits highlights what is referred to as the "spread". Equipment builders attempt to design machines that produce the narrowest spread within the stated limits of the equipment, increasing the probability that the equipment will operate within those limits.

Lastly, we draw our bell curve with 6 sigma zones to show what it means to state that a machine has ±25 micron accuracy and is repeatable to 6-sigma. You can see how the 6-sigma machine has a very much smaller standard deviation compared to the 3-sigma machine. In fact, the standard deviation is halved. This means the 6-sigma machine has less variation and therefore is more repeatable. Consider the very narrow bell curve of figure 4 in relation to the laws governing the normal distribution, which state 99.9999998% of measurements will lie within 6 standard deviations of nominal.

At this point, we can summarize a number of important points regarding the repeatability of a process:
" ANY process can be called a 6-sigma process, depending on the accepted upper and lower limits of variability
" The term 6-sigma alone means very little. It must be accompanied by an indication of the limits within which the process will deliver 6-sigma repeatability
" To improve the repeatability of a process from, say, 3-sigma to 6-sigma without changing the limits, we must halve the standard deviation of the process
Relationship to ppm
We can also now see why 6-sigma is so much better than 3-sigma in terms of the capability of a process. At 3-sigma, 99.73% of the measurements are within limits. Therefore, 0.27% lie outside; but this equates to 2700 parts per million (ppm). This is not very good in a modern industrial process such as screen printing, or any other SMT assembly activity for that matter. 6-sigma, on the other hand, implies only 0.0000002% or 0.002 ppm (2 parts per billion) outside limits. Readers familiar with the Motorola Six Sigma quality program will have expected to see 3.4 ppm failures. This is because the methodology allows for a 1.5 sigma "process drift" in mean not included in the classical statistical approach, which this article is following.
Whichever approach is taken all machine vendors, and also contractors such as EMS businesses, understandably wish to be able to say they have 6-sigma capability. For this reason, buyers of machines and manufacturing services need to be very careful when evaluating the vendor's claims.
For instance, if a machine vendor claims 6-sigma at ±12.5  m, you must ask for the standard deviation of the machine. Then divide 12.5  m by the figure provided to find the repeatability, in sigma, of the machine: if the result is 6, the repeatability is 6-sigma and you can rely on the vendor's claim for process capability. Depending on the intent of the vendor, you may find a different answer. For example, the machine may be only half the stated accuracy. This is because there is room for confusion over whether limits of ±12.5  m would allow repeatability to be calculated by dividing the total spread, i.e 25  m, by the standard deviation. This is not consistent with the laws governing the normal distribution, but it does provide scope to claim 6-sigma performance for a process that is, in fact, only 3-sigma. Be careful.
When purchasing a new piece of equipment