Destructive Gage R&R Analysis

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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 (45)

  • AnonymousOctober 30, 2013 Reply

    Wonderful! I like it! Please carry on similar study and please share the same time to will help all of our practitioners to get their further improving their body of the knowledge.
    With regards,
    K.M.mostafa Anwar
    Lean Six Sigma Green Belt

  • AnonymousNovember 3, 2013 Reply

    Good I like itPlease share simlar studies With RegaardsPVK RajuSix sigma Black belt

  • AnonymousAugust 5, 2014 Reply

    If are considering the parts within the batch are identical in that case why we were not able to calculate reproducibility?

    • billAugust 11, 2014 Reply

      You do calculate reproducibility.  It is just very small in this example.  If there were larger differences between the "same" sample results, it would show up. Bill

      • AnonymousSeptember 14, 2014 Reply

        Hi!!I tried to calculate the reproducibility standard deviation and its coming out to be 0.473 which makes the % Contribution to Total Variation = 16.22% and GRR % Contribution to Total Variation = 22.07%.Please correct it else let me know if I am wrong.RegardsAshok

        • billSeptember 15, 2014 Reply

          The formula for reproducibility is (MS Operator – MS(Batch/Operator))/(parts*samples)

          MS Operator = 2.18 while MS Batch = 3.134
          so MS Operator – MS Batch is negative – so it rounds up to zero.

  • AMDDFebruary 11, 2015 Reply

    This is great! It helped me a lot. Keep it up!

  • DeeMarch 11, 2015 Reply

    Hi,Can you provide wiith the formulas used to calculate all the ANOVA tables? I am unable to solve the problem.or attach a excel sheet that you may have put togther for solving this as a template to understand it better.Thank youDee

    • billMarch 13, 2015 Reply

      The basic calculations are covered in our three part series on ANOVA Gage R&R.  Please take a look at those and see if that helps you solve the problem.  If not,  I will put the formulas here.

  • XNNovember 8, 2015 Reply

    Bill,  Thanks for your writeup.  We are performing compressive strength testing.  Due to the natural of our products, there are variations from the same batch.  We just completed a GRR study using 15 batchs of samples, 4 specimens per batch, 2 operators.  Gage R&R is 80%.  However, the total COV (SD/Mean) of all specimens is less than 2%.  the COV of the specimens is about 2-3% range.  This cov is considered to be great for strenght testing such as compression and tensile strength. There are 2 possible conclusions among my colleagues:  1. our measurement is not good enough.  2. Gage R&R is not suitable for this application because it assumes the the 4 specimens in the same batch are identical.I would appreciate if you could shine some lights on this.Thanks,

    • billNovember 9, 2015 Reply

      Can you send me the data so I can run an analysis (<a href="mailto:[email protected]">[email protected]</a>).  Both possible conclusions are possible.  But I can see more by running the analysis to see the various source of variability.

  • MOHAMMEDFebruary 2, 2016 Reply

    Hi, you mentioned in the example about Nested Gage R&R that the tolerance is 8 but when I check the data depend on this formula UCL-LCL Ifoud the Tolerance is 6.4968 when UCL=X bar bar+3 sigma and LCL=x bar bar-3 sigma?

    • billFebruary 2, 2016 Reply

      The tolerance is the width of the specification limit.  In this case, USL – LSL = 38 – 30 = 8.

      • YogeshAugust 12, 2020 Reply

        Is it the tolerance or range? RANGE/WIDTH = UCL-LCL 

        • billAugust 12, 2020 Reply

          I am not sure what you are asking.  The width of the tolerance is USL – LSL.  You can also call it a range.

  • MOHAMMEDFebruary 8, 2016 Reply

    Hi,how we can compute the residuals for the data above because it is Nested design and is there any software can do that or your SPC pakage can do that because I need to analyze the data if it is has outlier or not through Residuals .I have similar dataThanks

    • billFebruary 8, 2016 Reply

      A Gage R&R study is really a designed experiment – whether it is nested or not.  You are looking for signals from the data.  You search for outliers by doing a range control chart on the "same" runs.  As long as there are no out of control points on the range control chart, you assume there are no outliers.

  • IjazMarch 14, 2016 Reply

    The most gage RR article/studies I've come across assume that there is only one operator involved. What if there are 2 group of operators in the process or for that matter two distinct measurement tools also. This is something that I need to test; we have one set of operators who pull a sample from a batch and another set of operators who run the sample on an equipment and there happens to be two pieces of equipment that they can run the sample on (same equipment but different generations). If there are 3 operators that pull the sample, and 3 operators that run the sample on any/both of these two equipment and we take 3 batches with 2 samples each (destructive) then it is 108 readings. But is this resolution good enough against the complexity or should we simplify by breaking the process into 2 groups or something similar. I think the equipment could be looked at as two separate studies. Thanks!

