-
什么是
CP
和
CPK
CP(
或
Cpk)
< br>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。
< br>
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
6
σ
(
即
μ
+
3
σ
)
来表示工序能力:
工序能力=
6
σ
若用符号
P
来表示工序能力,则:
P
=
6
σ
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
< br>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
Cp>1.67
1.67
≥
Cp
>
1.33
1.33
≥
Cp>1.0
1.0
≥
Cp>0.67
0.67>Cp
级别
特级
一级
二级
判断
能力过高
能力充分
能力尚可
双侧公差范
(T)
T
>
10
σ
< br>T
=
8
σ
—
10
σ
T
=
6
σ
—<
/p>
8
σ
处
置
p>
(1)
可将公差缩小到约土
4
σ
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
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)
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
< br>
(3)Cp
—
1.0
时,应检查设备等方面的显示器
(1)<
/p>
分析极差
R
过大的原因,并采取措施
p>
(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
(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
三级
四级
能力不足
能力严重不足
T
=
4
σ
—
6
σ
T
<<
/p>
4
σ
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
/<
/p>
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
p>
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<
/p>
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,
< br>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”<
/p>
,质量能力越强;而有
偏离的
Cpk
p>
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
P
pk
的关系参照上面。
③
关于
Cp
k
与
Ppk
的关系,
< br>这里引用
QS9000
中
PPA
P
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
<
/p>
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
can I be
sure?
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
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:
+25 m: this is not a
6-sigma process. The laws governing the normal
distribution say it is 3-sigma.
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
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:
deliver 6-sigma
repeatability
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
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 be sure the manufacturer provides some
proof. You should request a report showing
how the machine performed at the rated
specification.
Most SMT equipment has
built-in video cameras to align itself and in some
cases, inspect the product it produces. Screen
printers
use the cameras to align the
incoming board and stencil, Even though the board
/ stencil alignment is relative alignment to one
another, an independent verification
tool can be mounted in the screen printer to
produce an unbiased measurement verifying the
machine's stated accuracy and
repeatability.
The SPC tools used, for
example, by an equipment manufacturer, to
characterize their machines' ability to support
particular
processes,
will
calculate the standard deviation, σ, from
measurements taken directly from the machine. For
example, a number of
vendors use
Prolink's QC-CALC SPC tool to verify the
performance of each new machine, prior to
delivery, against their own
published
performance specifications for the relevant model.
Any manufacturer that follows a similar
characterization procedure
should be
able to provide a value for the standard deviation
of a particular machine when performing a specific
process.
Relationship to Cp and
Cpk
The term Cp or Cpk
describes the capability of a process. Cp is
related to the standard deviation of the process
by the following
expression:
where USL is Upper
Specification Limit and LSL is Lower Specification
Limit
But where the process capability
is expressed in these terms, the majority of
machine data sheets quote a figure for Cpk. Cpk
includes a factor that takes process
inaccuracy into account, as follows:
where is the center point
of the process.
You can see how Cpk
varies with any offset in the bell curve caused by
process inaccuracies. In the ideal situation, when
= 0, the
process is perfectly centered
and Cpk is equivalent to Cp.
Assuming
the machine is set up by the manufacturer to be
accurate, we can accept that = 0 such that Cp =
Cpk. In this case, we
can see from the
formula for Cp that 6-Sigma corresponds to Cpk
2.0, 4-Sigma corresponds to Cpk 1.33, and 3-Sigma
corresponds
to Cpk 1.0. Note again,
however, that the critical factors affecting Cpk
are the limits and the standard deviation of the
process.
It is also worth pointing out
at this stage that Cp and Cpk refer to the
capability of the entire process the machine is
expected to
perform. Consider the
screen printing example again. Repeatedly
measuring the board-to-fiducial alignment alone
will yield a set of
data from which we
could assess the capability of the machine,
expressed as Cm or Cmk. But several further
operations, beyond
initial alignment of
the board and stencil, are required before a
printed board is available for analysis. To
extract a true figure for Cp
or Cpk,
then, we must be sure that we are not merely
measuring the machine's capability to perform a
subset of the target process.
The
following section discusses this argument.
Process capability, or alignment
capability?
