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Capability Studies & Gage R&R with MMC Modifier

Discussion in 'Gage R&R and MSA - Measurement Systems Analysis' started by leftoverture, Aug 18, 2016.

  1. leftoverture

    leftoverture Member

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    I have a question. I am doing a capability study and a Gage R&R on a positional tolerance that has a maximum material condition (MMC) modifier. So with the MMC modifier, the tolerance is technically different for each sample, based on the amount of bonus from the feature and/or datum size. So how do I calculate my Cpk and Gage R&R for the position?

    Thanks,
    Tim
     
  2. ncwalker

    ncwalker Well-Known Member

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    Excellent question. The raw math doesn't lend itself to doing this. Here's how I approach it.

    1) Just calculate it RFS, don't use the modifiers at all. If it passes RFS, it will only be better with the modifiers. And, it's an easier math problem. Then should it fail ...

    2) What you do is scale it. For a given dimension, determine the tolerance as RFS + MMC Bonus. Call this 1. Then take the actual location and scale it. This would be actual / (RFS + MMC Bonus). As long as it is in tolerance, you will get a number less than one. If it exactly matched, you'd get 1. Out of tolerance would be greater than one. Do this for each subsequent dimension and do your capability study. With the total tolerance being 1.

    As to the Gage R&R, that's not as straightforward. Your best bet is to do this against RFS. If it doesn't pass this, what little gains you would get wouldn't be enough to make a bad one good. Think about it - if the gage was that close, improve the gage. Most likely you are talking about a CMM. Your steps would be: make SURE your datums were measured solid. Think about adding probe hits. Use appropriate probes (bigger rubys + shorter stalks).
     
  3. Miner

    Miner Moderator Staff Member

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    I have not seen any approaches for MSA, and I agree with ncwalker's recommendation of assuming RFS. This would be the worst case scenario, which is where you would place the greatest demand upon your measurement device.

    For capability, there are two different approaches that I have found. Each have advantages and disadvantages. The following are two papers written on the approaches available online.
    1. Calculating MMC Cpk: When there is a Maximum Material Condition or Least Material Condition True Position Specification; Revision 2; Marty Ambrose 2/11/99.
    2. Calculation of Cpk under conditions of variable tolerances; Marcel Dekker, 1991.
    I ran a Monte Carlo simulation on both about 5 years ago. Unfortunately, I cannot locate it, and all I remember was that both had situations where one worked better than the other. That is, under situation A, method 1 worked better than 2, but in situation B, method 2 worked better than 1. Of course you can also use the RFS approach, but this would definitely give very conservative results that would make your capability appear worse than it is.

    Another potential issue with these methods is that it could drive bad behavior such as deliberately running individual dimensions at sizes that maximize the bonus tolerance. That is, you sub-optimize in one area to optimize in another. One advantage of the RFS approach is that it does not drive this type of bad behavior.

    BTW, nice avatar and name. I'm a big fan of Kansas.
     
  4. leftoverture

    leftoverture Member

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    Thanks for the replies. I'm working through the data now.

    Miner - always nice to meet a fellow Kansas fan!
     
  5. Miner

    Miner Moderator Staff Member

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    IMO Leftoverture was their finest album followed by Point of Know Return.
     
  6. rmf180

    rmf180 New Member

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    Coordination with the customer is the most important thing. If you find that bonus is needed to show capability or conformance, we have used the technique of deducting the bonus from the positional deviation rather than trying to modify the tolerance based upon bonus. Our experience has been very good as long as we explain it to the customer's project team up front. Formulas can be generated in most inspection systems and if not possible, MS Excel formulas work to post-process the data.
     

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