    • billMarch 14, 2016 Reply

      GAge R&R is a study in variation.  Repeatability is the ability of a single operator to measure the same value on the test, while reproducibility is the ability of multiple operators to measure the same value on the test.  So one operator studies only give you the repeatability.  You should look at each measurement system individually.

  • DaleWMay 17, 2016 Reply

    Logically, it seems that one should only use a Nested design here IF one believes that parts from a given Batch are IDENTICAL when tested by the same Operator, but will be DIFFERENT when tested by different Operators.  (A Minitab blog makes this point directly in explaining the purpose of the Nested Gage R&R for destructive testing.)In most cases, attributing such adaptive behavoir to parts would be difficult to defend, so one should use the simpler Crossed design analysis, and accept that test Repeatability will be confounded wih part-to-part variation.  Here that gives the same low Repeatability of 0.284 (ANOVA, or 0.296 by SPC), but now Operator Reproducibility and Operator*Batch interaction (non-parallelism) become inconveniently large and significant.  After all, something must explain why the variation among the six samples from any Batch tends to be so much larger than the variation among two samples from the same Batch by any given Operator.  (It's not likely to just be bad luck in Part-to-Part variation than only shows up across different Operators!)My guess is that labs may use the Nested Gage R&R more than they should because they don't like to fess up to Operator irreproducibility, and would rather blame it on Part-to-Part variation typically outside their control.    

    • billMay 18, 2016 Reply

      Thanks for the comment.  It is uncommon for the batch-to-batch variation to be large compared to the witihn-batch variation.  I grew up in the PVC industry and that was very true.  So, if you did a control chart with subgrouping based on within-batch variation, the control limits were very tight and everything was out of control.  Hence, the need for the Xbar-mR-R chart.  Cross designs are great if you have the same part or sample to test for each operator.  But with destructive testing, you don't have the same part/sample.  Thus, the need for the nested design.  I know the logic of saying the parts from the same batch are the "same" and then you can use a crossed design.  But what is the operational defintion of the "same" or "identifical"?    I have seen variation in the hardness along a length of steel bar that was very large.   Cutting the bar into parts and calling them same is definitely questionable.   In the end, it is the choice of the person running the test.  He/she has to use his/her knowledge of the process and make that call.  But if you believe the parts are the "same," I would agree with your comments.

      • DaleWMay 18, 2016 Reply

        Bill,  thanks for your quick response, but I think you missed my point, so I'll try again.A nested model would apply if a given Operator (magically?) could test the same part twice, while different Operators could never test the same part.  That is what nesting by Operator implies.  My point is that is rarely the case with destructive testing, where each part usually can only be tested/broken once.  More typically, the logical Gage R&R for destructive testing truly would be an equal opportunity crossed design, with measurement repeatability hopelessly confounded with part-to-part variation for all Operators — unless there is information not in evidence to separate them outside of the core R&R design itself.Applying the logic of nesting to your example data set for a destructive test, without providing a reason to believe that a given Operator can replicate a test on essentially the same part while different Operators can't, seems totally wrong to me.  Taken at face value, your data set suggests major Reproducibility issues between Operators, while the combination of Part-to-Part variation and pure measurement error is relatively small (sterr=0.28 with dof=15).Minitab's "A Simple Guide to Gage R&R for Destructive Testing" (Paret, 2013) engaged in special pleading to argue that situational constraints would sometimes (certainly not always) naturally approximate a nested situation (even though the experimenter might prefer the more powerful crossed design).  I don't think your example and interpretation make sense without proposing a similar special case.  Nested R&Rs are not a general approach for destructive testing, nor will Crossed R&Rs give as much information as we'd like (unless part-to-part variation is relatively minor compared to batch-to-batch variation).  Analysis as Nested R&R while simply using representative parts from each batch as you seem to suggest would result in disguising any Operator Reproducibility issues under Part-to-Part variation.

        • SteveSJuly 22, 2016 Reply

          Thank you for the extremely thoughtful response, DaveW. Thank you also, Bill, for the very helpful articles.I am in a situation where my test is destructive. While it is difficult, we can get enough parts reasonably considered to be "the same" to perform repetitions across multiple operators. Understanding where error will be moved depending on my experimental layout is important to me, because I want to make improvements to my system, not disguise a problem. You have both been a great help in this effort. Thank you.