After the
alignment stage, several further elements of the
machine's design, its build, or its setup will
influence the repeatability of
the
print process. For example, the lead screw for the
table-raise mechanism could be warped or may have
been cut inaccurately;
on an older
machine it could be worn or damaged, especially if
the service history is not known. Other variables
include the stencil
retention or board
clamping mechanisms; these may not be fully
secure. Other machine components, such as the
chassis, may
lack rigidity. The act of
moving a print head across the stencil, exerting a
vertical force of some 5 kg while traveling at a
typical
excursion speed of 25 m/s, will
almost certainly make the print performance less
repeatable if the machine has weaknesses in
these areas. Figure 5 illustrates the
conundrum. To assess whether a machine will
produce the print results required in a particular
target process, the buyer needs to know
that the capability figures refer to the machine's
overall ability to output boards that are
printed accurately to within the quoted
limits.
Figure
5. Alignment capability versus full process
capability
Home
and Dry…
OK, so you have
quizzed your machine supplier about its standard
deviation, and the stated limits of repeatability.
You have made
sure the quoted
performance figures relate to overall process
capability, not to one aspect of its activities,
such as alignment. You
have verified
the manufacturer's claims using your newfound
familiarity with statistical analysis; and your
new machine is now up
and running on
your line. But it is not producing the
repeatability you expected when running your
target process. What do you do?
Depending on the type of machine, any
number of factors could work alone or
interdependently to cause a gradual or more abrupt
deterioration in repeatability. In a
screen printer, selection and setup of tooling,
for example, is very important. Inadequate
underscreen cleaning may be causing
blocked apertures over a longer time period. Or a
change in solder paste supplier could
introduce a step change in the results
you are experiencing.
Some of these
issues can be identified and resolved quite
easily. Others may demand a more scientific
approach to arrive at a
satisfactory
solution. Using a data collection and SPC package
can help machine owners analyze their machines'
performance
historically or in real-
time, in the same way that the machine vendor may
use such a tool to accurately characterize the
machine
before delivery. A tool such as
QC-CALC has comprehensive reporting features,
including graphical tools showing process
capability, ranges, pareto charts,
correlation, and probability plots to help process
engineers locate just where errors are occurring.
You can also perform trend analysis and
have one or more actions, such as a point outside
sigma limits, trigger automatically to
help you isolate the causes of poor
performance.
Remember there is a
difference between machine parameters and process
parameters. The OEM gives you the machine
parameters to work within and you set-
up the machine with your process parameters. Stay
within this limit and you will produce
good product. This is similar to buying
a car that has a guaranteed top speed of 125 mph
but you can't make the car go beyond 70
mph. Upon further investigation the
service department determined you never shifted
the car out of 1st gear! Don't
machine!
Summary
Reading
this article should have provided a number of
points to consider when evaluating and operating
industrial equipment:
1. Be aware that
many people, including machine manufacturers, may
be confused about how to calculate the capability
of a
process or machine.
2.
Test the performance figures published by the
machine vendor, by asking for the machine's
standard deviation. Divide the
standard
deviation into the upper or lower limit quoted by
the manufacturer to find the machine's capability,
in sigma.
3. Find out if the figure
quoted applies to the entire process or only a
certain part of it, such as dry fiducial
alignment.
4. Depending on the answer
to 3, above, this may change your opinion of the
machine's capabilities.
5. Be aware
that your selection of other components, such as
tooling, machine settings and process parameters
also influence the
repeatability you
will see on the factory floor.
6. Wear
or damage to the machine may also impair
repeatability.
7. Monitoring via a
statistical process control tool allows an
assessment of repeatability, can help identify
trends, and can aid
troubleshooting and
continuous process optimization.
