Cpkm capability index: Make sense when the target is the lower tolerance limit?

S

silvestri

#1
Hi all,

we are checking an assembling process in which the optimal position of a component is not in the centre of the tolerance range, but on one side of it. Hence, we decided to use the capability index Cpmk instead of the traditional Cp - Cpk.

First question: do you think it makes sense if the T value (the target) is - at the same time - the lower tolerance limit?

Second question: if yes, do you think we should refuse the qualification of this process, because of its poor Cpkm value (Cpkm = 0,32)?

You can find figures and pictures in the attached worksheet.

Thank you all.

Silvestri
 

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D

Darius

#2
Re: Cpkm capability index: does it make sense when the target is the lower tolerance

:(for the first time I don't recommend Cpmk.....:applause: (another bit of info to my knowledge, thanks)

First I checked the calculus (and they where OK), then I determined the ppm and using the availables tables Cpk vs ppm and determined the theorical Cpk.

This process look fairly good (of course you saw that, according to your questions).

-----------------------------------------------------

ppm =(1-NORMSDIST(((average-Lower)/sigma)))*1000000= 55.86

I used a Cpk vs ppm table (I searched thru the web) and found

http://www.siliconfareast.com/cpkppm.htm

but as a good aproximation a did some regression

Cpk = 2.522872-0.88947* ppm^0.068944 = 1.34

very close to your Cpk (calculated the traditional way).
:D
 
D

Darius

#3
Re: Cpkm capability index: Does it make sense when the target is the lower tolerance

First question: do you think it makes sense if the T value (the target) is - at the same time - the lower tolerance limit?
The target as a minimum or maximum happens and your data looks like USL really doesn't even exist (too far away).

The cpmk is 0,32 , so what...., my answer is :2cents: you can use it as an indicator but don't try to relate it to Cpk standards (if you want to use it, use Cpk insteed), you can meassure your process and if your process get worst or better you will notice allright with it, but the meaning will be different.

Sometimes I try to tell to other colleges, that Cpk is sort or an indicator that gives a penalty because of the spead and location (if you are away from the middle between USL and LSL), and even in some cases even doesn't have to do anything with ppm (if variation spead is larger than USL - LSL).

There Cpmk is good for target out of the middle between USL and LDL case, but if the Target is a spec limit or too close.., you will get penalty for being there because you shouldn't be near the spec limit but you will get penalty for not being there because the out Target penalty. Looks waky :bonk:
 
S

silvestri

#4
Re: Cpkm capability index: Does it make sense when the target is the lower tolerance

:D Thank you for your observations, Darius, they are useful in our internal debate over this strange case.
 
Z

zancky

#5
Re: Cpkm capability index: Does it make sense when the target is the lower tolerance

my modest opinion.
cpk gives you the extimation of how many parts are out of tolerance

in my point of view what you are looking for is something like Taguchi loss function.

Try to find a formula for convert "optimal" "quite optimal" "good" in number (may be f(x)=exp(Target-x) for x>=lowerTolLimit or x <=UpperTolLim, -1 otherwise ) Then from the data distribution (N(x;mean;sigma)) calculate the integral f(x)*N(x)=OptimalExtimator

with both cpk and OptimalExtimator You can analyze the trend of the production.

if you can accept out of tolerance parts you can adapt/change the optimalExtimator according to your needs and forget cpk.
 
D

Darius

#6
Re: Cpkm capability index: Does it make sense when the target is the lower tolerance

in my point of view what you are looking for is something like Taguchi loss function.
if far as I remember, the cpmk is based on Taguchi loss function, to include the Target (and the way is included) in the cpmk calculus.

http://elsmar.com/Taguchi.html

I said is a good indicator, but they can not use the 1.33 or 1.66 as objectives (the at least case).
 

bobdoering

Stop X-bar/R Madness!!
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#7
Darius has some very good points, and I am going to likely add more discussion than answers to the issue.

