iSixSigma

Gage RR

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  • #32939

    R
    Participant

    Why is 5.15*Std Dev used in the calculations for gage R&R (as opposed to 6*Std Dev)? 
     
    What is the significance of 5.15?

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    #88514

    Bee
    Participant

    The idea is to cover 99% of the area (leaving 0.5%) on either side.
    If you see 99.5% of the area under the curve for one-side limit corresponds to 2.575 std. deviations from the mean.
    Therefore for both sides 2.575+2.575 = 5.15 std. deviations cover 99% of the curve (leaving .5% on either side, therefore totally leaving 1% on both sides.)
    Hope this helps.
    Bee

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    #99092

    Wagh
    Participant

    Bee-
    1. Why leave 0.5 % on either side ?
    2. Why not cover 99.73 % which corresponds to 3 + 3 = 6 std. deviations ?
    Awaiting further clarification.
    prasad
     

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    #99096

    Mikel
    Member

    When awaiting a reply to a 9 month old post – be patient.
    Why do you want 99.73%? It is just a convention and the real trick is understanding how the rules for interpreting GR&R relate to whatever your +/- sigma decision is. Do you understand the interpretation rules and what they actually mean?

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    #99097

    Devashish
    Participant

    Dear all,
    In fact as per AIAG RevIII it has been changed to 6*SD instead of earlier 5.15. to include 99.73%. It also makes calculation easier(multiply by 6 rather than 5.15)
    Devashish

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    #99101

    Wagh
    Participant

    1. Thanks DD. It now seems more logical to have GRR =  ( 6*sd ) / Tolerance. Awaiting yr other clarification as discussed this evening.
    2. From Stan’s post i understand that  99 %  is just a convention- thanks for the same
    3. Stan – as for a 9 month old post I thought the answer to the question raised by the previous person was not complete which u have now done. Besides I chkd the string for some info on the same subject.Further abt the significance of the GRR =  ( 5.15 * SD ) / tolerance expressed as a % is ok by my understanding. 
    Prasad  

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    #99107

    Mikel
    Member

    Did they change the acceptance criteria as well? If not, they just made it easier to have an acceptable gauge compared to total variation. That doesn’t make sense.

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    #99114

    Mario Perez-Wilson
    Participant

    To answer the question:
    Why is 5.15*Std Dev used in the calculations for gage R&R (as opposed to 6*Std Dev)?
     
    Measurement System Variability (Gauge Variability)
    The reason you want to use 6 instead of 5.15.
     
    When you compute 2 x Z (where Z is the standard z-score and can be equal to 2, 2.575, 3, etc.) times the standard deviation of the measurement error, óR, you are predicting or modeling the risk (uncertainty) with the normal distribution.
     
    By computing 99.73% of the distribution, that is, multiplying +/- 3 (Z=3, 2Z=6) by the standard deviation of the measurement error, óR. This value, 6óR, is then a prediction of the precision of the measurement system or gauge, which is commonly referred to as the repeatability.
     
    Why do we choose +/- 3óR (99.73%) instead of any other prediction?
     
    Because, this prediction will later be compared against other predictions, such as, the product tolerance, process stability, process capability, process potential, all of which are computed using +/- 3 sigma limits.
     
    The value 6óR, is then compared against the product tolerance, to compute the percent of
    variation consumed by the measurement system (gauge) uncertainty.
     
    This explanation has been modified from the book: Gauge R&R Studies. I hope the symbol for sigma shows as a Greek letter, as it does in my WordPad.
     
    Mario Perez-Wilson (mpcps.com)

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    #99115

    Mario Perez-Wilson
    Participant

    That wierd symbol ó is supposed to be sigma.
    Mario Perez-Wilson (mpcps.com)

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    #99118

    Mikel
    Member

    Mario,
    The choice of 5.15 or 6 is not relevant. The rules associated with that are. 5.15 gives 0.86 of the value 6 gives. If your rule is <10% P/T using 5.15, the same rule using 6 would be <11.6%.
    If the rules don’t change going from 5.15 to 6, we just tightened the criteria for P/T by a little more than 16%. P/TV doesn’t change.
    It turns out that the rules are quite conservative as it is, why make them more conservative?

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    #99136

    Mario Perez-Wilson
    Participant

    Stan,
     
    My post is not a response to your question about a change in acceptance criteria. I just replied to the original post, while reading the latest post in the thread, which happens to be yours.
     
    Nevertheless, the acceptance criteria is arbitrary.
     
    Mario Perez-Wilson (mpcps.com)
     

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    #99138

    Mikel
    Member

    Mario,
    Whether or not you were responding to my post, I responded to yours. You said we use 6 to facilitate comparisons – comparisons to what?
    The acceptance criteria has its basis in the old 10:1 rule that test engineers have always used.
    The choice of 5.15 or 6 is arbitrary. The systems question to be answered is how much uncertainty do we want at the edges of our acceptance criteria and what do we do about it. The secondary six sigma question is whether the measurement is one of the big bars on our pareto if we are trying to reduce variation. If it is, we need to address. If it is not, who cares?

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