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# Cp/Cpk & Flatness Tolerances3

## Cp/Cpk & Flatness Tolerances

(OP)
Hi Guys

I have a general flatness tolerance on a drawing of 0.0015”.

And some inspection data from a supplier. I want to determine if their process is capable.

So I’ve put their data into a spreadsheet to calculate Cp/Cpk.

My question (which is probably stupid – but if in doubt ask)

I would interpret this as +0.00075”/-0.00075” with the “theoretical” nominal being zero i.e. totally flat. Is this correct??

(The surface should be between two imaginary planes 0.0015” apart)

J

### RE: Cp/Cpk & Flatness Tolerances

Theoretical Nominal = 0
Upper Specification Limit = +0.0015"
Lower Specification Limit = -0.0015"

Your spreadsheet should be able to utilize these values to calculate Cp/Cpk.  I am not sure where you are getting your +0.00075"/-0.00075" range from.

Regards,

### RE: Cp/Cpk & Flatness Tolerances

Flatness is a unilateral tolerance not to exceed .0015 with 0 being perfection. There is no lower specification limit.

To calculate your Cpk, subtract the average from .0015 and divide by 3 estimated standard deviations

BUT

applying stats on flatness is not practical. How many points did you take? Did you take you measurements using a CMM or a dial indicator? Did you measure the exact same points on each product? Was your R & R value around 10%. It is your measuring variation which may pick up most of your values.

You may obtain a Cpk value but I don't think it is valid.

Dave D.
www.qmsi.ca

### RE: Cp/Cpk & Flatness Tolerances

(OP)
Hi Guys,

Thanks for the replies!

But Erm aren't you contradicting each other?

My supplier did the measurements on 50 parts using a smartscope. I have one measured flatness value per part. i.e. 50 results.

Some values are negative – indicating concave
Some are positive – indicating convex
The part is a small metal laminate (made of copper plates brazed together)

Looking at the results – they have a high standard deviation.

I want to calculate the Cp & Cpk to get idea of whether their process is in control – flatness is critical to the design and we want to either tighten the spec or perhaps forbidding concave parts.

But I am not certain if it is valid apply SPC to flatness (Nor am I that familiar with flatness).

In my ISO spec, it states that “indicated surface is required between two imaginary parallel planes X apart”  (X in my case being 0.0015”)

It’s this concave/convex situation that is confusing me.

1) Are the two planes from 0 – 0.0015” or from -0.0015’ to +0.0015”??

I was thinking from –0.00075 to +0.00075 (total 0.0015”)

J

### RE: Cp/Cpk & Flatness Tolerances

Jalipa:

Yes, there are two (2) parallel planes, as stated, being .0015 apart with one (1) plane being 0 while the other plane is .0015. I think the ISO specification forgot to include that one (1) plane is 0 and the other plane us the upper specification limit.

It could be all concave or all convex, depending upon how one sets it up using 3 points and zeros off the indicator. In most cases, the readings are + and - from your set up points. The actual flatness is a range from the smallest reading to the largest reading using your dial indicator and a base.

We can calculate the Cpk but thereis no Cp since we do not have a lower specification limit.

Dave D.
www.qmsi.ca

### RE: Cp/Cpk & Flatness Tolerances

I believe Dingy is correct.  The total range is .0015.  It is not +-.0015.

KENAT, probably the least qualified checker you'll ever meet...

### RE: Cp/Cpk & Flatness Tolerances

(OP)
Hi Dave, Kenat

I have converted the –ve values to absolute values.

And have calculated a Cp = 1.47

For the sake argument I have used a “nominal” of 0.00075” and put it into statistica...see what you think.

(I hope this upload works :)

J

### RE: Cp/Cpk & Flatness Tolerances

Your program is incorrect. One does not have a Cp on a unilateral tolerance since 0 is not a specification limit. Only Cpk applies.

Dave D.
www.qmsi.ca

### RE: Cp/Cpk & Flatness Tolerances

I just look at it again and the Cpk value should be 2.65 rather than .84 as noted.

Apparently, some programmer thought that 0 was a specification limit and the closer the average came towards 0 the less the Cpk value. Go figure that one on a unilateral tolerance.

Zero is perfection. If your average was .0001, you are great but not according to the program you are running. It would reflect a very low value when, in fact, it would be extremely high.

Do not take the Cp and Cpk values from the program but calculate it yourself using the estimate of the standard deviation provided.

I wo

Dave D.
www.qmsi.ca

### RE: Cp/Cpk & Flatness Tolerances

Calculating capability indices such as Cp and Cpk on geometric characteristics can be very misleading.  Unlike most "linear" characteristics, one-sided characteristics like Flatness generally do not have normal distributions.  Plot a histogram of the Flatness values from the 50 parts and see what the shape is.  For a typical process, the distribution will rise steeply from zero and tail off more gradually to the tolerance limit.  Cpk quantifies how close the "extremities" of the distribution are to the specification limits, based on the mean and standard deviation.  This only works if the distribution is reasonably close to normal (symmetric, bell-shaped curve).

Evan Janeshewski

Axymetrix Quality Engineering Inc.
www.axymetrix.ca

### RE: Cp/Cpk & Flatness Tolerances

Glad I found this.  I'm trying to do the exact same thing today.

### RE: Cp/Cpk & Flatness Tolerances

Is 50 parts enough for an accurate measurement?  I'm working with a volume of 250,000 annually.  Won't I need a very large sample?

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