Calculating surface profile Cpk

[dgallup]

I have an insert molded piece of plastic that has a bilateral surface profile tolerance of 0.020 (.010 in either direction). We have traced across the surface using a profilometer in 2 orthogonal directions and recorded the highest positive and negative deviations from nominal. Various people have proposed 3 different ways to calculate the process capability from this data:

1) Calculate individual capability for the deviation in each direction using half the total tolerance (.010), take the smallest result.

2) Calculate the capability using the absolute value of the largest deviation (positive or negative) and half the total tolerance (.010).

3) Calculate the capability using the largest signed deviation and the total tolerance (.020).

Needless to say, these methods give 3 different results. Any ideas what would be the correct way? I'm open to other methods.

I really don't see this as giving a true statistical representation of the surface as the vast majority of the data is thrown out and only the extremes are being used.

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[pmarc]

How many parts have you probed?

 

[dgallup]

192

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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

 

[dgallup]

Actually 96 parts x 2 directions = 192 traces x 4 measurements/trace = 768 values.

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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

 

[Belanger]

Since capability is looking at how much of the allowable spread the measured parts are using up (IOW, a ratio), I think option 2 might be the way to go.
Option 1 doesn't seem to make sense -- who cares what the smaller deviation is? The larger deviation will make or break a part's validity.

John-Paul Belanger
Certified Sr. GD&T Professional
Geometric Learning Systems

 

[dgallup]

I should have been more clear in my first post. Option one: It's not the smaller deviation that is chosen, it's the smaller Cpk. You normally have 2 Cpk values for a bilateral tolerance, one to the upper spec limit and one to the lower spec limit, the reported Cpk is always the smaller of the two (unless you have a perfectly centered distribution, never happens).

So in this case I'm treating it like 2 separate unilateral distributions, 0 to +0.010 and 0 to -0.010, calculate each Cpk and take the smaller value. This method results in the highest Cpk value of the 3 methods.

I've also tried a 4th method which is to use all 768 signed values and full .020 tolerance.


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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

 

[pmarc]

To me there are two parameters that should be investigated in order to get relatively good grasp on the process behavior:
1. Value of actual profile of surface error for each of 96 parts, i.e. the minimum actual distance between two boundaries within which all probed points of toleranced surface lie.
2. Shift of the center of the zone described in point 1 relative to the center of profile tolerance zone.

Unfortunately, as far as I imagine, commonly known and used formulas for Cp or Cpk will not handle with this data properly. Not to mention that they work only if investigated process meets normal distribution criteria.

 

[PSE]

You may wish to query the design group for clarification regarding the surface profile. Another option would be to use the full tolerance of the specification and the Root Mean Square (RMS) value of the profiles for each part.

Regards,

Bruce Youngman

http://www.dynamicsolutions-mi.com

 

[Tarator]

I am not an expert on statistical analysis, but why don't you treat it as a dimensional tolerance: .000 ± .010 (nominal of a bilateral profile is zero)?

 

[thepete]

I'm with Tarator; why bilateral?

Your intent is to compare the limits to the observed variation, yes? If I was worried about the profile as a whole, then I'd use all 768 data points together in your calculations. If I was worried about the four inspection points individually (probably to hone in on a problem area), then I'd record 4 different Cp without combining them to allow for individual evaluation.

http://en.wikipedia.org/wiki/Process_capability_index

 

[dgallup]

If I use the 4 individual values (left min, left max, right min, right max) I get a Cpk of 1.40. If I take all the data points together I get a Cpk of 0.99. Note that the min and max values can be anywhere on the surface, we simply pull a trace across it and find the high and low spots. It's a 16 cavity tool so we are really looking at 16 populations combined.

I guess what confuses me is profile applies to the entire surface yet I am pulling off only the extreme values. The vast majority of the surface is much closer to 0. So statistically, the surface is much better than what we are calculating.

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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

 

[Belanger]

Was there any definite answer to this thread -- how to do capability for profile?
I have a real-world situation I'm dealing with right now where some people want to use just the highest point on a given part for the capability recording, and others say that each finite point sampled on the one part is used for capability studies. But that doesn't sound right.

John-Paul Belanger
Certified Sr. GD&T Professional
Geometric Learning Systems