ANOVA Gage R&R – Part 1

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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 (29)

  • AnonymousOctober 17, 2012 Reply

    Very well written post. It will be valuable to anybody who utilizes it, as well as myself. Keep doing what you are doing – for sure i will check out more posts.

  • Dinesh GanesarajanMay 8, 2015 Reply

    Sum of squares for parts are wrong because, the upper limit for the summation should be n(number of parts) instead of k.

    • billMay 13, 2015 Reply

      Thanks for catching that.  It has been changed.

  • angel hernandezDecember 8, 2015 Reply

    the formula to calculate the SSp has a term that must be (n*r) instead of (k*r)

    • billDecember 8, 2015 Reply

      I believe the formula is correct.  It is measruing the sum of squares of the parts.  k =number of operators and r = number of trials (replicates), so it gives 9 results per part. 

  • Johnny WindMarch 2, 2016 Reply

    Firstly thank you very much for this work, much appreciated!My quesiton would how you get from "Sum of Deviations" to "15(Sum of Deviations)" – for example the value for the operator is SS<sub>O</sub> = 1.6304 but the calculations seems to be missing in the math expression and the explanation:"n = 5 and r = 3, so there are 15 results for each operator" will just not match up for me.I would appreciate if you could explain the math a bit more in details – thanks in advance.

    • billMarch 2, 2016 Reply

      It appears I had the parts sum of squares in twice – for the parts and for the operators.  Take a look at the equation SSo now.  Thanks for pointing that out.

  • Esther SHIApril 12, 2016 Reply

    I am doing a Gauge R&R study for our test equipment.As we know, the %total variation is the sum of %variance contributed by part-to-part, operator and repeatability. The % total variation is always equal to 100%. In the other words, if the part-to-part variation is very big, then the %Gauge R&R(=%variance of operator+%variance of repeatibility) will be small and likely will pass the Gauge R&R. Is that true?If this is true, in order to pass the Gauge R&R we can select the big variance of the parts. Is that right thing to do?

    • billApril 12, 2016 Reply

      Three methods for comparing results.  One is to compare the gage variation to the variation of the parts used in the study. In this case, the parts should be selected to reflect the range of variation in the process. In other words, don't just take 10 parts off the line right in a row. You need to select the parts so they reflect the variation seen in the manufacturing process.  This is the approach to take if you want the test method to be able to tell the differnce between parts (i.e., control the process).
      The other two ways to determine the % gage R&R is to use an independent estimate of the process variation or to compare the results to the specification range. If you have an independent estimate of the process variation (e.g., from a control chart kept on the production process), the requirement for the parts spanning the production range is less critical. This is also true if you are comparing the results to the specification range.  On the specs, in this case, you are just using the test to accept or reject parts.

  • AnonymousApril 13, 2016 Reply

    Thank you so much for your clear explaination! I will try to compare the results to the specification range and see what is the different in the %gage R&R result then. 

  • David JamesOctober 10, 2016 Reply

    Hi Bill.Thanks for this example. My question is that having done a similar study using Minitab and excel, I get different results from the two methods. I have checked it with my colleagues and still its the same issue. Do you happen to know why that could be?Thanks

    • billOctober 10, 2016 Reply

      Hi David.  Our SPC for Excel software gives the same results as Minitab.  I assume you are doing this manually in Excel.  Please send me the workbook and I will take a look at it.  Send it to [email protected]

  • Andy LunaMarch 15, 2017 Reply

    Muy bien!! Muchisimas gracias excelente explicación.

  • David ShinozakiJuly 19, 2017 Reply

    In the ANOVA Table for Gage R&R, Column F, all three items should be divided by the Mean Square (Equipment) MSe, not just the last one. Other Authorities use MSe as the divisior. MiniTab uses both MSe and MSo*p depending of an undisclosed calculation.

    • billFebruary 15, 2019 Reply

      The table is correct if you keep the inteaction term in the model, which this article does.  The part and operator F values are determined by dividing by MSo*p as shown in the table above.  The F value for the interaction term is determined by dividing by MSE.  Minitab does this as well.  
      If the interaction term in not significant and is removed from the model, then the F values for the parts and operators are determined by dividing MSE.  This is also how Minitab handles it.

  • Vishal singhJanuary 9, 2019 Reply

    I have read your article on the topic Variable Gauge R & R study. 1 confusion is still running in my mind that how could be find if Instrument or Appraiser take wrong value(reading).

    • billJanuary 9, 2019 Reply

      Not sure what you mean by wrong reading.  A gage R&R is a study of variation.  The equipment variation is a measure of the variation in the instrument.  The operator variation is a measure of the variation in the operators.  You can compare those two variances to see which is larger.

  • Vishal singhJanuary 11, 2019 Reply

    If %EV = 23.3 and AV = 25.3% then what it's meaning? 

    • billJanuary 11, 2019 Reply

      You appear to be looking at the average/range method. Please see this link:
      The equations are given there, e.g.

      %EV = 100(EV/TV) = 100(0.217/0.9285) = 23.3%

      % AV = 100(AV/TV) = 100(0.235/0.9285) = 25.3%
      where TV is the total variation based onthe standard deviation (not recommended to use this method – use ANOVA or EMP.)
      So it is telling you how much of the 6*standard deviation is taken up by the equipment variation and the appraiser variation.

  • Vishal singhJanuary 16, 2019 Reply

    Please describe briefly about NDC value. On what factors NDC depends? In what ways we can increase NDC value.

  • AnonymousFebruary 7, 2020 Reply

    Sir is it standard to arrange the data this way in order to obtain a Gage R&R via Anova method? Is it such that the software understands just this format?

    • billFebruary 7, 2020 Reply

      When you run the ANOVA method with SPC for Excel, you select the number of operators, trials and parts. A template is then generated to fill to do the analysis.   The software runs based on the tempalte design.

  • Mohammad MajdOctober 5, 2020 Reply

    I am doing a gage r r analysis but the variance of error for each operator is different. Is my analysis valid? If not what can I do? If yes, how my interpretation of results is different from the typical gage r r  analysis? 

    • billOctober 5, 2020 Reply

      Hello.  I need to see the data to see what is happening.  Can you send it to me?  [email protected].    Thanks

  • SridharOctober 30, 2020 Reply

    How do you conduct a R&R study? Is it done for any feature on the drawing? How do you select a dimension on which you conduct a R&R? Does it have to be done on all dimensions / features? If the R&R is done for a particular dimension and an instrument does it hold good for all other domensions if we are using the same instrument?SridharFrom [email protected]

  • ntmhxApril 1, 2021 Reply

    You can apply R&R only at primary data or it is possible to apply it for combination of data. e.g R&R for A & B but also R&R for the difference: A-B?Is it possible to get R&R<20% for A & B and R&R >20% for A-B?

    • billApril 2, 2021 Reply

      Not 100% sure of what you are trying to it – but i imagine you can design an experiment to  look at A&B and A-B.  Not sure what hte possible outcomes are.

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