Cpk When Tolerance is Tight

If all parts are within limits the result could depend on the way you compute the value.

Could you give a sample of measurements done, upper and lower limit and the way you made the computation? I shall have a look and try to give you the necessary hint.

To characterize the statistical behaviour of the process there are usually 2 parameters one defining the dispersion with respect to the specified tolerance and the other giving an information about the eccentricity of the distribution. Both are based on the standard deviation. It will be difficult to give you an explanation without data.

Since the standard deviation is related to a Gaussian distribution the sampling has to be big enough in order to show if the distribution is Gaussian and also to give results near to the Gaussian one so that at least 30 samples are required.

If the sampling is small then the Student approach has to be used.

We used 144 data points.

The problem as I see it is not so much the calculation, but the physical limits that exist today. I don't see any way to produce these parts without using the entire 6 microns of tolerance.

What is the school of thought when this condition exist?

If the distribution is NOT Gaussian then the Cpk as you compute it is not a valid criterion.

As far as I know the Cpk is a measure of the scrap risk due eccentricity of the manufacturing dispersion with respect to the tolerance field and can be corrected by a mean value shift of mentioned dispersion. Important is the process dispersion. Which value do you get for T/σ where T is the tolerance field and σ the standard deviation?

Have you made a conformity test to see if the distribution is Gaussian or not? It would be wise to do it.

In my limited experience it depends on the Quality control methods. Is it a high volume part? If that is is the case and you want to run 1000, 10000 or more of the parts you would want to ensure a good Cpk. That way you can establish a quality control that checks 1 out of 10 or 1 out of 100 parts, the Cpk tells you then that you have a reason to believe that the rest of the parts will be in spec. (Obviously a more intensive QC should be used until the process is set up and running)

If you are only going to be producing a few hundred parts, or the ongoing production is a small quantity, you can be confident in checking each and every part and assuring it is in spec. That way you don't need the Cpk to tell you how reliable and predictable your results will be because you are checking each part. If your company is held to ISO 9001 Standards (or the like) I think you have to have documented Cpk's of 1.33 or better. But otherwise as long as each part matches the spec. you would be fine.

Just my two cents.

-T

edit: On rereading your Original Post, If your tolerance is tighter than the machine can provide you need to tell management that

A) Each part has to be INTENSIVELY QC'ed
2) You need more advanced machinery
C) They should expect a high fallout/scrap rate to ensure only good product is kept

Also can you tell us at all what the product is and why it has such a fine tolerance? My interest is piqued.

Thanks for your 2 cents.

The parts are screws that go into a screw compressor. We have the most advanced machinery available on the market and my research shows that our sister companies produce Cpk's less than ours and they don't have any problems with rejects, fit up or performance.

As a side bar, one of the old time design engineers, and a well respected one at that, said that if the rotors are not exactly to print, then to let them run-in for about 3 hours and the performance will be there. So, the tolerance is so tight, they have never held it. Worse, they know that after 3 hours of running, the rotor will "wear in" and achieve the desired performance levels.

So, as I listened to his comments, tighter is good, because the rotors will run in, looser is worse as they won't and will leak air.

Now we have a new crop of managers, (and I'm a new crop of engineers) and the managers are saying achieve the 1.33, to that I'm asking..."HOW?"

Average lot size of the run is about 50 to 100 parts, a small run will be 10, (when they need 4.)

So my question stands, Is "Cpk" a good yard stick when you use 100% of the tolerance?

Laby

"...our sister companies produce Cpk's less than ours and they don't have any problems with rejects, fit up or performance"

Do you really need the tol to be so tight? Does the application demand it? I don't think so, or you would have had complaints by now if your Cpk is that low.

Can you post the data?

"So my question stands, Is "Cpk" a good yard stick when you use 100% of the tolerance?"

Yes.

I doubt your tolerancing.

my research shows that our sister companies produce Cpk's less than ours and they don't have any problems with rejects, fit up or performance.

tighter is good, because the rotors will run in, looser is worse as they won't and will leak air.

I am sorry to say that after #5 (which still holds good) I doubt the tolerancing itself.

has any one done any study on the amount of wear-ins after run? What about prototype testing? You can change the whole concept of initial dimensions and its tolerances after the test.

I don't know what is the basic dimensions of the components (diameters, lengths etc) but did any one in design department thought out of the table about the actual working condition?

The screw will mate with the bushing - what are the tolerances on those?

