Is Cpk a good measure of capability? There are several shortcomings of Cpk

A

Arvind

#21
Here are clarification for clearing confusion about Cpk

1) Most physical manufacturing processes are normally distributed about the mean. This is irrespective of the specifications needed by the user. Hence in dealing with cases of non symmetrical specifications, process mean has to be mean value of tolerance band of specification. With this approach, you minimize % of tail portion of distribution going out of specifications.

2) Cpk is a ratio of
Numerator-How much mean is away from target
Denominator- How much is the spread
Unfortunately when numerator is zero, denominator doesnot matter. In such cases, increase resolution or decimal accuracy of your equipment to avoid non zero numerator.

3) Cpk is a variable data like loss function. Any variable data can be converted to attribute data. Unfortunately many people convert and interpret Cpk that way. There is no practical physical difference between Cpk of 1.31 and Cpk of 1.35. However people call it as " Fail" or "Pass"
 
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Tim Folkerts

Super Moderator
#22
Chakravyuha said

Cpk, Cp and Cpm are not designed for measuring process capability in case of asymmetric specifications. This is well known in statistical literature. Instead a better choice is to use Cpmk or C'pm. Here I must mention that these indices are not popular within the industry because they are found out to be mathematically rigorous to calculate.

Just for information: Cpk was was defined by Juran in 1974.
Thanks.

Thanks, I hadn't seen Cpmk before , but a quick web search shows that it does effectively address the issue of asymmetric spec limits. And in the case where the specs are symmetric, it gives the plain old Cpk.

I agree it is more difficult to calculate, but in this age of computers, that seems to hardly be a concern. When Juran invented Cpk in 1974, computeres were rare and calculators rather simplistic by today's standards, so the calculations would have been a royal pain. Today, with computers everywhere, having a slightly more difficult equations doesn't seem to be much of a concern.


Then Arvind said

Hence in dealing with cases of non symmetrical specifications, process mean has to be mean value of tolerance band of specification. With this approach, you minimize % of tail portion of distribution going out of specifications.
This depends on your goal. It you want as few outside the tolerance limits, then I agree -- the process should be centered between the two limits, regardless of the stated target value. But that may not be what the customer wants! If the process can produce a fairly tight spread, then very few parts would be out of spec in eiter case, but the off-centered process would improve the performance for most of the parts.

I guess it all comes back to good communications between supplier & customer.

Thanks, everyone for the thought-provoking discussion. It's given me some fresh insights to mathematical subtleties and practical realities of capability indices.


Tim F
 
D

dfirka

#23
Arvind said:
3) Cpk is a variable data like loss function. Any variable data can be converted to attribute data. Unfortunately many people convert and interpret Cpk that way. There is no practical physical difference between Cpk of 1.31 and Cpk of 1.35. However people call it as " Fail" or "Pass"
Arvind,
Let me give two unrelated comments on your point, and please clarify if I didn't get the spirit of what you wrote.

1- I would say that although it seems an attribute, aiming to reach a certain Cpk is a valid approach. You are just setting a specification for the "variable data number" Cpk that you define as a performance objective.

In that way, you can consider certain Cpk (Cpk0) as OK for a process: If the CPK is under that threshold Cpk0, you need to improve now; if the Cpk is higher than Cpk0, you will concentrate first in other processes less capable.

In this case, the "pass" (Cpk>Cpk0) relates to an acceptable synchronization between the Voice of the Process (summarized by avg and dispersion) and the Voice of the Customer (spec limits).

Let's say that the "Voice of the Company" establish this Cpk0, that is always provisory, specially at the "quality control" phase in Juran’s quality method. Like Juran, I think that continuous improvement works on a project basis, and the Cpk0 could be a valid metric for an improvement project.

2- Your point goes from Cpk to a Pass-Fail attribute. Interestingly, the reciprocal argument is used to derive a Cpk/Ppk value from attribute data (Bothe, Measuring Process Capability, 1999).

In this case, the percentage nonconforming is used to obtain a Z value and from there derive the Ppk using the formula (Zmin/3). D. Bothe calls this metric "Equivalent Ppk".

