ANOVA Gage R&R – Part 2

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Thanks so much for reading our publication. We hope you find it informative and useful. Happy charting and may the data always support your position.


Dr. Bill McNeese
BPI Consulting, LLC

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Measurement Systems Analysis/Gage R&R

Comments (28)

  • AnonymousOctober 3, 2012 Reply

    Anova Gage R&R process for attribute data?

  • VenugopalSeptember 28, 2015 Reply

    HelloI am Venugopal from India. I am in Automotive field in Quality and i am also certified Six Sgima Black Belt from ASQ.Just to understand the concepts behind how minitab calculates all these, i went trough all the above articles series 1 to 3.Very intresting and detailed. Thanks for the same.I have some doubts on Expected mean Square variation. Can you throw some more details for this?ThanksVenugopalmail ID – [email protected]91-9790888731

    • billSeptember 28, 2015 Reply

      What doubts do you have the EMS?

  • Frank van der Ham, ( [email protected])October 14, 2015 Reply

    The denominator in the formula is r, which was explained as the number of replicates.  number of replicates given was 3. But in the formula is filled in 5, which is the number of parts. What is right?

    • billOctober 14, 2015 Reply

      Hi Frank,
      Good catch.  The denominator is r = the number of replicates.  So, it should be 3, not 5.  I made the change.  Note that the denominator for each EMS contains those not in the EMS.  For example, the operator EMS denominator contains the number of parts times the number of replicates.  So, the EMS for operators*parts contains the number of replicates.

  • AnonymousNovember 21, 2015 Reply

    For Simplicity , can we use Sum of Squares contribution to calculate Gage R and R. for example Can we say:Gage R&R ~ (SSo+SSo*p+SSe)/SSt

    • billNovember 21, 2015 Reply

      No, because the relationship is based on the variances, not the sum of squares.  You use the EMS to find out how the mean squares can be used to determine the various variances.

  • AnonymousDecember 20, 2016 Reply

    As the equation shows GRR^2 = EV^2 + AV^2, wouldn't you need take the square root of 0.1109 to get GRR?  In that case, the %GRR should be much higher.

    • billDecember 20, 2016 Reply

      The equation left off the squared.  % GRR = GRR^2/TV^2/  Equation is corrected above.

  • AnonymousJanuary 11, 2017 Reply

    I would expect for the equation for GRR^2 that the /sigma_Operators*Parts^2 would also contribute, since I think it is part of the appraiser variation. Well, in this case since interaction is small, it wouldn’t make a difference. But since you say you will include it… Am I right?

    • billJanuary 11, 2017 Reply

      Not sure I understand the question but,the MS for Operators*Parts is like the MS for parts or operators by themselves.  

    • JessicaJuly 23, 2019 Reply

      Yes, you are correct!  I was stuck on this for the longest time because the calculations I made did not match my data.  That's when I noticed my /sigma_Operators*Parts^2 value is significant (as compared to the insignificance of this dataset) so I included it in the equation for GRR^2.

  • nedNovember 2, 2017 Reply

    hi there, how would you calculate the variance of each component, the expected mean square, in stata?

  • billNovember 2, 2017 Reply

    I am not familiar with stata.  

  • Daniel MorenoJanuary 5, 2018 Reply

    The results of GRR study changes if the piece that we want to measure is out of tolerance?

    • billJanuary 5, 2018 Reply

      If you are using a historical standard deviation for the total variation, then the answer is no.  If you are using the parts in the gage R&R to determine the total variation – and you substitute parts with mroe variaiton – then total variaiton will change.

  • Tomas NestorovicNovember 14, 2019 Reply

    The "% of  Total Variance" in the final table sums up to 112,14 %. Probably shouldn't?

    • billNovember 14, 2019 Reply

      It sums to 100%. The Gage R&R (12.14) is broken in the two R components in the table.  So you are double summing them when you get 112.14.

  • sridharOctober 30, 2020 Reply

    The articles are quiet interesting and detailed.Unfortunately all links given on the right of this webpage are available as pdfs for future reading. Is it possible to provide the same.SridharFrom [email protected]

    • billOctober 30, 2020 Reply

      Our older articles do have pdf downloads.  Sorry.  You may copy the webpage and paste it into Word though if you like.

  • Jose ChvaicerJanuary 5, 2021 Reply

    Hi, at the ANOVA table resuts F.DIST gives a different result for the O*P p-value.<br />Is there an available way to calculate the p-value in the table? How was is done here? 

    • billJanuary 5, 2021 Reply

      The software uses FDIST.  If you are using F.DIST, you have to use the following:  1 – F.Dist(.142, 8, 30, True).

  • JDFebruary 26, 2021 Reply

    Thank you very much for the analysis explanation. My statistics skills are not best. I would like to know if I can extract an uncertainty value range for my measuring system from the repeatability values. For example, the minimum uncertainty of a measurement is ± VALUE%

  • Mario_LOctober 18, 2021 Reply

    Hi, this two way ANOVA does not need need to meet any assumptions? I learned that a two way ANOVA needs to meet errors normality, variables independence and variance homogeneity. I have tested normality and the data is not normally distributed. This means this ANOVA results can not be trusted, right? 

    • billOctober 20, 2021 Reply

      Measurement error is normally distributed.  Not sure how you tested for normality.  But I would not worry about that here.

      • Mario_LOctober 21, 2021 Reply

        I have made the non-parametric Lilliefors test. I have already checked it and with level of significance of 5% errors do not follow a normal curve. Can it be a problem or, for those cases of gage r&r this should not be important?

        • billOctober 21, 2021 Reply

          I would not worry about that with Gage R&R.

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