How does one calculate Cpm (Taguchi process capability)

S

si kang

#1
Hello, sir
I am QA engineer who is in charge of SPC activity in the field of semiconductor assembly in korea.
The question is that I heard that there is a new procability capability index not Cpk.
That is Cpm(Taguchi process cability index) which is from A.I.A.G Manual and JMP Statistical software.
Exactly,I know the meaning of Cpm and what the calculation is.
If possible, Could you specify your answer on the above my questions.


Thanks and best rgds.
SI Kang from korea.
 
Elsmar Forum Sponsor
D

Don Winton

#2
I have never heard of 'Taguchi Process Capability Index' but I have heard of Cpm. Process capability index Cpm is used when a target value other than the center of the specification spread has been designated as desirable. Maybe AIAG has modified the Loss Function equations to relate to process capability. Perhaps some QS folks could elaborate as that I stay away from AIAG's stuff as much as possible.

Regards,
Don

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Just the ramblings of an Old Wizard Warrior.
 
B

Batman

#3
As far as AIAG, I know that Cpm is mentioned in the QS9000 SPC manual, but only mentioned. It does not seem to be popular with the automotive folks. I remember reading about it some years ago, but it was not top on the list, so I recall little. Don has more than I remember.

If you need Cpm capability software, my company has used Statgraphics for many years, and it reports Cpm with the capability study module.
 
D

Don Winton

#4
I checked AIAG, Alta Vista and JMP and cannot find any reference to 'Taguchi' and 'Process Capability' anywhere (linked together, anyway). Perhaps you were misinformed.

You can find additional information on Cpm at:

http://Elsmar.com/pdf_files/ Look for CPK.pdf

which may (or may not) help.

Regards,
Don

------------------
Just the ramblings of an Old Wizard Warrior.
 
S

si kang

#5
Hello,
Thank you for your reply on the Cpm.
But I have wondering about Cpm calculation with target value.
If one side spec limit exists, how could the calculation be?
The reason is that Cp=(USL-LSL)/6*SIGMA.
in case of only existing USL or LSL,the index of Cp is not available.
Eventually, Cp can be calculated from having both two sides spec limit such as USL and LSL.
Is there any alternative or not?
To get Cpm for measuring process capability , It is necessary to have two sides spec limit not one side.
And Batman has mentioned Cpm not popular in automotive site for measuring process.
only automotive site or not?

Could you Please confirm the above my questions?

Thanks in advance.
SI Kang from korea.
 
D

Don Winton

#6
If one side spec limit exists, how could the calculation be?
If a one sided specification limit exists, you use Cpk(max), sometimes referred to as Cpku, or Cpk(min), sometimes referred to as Cpkl.

Cpk(max) = (USL-Xbar)/(3*s)

Cpk(min) = (Xbar-LSL)/(3*s)

To get Cpm for measuring process capability , It is necessary to have two sides spec limit not one side.
Correct only in that the calculation for Cpm requires Cp in the numerator. As I mentioned earlier, Cpm is used when the target value is not the center of the specification spread.

Perhaps this will help:

Cp = (USL-LSL)/(6*s); Process capability when Xbar = Specification center

Cpk = Minimum[(USL-Xbar)/(3*s);(Xbar-LSL)/(3*s)]; Process capability when Xbar <> Specification center

Cpk(max) = (USL-Xbar)/(3*s); Process capability for USL only

Cpk(min) = (Xbar-LSL)/(3*s); Process capability for LSL only

Cpm = Cp/[1+((Xbar-T)^2/s^2)]; Where T is the target value. Explained above.

And Batman has mentioned Cpm not popular in automotive site for measuring process.
Cpm is not popular anywhere because it usually means the process is running off-target and the calculation is made to the off-target value rather that the preferred target value.

Regards,
Don

------------------
Just the ramblings of an Old Wizard Warrior.
 
S

si kang

#7
Hello,
Thank you for your continuous and quick response on my question.

You have mentioned that "Cpm is not popular anywhere because it usually means that the process is running off-target value and calculation is made to the off-target value rather that the preferred target value."
I'm really sorry that I don't exactly understand those meanining you have mentioned.
Your more details are needed to me at this time.

Thanks & best regards.
SI Kang.
 
D

Don Winton

#8
I'm really sorry that I don't exactly understand those meaning you have mentioned.
My explanation above is not very clear and stems from my personal applications of process capability. No apologies necessary.

I should expound upon the use of Cpm. Most of my references are rather vague on Cpm as it is not a popular measure of process capability. Thus, the following is not from any official reference I could find, but it seems the logical one.

I believe the original concept of Cpm comes from the application of unilateral and bilateral tolerances. A bilateral tolerance expresses the value as a target value and a range, i.e. 2.0cm +/- 0.1 cm, with the target value and the center of the specification being equal. For bilateral tolerances, Cp or Cpk are applicable.

Unilateral tolerances are given as a target value and a single limit, i.e. 2.0cm +0.0cm/-0.1cm. For unilateral tolerances, Cpku and Cpkl are applicable (other expressions are CpU and CpL, respectively).

I believe Cpm came from a variation of the bilateral tolerance. Tolerances are expressed as a target and a nonsymmetrical range, i.e. 2.0cm +0.2cm/-0.1cm. In this case, 2.0 cm is the target but is not the center of the tolerance (2.05cm is the center). From the definition of Cpm above, "…target value other than the center of the specification spread has been designated as desirable." However, nonsymmetrical tolerances are rarely used in these days of CAD, so it appears that Cpm is also rare, thus rarely used.

Suggestion: Forget Cpm all together and use the four basic definitions of process capability. Besides, if it is indeed from the "A.I.A.G Manual," I personally would not put a lot of stock in it.

Regards,
Don

------------------
Just the ramblings of an Old Wizard Warrior.
 
D

Don Winton

#9
si kang,

Did my last reponse answer your questions?

Regards,
Don

------------------
Just the ramblings of an Old Wizard Warrior.
 
S

si kang

#10
Hello,
Pls reconfirmation Cpm formula, the difference is whether denominator has square root or not as below two formula seeming alike. which is correct?
Cpm=(Cp)/[(1+((Xbar-T)**2)/(S**2))]
or
Cpm=(Cp)/{sqrt[(1+((Xbar-T)**2)/(S**2)))]

and today, I have two questions to you.
How does we understand and recognize Cpm in our process?
For example, we have condidered the meaning of Cpk=2.0 as 3.4dpm very easily.
Hence, is there any relations between Cpm and defects.
If yes, What is that?

Another question, how to determine the target value?
any rules exist or not?
if not, is it possible to make use of the past 3 months' data and calculate arithematic average from the indivudual readings?
if the past three months' data is used, will it be do?

Your quick response will be highly appreciated.

Thanks & best rgds.
SI Kang.
 
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