Capability for Correlated Charteristics



can anybody please advise with the situation below. I tried seaching the forums but didn't find anything relevant.

We are producing a steel part that has 3 important geometrical characteristics A, B, and C defined in a drawing.

A, B and C are correlated, so we can, for instance, adjust the mean value of A in the process but this also changes mean values of B and C.

Customer require us to submit Cpk/Ppk for A, B and C.
Even if we adjust the process so that Cpk/Ppk for A exceeds e.g. 1.33, the capability indices for B and C will become low (because B and C will not be centred). Same thing happens if we adjust for B or C.

So we are struggling to submit to customer Cpk/Ppk > 1.33 for all 3 characteristics.
What is a strategy that is in practice used for such correlated characteristics?

Thank you,

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The "correlated" word through me a bit. I think what you mean to say is they are "related" or the features are dependent.

You do not give us a very clear picture of what you are trying to make so it is a little hard to answer.

My Answer given what you said: The best strategy to do this if they are truly related is this... You have at least one study done, if not more, to know this effect. What I would do is:
1) Confirm the sigmas are equal for A, B, and C in the studies. This will tell you if you truly JUST have a mean shifting problem.
2) Quickly model up a study. You know sigma from 1) above. Make your three means variables and one changeable. Change the others with math based on your observations. The output of this math model is Ppk and/or Cpk.
3) Use a goal seak or linear search function in Excel (Google them) to change your one input to optimize your outputs.
4) You could do 2&3 by many means. The end goal is - keep your (known) sigmas fixed and diddle with the means optimizing the Cpk for all three.
5) IF it can be arranged so that all the Cpks are passing, run your process at this point and there's your passing study.

My answer with making assumptions on what you said:

My best guess is you have a stamping or forming operation and you are loading a blank into a tool. If you set your reference edge to center A, then B and C are not centered. Choose any one. This is a tooling problem. Your die or punch or whatever is not quite right and is not centered for each of the features. If I was your customer, I'd be telling you to fix the die, not monkey with the numbers. Reason? Let's say you find this "optimal" location in my steps above.... You are going to have a REALLY SMALL process window. My expectation would 6 months in, your employees will go back to "normal" mode they follow on every job and will NOT keep this one super-secret-centered-with-care. And I will get B and C out of spec (statistically). Fix the tool.


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This is an unfortunate situation in which to be placed. Not knowing anything about your process or product, the following advice may or may not be helpful.

As you describe it, I visualize a process with (1) single control factor. I adjust this control factor (X) and it affects the mean location of all three dimensions (A,B & C). However, most processes are not that simple.

Dimension A might be affected by controls X, Y & Z.
Dimension B might be affected by controls X alone.
Dimension C might be affected by controls X & T.

You may need to run experiments (e.g., DOE) to determine these. In the above scenario, you adjust X to optimize B, then use Y & Z to optimize A, and T to optimize C.

Even then, you may not be able to achieve capability on all three simultaneously.

If this is not feasible, and it is not a tooling issue that can be corrected, you may have to ask the customer for tolerance relief.
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