What will happen to the components when the run? You have a temperature differential (screw and the casing/ bushing) then you have a material and hence coeff of thermal expantion difference- which at any dimension more than compensate for the tolerance that you have put.

Assume your equipment can run at 50± 20μ , it obviously will run at 50± 6μ with same performance level, only the output characteristics will be more stable (ie equipment to equipment variations will be lower- but that is provided all other things remain same)

What I have seen in my long experience is that we some times while designing - do not take care of the sn ratio (signal-noise ratio) - attack one main cause and try to make it nearest to zero tolerance - increase the cost without adding sufficient value- since the noises of the random variables more than negate the gains.

And that's what I interpret from your comments. Question whether the tight tolerance is really required? A grade of tolerance relaxation will significantly reduce your costs.

±Just a few questions- the data looks too odd

The sample size of 144 is quite large. You have a Cpk=0.47, The component /orocess should give you a normal distribution. as per that your % defective, expected is around 16%.

However you mentioned none of the parts are out of tolerance.

This means

Either your measurement system is wrong. You mentioned your tolerance is ±6μ. What is your measurement system accuracy? Can you measure with 1/10th accuracy (and that includes all its subparts- error, repeatability, least count,... ) as recommended statistically? This boils down to 1.2μ.

Other is since the accuracy is high, you are gettinng filtered data. At the manufacturing level the defectives are seggregated and you are analysing on one or both tails truncated normal distribution.

There are a few other reasons available for this type of abnormal pattern, but the above two (individually or both) are the probable.

However the end result is with Cpk as low as this you do not have a choice. Go for the process analysis, DOE and improve the process, meanwhile continue with 100% inspection.

how was the gage R&R on your measuring device?

We are doing the Gage R&R today, we expect it to fail, again due to the fact that we have 6 micron tolerance and the best we have is a 2 micron resolution gage...

Your gage accuracy is undoubtedly less than your resolution, so much of what you are measuring to calculate Cpk is the uncertainty in your gage. As you suspect when you add your actual part deviation from nominal along with part variation you do not have a chance of making a 1.33 Cpk. Your statistical variation due to the resolution of your gage alone makes a 1.33 Cpk unlikely even with "perfect" parts.

There are commercially available gages that can hold 1 micron accuracy and .1 micron resolution for size, roundness, and flatness. Make sure you are considering all the potential sources of error in your measurement, including thermal and coefficient of expansion.

As a final word, if you are talking about a form tolerence you are probably completely screwed.

How do you know all your parts are in spec? The reason I asked is because to have a Cpk of 0.47 or under 1.0 means a portion of your bell curve (population spread) is guaranteed to be out of spec. Ideally in the design stage if your part was developed properly where the UCL and LCL were determined using 6 sigma then your optimum Cpk should be around 2.0. A Cpk below 1.66 should trigger an alarm to begin investigating but still allow production to run and when it falls below 1.33 production should be stopped and the problem corrected to ensure the process doesn't fall below 1.0 where you would be guaranteed to have failures.

Now this is all based on the fact that you are actually sampling and using Cpk to predict the quality of the whole population. But if, as I am guessing, you are are measuring 100% of your parts (since you say none of the parts are out of tolerance) then there is no practical purpose to using Cpk other than as selling point to some customer and I would have to ask, 'what is there to sell about having a 0.47 Cpk'?

The real question is how you can have 100% in spec and have Cpk below 1.0? It seems to me like there is something wrong in the whole setup.

Problem number one: Tolerance is tighter than it needs to be in the application. Problem number two: Gaging is inadequate to task of measuring at the tolerance, thus lowering Cpk, your GRR will prove this. Problem number three: Cultural.Since nobody there but you understands what any of these terms really mean, and their consequences, You will be the go to guy/whipping boy on this project forever. Only you can read the tea leaves. ANSWER to these problems, After your GRR, calculate the tolerance range where your process will be at Cpk of1.00 Tell them that this is what you can honestly inspect to in short runs on a non fiction non BS basis. Then calculate what the tolerance would have to be to give them the Cpk of 1.33, and when they give you crap, hand them a small cup and ask them to give you a urine sample , because they clearly don't understand the issue and you suspect they are impaired by drugs. I did that at a customer once, it was what it took to break through. (we were at 30 ppm, they wanted us to do a test of a modified process, using 1000 piece sample. Idiots!) milo