First, you distribution is likely to be a normal distribution due to the combination of measurement error and the nature of the process. Even though your target is a spec, your mean can not reside there, as you will have portions of the distribution out of spec. This is different than a unilateral specification with physical limitation to the lower specification, such as roundness or flatness. So you need to ensure the entire distribution falls within your tolerance range - no matter where it resides, which I would think is more along Cp or Pp.

Cpk is designed for central controls, as in a centered distribution within the specification. It is designed to determine how far from the center of the specification range you are. In your case, that is not relevant at all, so it is not an appropriate statistic.
 
S

silvestri

#8
I would like to add a couple of detail, in order to keep this discussion interesting:

1. This case seems to be a good example of a Taguchi loss function. In fact the distance from the target value (that is also the lower limit) causes a more -than proportional loss of retention of the plastic pattern on the metal component. For instance a -5% distance from the target could cause a let's say -10% of the retention force and so on...
I updated the worksheet with a little diagram, trying to show it...

2. If we use the Cpk, our target is exactly in the middle of the distribution, then in a position with a high loss of retention.

Of course, we cannot expect the mean of the distribution to be on the lower limit, because we should get the 50% of the production scrapped... :)
But, on the other hand, what is the meaning of the Cpkm = 0,32?
Which is, in other words, the real acceptability criterion? 1? 1,33? Some idea?

Thank you all
 

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bobdoering

Stop X-bar/R Madness!!
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#9
1. This case seems to be a good example of a Taguchi loss function. In fact the distance from the target value (that is also the lower limit) causes a more -than proportional loss of retention of the plastic pattern on the metal component. For instance a -5% distance from the target could cause a let's say -10% of the retention force and so on...
I updated the worksheet with a little diagram, trying to show it...
If this is true, what happens beyond the spec? Does the retention force drop suddenly to zero? (I know the answer, but I am building a visual here....) If not, do you have a collision of distributions - that which is acceptable per location, and that which is acceptable per retention force? And, if so, does this intersection create a truncated acceptance criteria, whereas the physical product characteristic is not a truncated distribution?

2. If we use the Cpk, our target is exactly in the middle of the distribution, then in a position with a high loss of retention.
Yep, Cpk is meaningless here.

But, on the other hand, what is the meaning of the Cpkm = 0,32?
Which is, in other words, the real acceptability criterion? 1? 1,33? Some idea?

From wikipwedia: Cpkm estimates process capability around a target, T, and accounts for an off-center process mean. Assumes process output is approximately normally distributed.

Your data is approximately normal, so that works. But, either of the "k" statistics is assuming your mean is either over your target (Cpkm, or over the center of your specification (Cpk). Either way, you are "dead" with a target over your lower specification. It would be impossible for a normal distribution to "cut off" exactly at a specification, and also be at its peak at the same location. That is why neither of these calculations are going to work for you. Worse yet, the Cpk value is the lowest value of Cpl and Cpu. As soon as the mean leaves the target, your value drops. Yet, you need to to leave the target, by about 3 standard deviations to reduce the probability of out of spec parts. In essence, your spec can not be your target. It MUST be above the lower spec to make any sense with your distribution.
 
A

adamsjm

#10
Silvestri,

You stated:

We are checking an assembling process in which the optimal position of a component is not in the centre of the tolerance range, but on one side of it.
Per your data, in the short term the parts produced by this process will be within tolerance range.
However, over the long term about 11,000 PPM will be out of tolerance range.
Ref. the attached workbook that shows your data on a “Normal Probability” plot. It helps looking at the data and not getting lost in the calculations. As Art Bender use to say, “Show me the data.”

What makes the process “Optimal”? Your second posting suggests that it is retention force. If that is the design criteria for the tolerance range then the design owner should change the tolerance range on the print to meet long-term process spread at a minimum. If the design has set the tolerance range based upon other parameters, then the process must be modified to move the center of the process 0.019 larger (at a minimum, but not necessarily centered to the tolerance range).
 

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