  • dharshanaJune 29, 2016 Reply

    what is the relation ship between GR&R and CoV study 

    • billJune 29, 2016 Reply

      The coefficent of variation is the ratio of the standard deviation to the mean.  I am not sure what you are asking.

  • JamesAugust 16, 2017 Reply

    bill,% of total tolerance  results are different from minitab

    • billAugust 18, 2017 Reply

      Why do you think the % total tolerance is different from Minitab?  The specs are 30 to 38.  The numbers in the newsletter match Minitab results.

  • pardeepJanuary 25, 2018 Reply

    Hi bill thanx for such useful information. I hv a question on process capability cpk. Why we take cpk min. In thr results of cpu &cpl.

    • billJanuary 25, 2018 Reply

      That gives you the mimimum capability value.  If  you just see Cpk, you don't know if it is Cpl or Cpu – you just know the minimum of the two  If Cpk = 1.33 then you know the spec limit that is closest to the average if 4 standard deviations away and essentially nothing is out of spec at all.

  • Mario_BTJune 22, 2018 Reply

    Hi Bill,Thanks a lot for this nice example. A minor observation if I am not mistaken. The Gage R&R acceptance criteria you are referring to are valid for the Gage R&R standard deviation (%) and not for the Gage R&R variance (%).% Gage R&R ≤ 10%: measurement systems is acceptable;10% < % Gage R&R < 30%: measurement system may or may not be acceptable depending on its use and the customer%Gage R&R ≥ 30%: measurement system needs improvement So these rules for the Gage R&R variance (%) are:% Gage R&R ≤ 1%; measurement systems is acceptable;1% < % Gage R&R < 9%; measurement system may or may not be acceptable;% Gage R&R ≥ 9%: measurement system needs improvement.In your example, the Gage R&R variance (%) is 5.02%, the system may or may not be acceptable. Taking the square root of 5.02% gives us 22.8% with the same conclusion.

  • JOSE JUANSeptember 27, 2018 Reply

    Hola, por favor asesoramiento para llevar a cabo un sistema de medicion no replicable para una camara salina.Saludos

    • billSeptember 28, 2018 Reply

      Not sure i understand what you want.  Is there no way to divide a sample in half and test both havles?

  • BinSeptember 30, 2018 Reply

    Hi, thanks for sharing the knowledge here. Can you please tell more about the Resolution in MSA. When do we need to lood at Resolutioin, how to calculate, and is there's a spec/standard for judging it? Thanks.

  • Anil Singh RawatJuly 22, 2020 Reply


  • KhorAugust 18, 2020 Reply

    Hi, May I know what is the formula for degree of freedom in Batch and Repeatibility?I referred to previous 3 series but seems like there is some differences.Thank you. 

    • billAugust 19, 2020 Reply

      Let o = number of operators, df = o – 1 = 3 -1 = 2
      Let b = number of batches per operator: df = o(b-1) = 3(5 – 1) = 12
      Let r = number of replications: df = ob(r – 1) = 3*5*(2-1) = 15
      Total df = obr-1 = 3*5*2 – 1 = 29
      Remember that this is a nested gage R&R; the equations will be different for a crossed Gage R&R.

      • SYPJuly 5, 2021 Reply

        Hi.. What will be the degree of freedom for reproducibility?

        • billJuly 5, 2021 Reply

          Reproducibility is a measure of the difference between operators.  Since this is a nested design, the impact of operators are spread over two things: Operators and Batch(Operators).

  • Madhuranthagan BalasubramanianNovember 7, 2021 Reply


    In Table 2 how the value 37.606 arrived

  • Sky WalkerJanuary 6, 2022 Reply

    Hi Bill,Thanks for your detailed explanation. I would like to ask for guideline of part/batch. In your example, 2 parts each are drawn from 15 batches. Can I draw 10 parts each from 3 batches(assuming my processa is stable)? In short, do we prefer more parts from less batches or less parts from more batches?

    • billJanuary 7, 2022 Reply

      Thanks.  Yes you can use 10 parts from 3 batches.  The key is to get enough data.  you want around 30 degrees of freedom total.

  • Cedric DMarch 15, 2022 Reply

    Hello Bill,
    Thank you. I was struggling to design a study for tensile strength measurment when I found thisvery detailed post. I have a question about the way SSbatch was obtained. As you said last year when answering Khor message, the equations are different in nested and crossed gage R&R. Could you give us the formula? Thanks Cerdic

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