[
原创
]Cp,Cpk,Pp,Ppk,Z
在
MINITAB
中的计算公式
有的时候有人会问在
M
INITAB
中的
Cp,Cpk,Pp,Ppk,Z
怎么计算出来的?怎么和我们自己手工计算的有差别的呢?看看这些计算公式吧。
Cp,Cpk,Pp,Ppk,Z
在
MINITAB
中的计算公式:
CCpk = min { (USL - uST)/3sST , (mST -
LSL)/ 3sST}
Cp = (USL - LSL) / (6sST)
Cpk = min { (USL - uLT)
/3sST
, (uLT - LSL)/3sST}
CPL
= (uST - LSL) / (3sST)
CPU = (USL -
uST) / (3sST)
Pp = (USL - LSL) /
(6sLT)
Ppk = min {(USL -
uLT)/3sLT
, (uLT - LSL)/3sLT}
PPL = (uLT - LSL) / (3sLT)
PPU = (USL - uLT) / (3sLT)
注
解:
u=[
平均值,读
miu]
,
ST=Short Term,
LT=Lonterm
平均值计算公式:
uLT
=Sum(X11+X12+...Xnk)/Sum(n1+n2+nk), n
为组
数,
k
为每组的样本容量。
注解:也就是整个样本的平均值。
uST =(USL+LSL)/2
注解:也就是公差中心。
标准差计算公式:
sLT =
Cum SD(LT)K
sST = Cum SD(ST)K
(LT)j = F(P
.Total(LT)j)
(ST)j = F(P
.Total(ST)j)
(LT)j = (mLT - LSL) / Cum SD(LT)j
(ST)j = (mST - LSL) / Cum SD(LT)j
(LT)j = (USL - mLT) / Cum SD(LT)j
(ST)j = (USL - mST) / Cum SD(LT)j
= (ST)j - (LT)j
CCpk
CCpk is a measure of
potential capability. It is identical to the Cpk
index except that, instead of being centered at
the process mean
all the time, it is
centered at the target when given or the midpoint
of the specification limits when the specification
limits are given.
CCpk is precisely Cpk
when one of the specification limits and the
target is not given
Cpm
Cpm
is an overall capability index defined as the
ratio of the specification spread (USL - LSL) to
the square root of the mean squared
deviation from the target.
给大家澄清一下看法!
1. Cpk
--
短期过程能力指数;
Ppk
--
过程性能指数,即长期过程能力指数。
2. Cpk=min{CpL,CpU}=(T/2-|M-
μ
|)/3
σ
ST
;
Ppk=min{PpL,PpU}=(T/2-|M-
μ
|)/3
σ
LT
;其中,
σ
ST
为短期过程标准差
,
σ
LT
为
长
期过程标准差。
3. Cpk
的测定要求过程稳定,而
Ppk
不要求过程稳定。
第
1
点:概念不能说不对,很多书上是这样说的,但
会误导观众;
第
2
< br>点:公式基本正确,
σ
ST
和<
/p>
σ
LT
提法不大好,请参阅
MINITAB-help-Method and Formulas Process
Capability
(可搜索)
:
CP=(USL-
LSL)/6σ
within
PP=(USL-
LSL)/6σ overall
第
3
点:非常正确。此为
CPK
与
PPK
差异所在:以
Between/Within/Overall
的角度来理解
CPK
和
PPK
比长
< br>/
短期制程能力更有说服
力。
案例一:
1
、打开
MINITAB
数据表:
(共<
/p>
75
个数据、子组数
=3
,
SPEC
:
50+/-
3
)
2
、用
Quality tools-
Capability Analyze -Normal
:
请自主计算
CPK=
?、
PPK=
?
用
Quality tools-Capability
Analyze -Between /WIthin
:
再请自主计算
CPK=
?、
PPK=
?
为什么有不一样?
您再进行
Xbar-R Control
Chart
试试,有什么发现。
案例二:
Part 01:
600.744
599.106
599.207
Part 02:
599.054
600.1
599.432
599.242
从上述几个案例,您有什么发现?
、用
Quality tools-Capability
Analyze -Normal
:
598.726
599.432
600.234
600.124
600.465
600.782
601.573
600.768
601.023
600.886
600.782
601.046
601.467
601.282
601.447
602.04
603.691
601.803
602.333
599.414
600.171
599.987
600.849
600.779
601.983
602.21
602.102
601.803
598.414
599.777
600.239
600.592
599.125
600.443
600.773
599.303
600.134
599.403
599.243
599.596
600.277
599.8
600.406
599.81
599.91
598.134
599.263
601.604
(
SPE
C
:
600+/- 2
、子组数
=6
)
,请计算
CP
K
和
PPK
;
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