An extreme of this "inversion" is the procedure used by Six Sigma to transform DPMO to Sigma Level: As 6 sigma means 3.4 ppm (1.5 shift), then 3.4 ppm means 6 sigma.


Daniel
 
C

Chakravyuha

#24
More about Process Capability Indices

Tim,
You will be surprised to know that there are around 25 process capability indices defined in statistical literature. But owing to their complexities and lack of practical usage only Cp, Cpk, and Cpm are used popularly. One must remember that every PCI has some advantages and weaknesses and no one PCI is appropriate for all situations.
In fact, as part of my Masters thesis, I have designed a Decision Support System which selects, calculates and then interprets the appropriate process capability index depending on the various types of process data. In fact, it handles virtually all kinds of data usually encountered in manufacturing industries. The user just has to enter the data values, the software does the rest i.e it first does control charting (for subgrouped data, individual observations,etc using Xbar and R, Xbar and S charts,MA charts, etc), then once the process is in control, it performs the PCI calculations after careful selection of the appropriate PCI. Morever, it can handle short-run data, bivariate data, and non-normal data also !!!

Anyone wants to know more ?

Thanks.
 
D

Darius

#25
Chakravyuha said:
... then once the process is in control, it performs the PCI calculations after careful selection of the appropriate PCI. Thanks.
What if... the process never reaches the "in control" attribute? :confused:

I think it's not part of this tread but, can you define "in control"?. There are many and some say this can never happen (no patterns).
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#26
Darius said:
What if... the process never reaches the "in control" attribute? :confused:

I think it's not part of this tread but, can you define "in control"?. There are many and some say this can never happen (no patterns).
There are several variations on the definition of "in control", but here is the one I use:

You must have at least 25 data points that have a single average and control limits fit through the data such that none of the following criteria are met:

One point outside the control limits
Two out of Three points two standard deviations above/below average
Four out of Five points one standard deviation above/below average
Seven points in a row all above/below average
Ten out of Eleven points in a row all above/below average
Seven points in a row all increasing/decreasing.
 
D

Dave Strouse

#27
I Like Your Definition in General, but...

Steve -

I agree as usual with what you say, but think you should add caveat to examine plot for "patterns”. Perhaps you believe this is self evident, but many beginners in particular don't. Rather they rely on statistical software to flag the WE tests you mention.

Take a look at the obviously stylized chart attached. I believe it violates control definition in "hugging the centerline" (which could be set up as statistical test) and pattern tests (which would be very difficult to put into software test).

Thoughts?

Dave
 

Attachments

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#28
Dave Strouse said:
Take a look at the obviously stylized chart attached. I believe it violates control definition in "hugging the centerline" (which could be set up as statistical test) and pattern tests (which would be very difficult to put into software test).

Thoughts?

Dave
Yes, I admit I left off the general statement of "patterns and non-random cycles". Your chart is a good example of that. The difficulty I have had is proceduralizing (making an operational definition) out of that criterion.

I have also seen some folks use a rule for too many points within one standard deviation of the average in order to catch that the points "hug" the center line too much. Of course, that can be also accomplished by the Range chart.

Personal experience so far is that I have only seen one chart in the thousands I have done with a seasonal cycle - insect and animal bites and stings. And that tripped other statistical criteria when plotted on a monthly basis.

So, I have stuck to the list I posted in the previous message. I figure that it is straight forward, and if a person gets proficient at that list we can talk about the non-random cycles issue.
 
C

Chakravyuha

#29
More about Process Capability Indices

Hello again,
I have done extensive research in the topic of process capability indices and if anyone wants more information about the same, feel free to contact me. Actually, it was part of my Master's thesis. As a starter, I would like to inform that most of the commonly used PCIs are limiting values of Vannman's index Cp(u,v) with different values of u and v, resulting in indices such as Cp, Cpk, Cpm and Cpmk.
Anyone interested in this topic and in knowing how to choose an appropriate PCI ?
 
F

fsamyn

#30
Vannman's Indices

It was interesting to find out that the PCI belong to a more general class. Therefore it would be very helpful if someone could indicate where this information can be found.
Attempts to contact the author have not resulted in any reply. Also a web search did not help either.
Is there someone who can shed some more light on this topic?
 
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