% GR&R as a ratio of standard deviations vs. %GR&R of Variance Components

[#1]

I have been completing GR&R studies for many years and have always used the %GR&R calculated in the lower portion of the GR&R report using Variance Components. JMP also reports a % GR&R in the upper part of the screen as a ratio of the RR standard deviation to the Total Variation. Can you please help me understand the benefit of one vs. the other. I seem to remember the the Variance Components number is the correct one to use, but would like to better understand this. Can someone please help to explain this? I have not found a clear explanation on this forum or in the JMP documentation on GR&R.  Thank you.

[#2]

Hey @Jens_Riege ,

They are both correct, they just have different meanings.  The variance component % RR is nice because they all sum to 100%.  However, variance component values are not in the units of measure so can be harder to compare to your measurements and tolerance.  For variance components you use 1% or less as great and 10% or less as acceptable.  For % Total in the upper table (also known as % study variation) that uses the stdevs of the components, they don't add up to 100% which some people don't like as well as they use a different threshold for acceptability with 10% or less being great and 30% or less being acceptable.  Since you have to use something in the same units as the tolerance, that is why you see the stdevs used to get a % tolerance in the upper table as well.

Hope this helps!

[#3]

Thank you Shampton82 for addressing my question. Your explanation matches what I am finding in some of other forums on GR&R.

The purpose of my inquiry is purely to find a clear explanation that explains why only one methodology, within the ANOVA approach to GR&R and backed by mathematics, can be used to define that a gauge is deemed capable. JMP's way of displaying both has been a concern of mine for a very long time as I have not seen a good argument to decisively choose one over the other. Having two answers adds confusion and leaves it up to the user to decide if the gauge is capable. One could just pick the better of the two numbers.  

Having data in the same units as the measurement may apply to common sense, but does not really make mathematical sense. 

Don Wheeler (reference below) makes a good case that these are just ratios, but cannot really be compared. Adding all percentages of variation gives more than 100% variation, as you mentioned. This does not seem physically possible if the total variation is 100%. To properly compare ratios, and indicate which one is a fraction of the total, it would be a % of 100, not a % of some number. 

Using variance components preserves the mathematical integrity, since variance components add to 100%. Wheeler also states that using standard deviations does not properly account for measurement error, and variance components do.

This would lead me to conclude that comparing variance components when completing a GR&R using the ANOVA method is a more appropriate solution. 

I would be interested in your and anyone else's ideas, as it seems there are a diversity of opinions, but no clear rigorous definition.

-Jens Riege

"Problems with Gauge R&R Studies: How to make sense of your R&R value"  Donald Wheeler

https://www.spcpress.com/pdf/DJW223.pdf

[#4]

Sorry, but I don't really understand what your question is?  What do you mean by "Having two answers adds confusion and leaves it up to the user to decide if the gauge is capable".  What is the confusion?  Could you please define: "gauge capability"? One statistic is expressed in the units of the measurement, the other is squared. When using the variance, you no longer have direct interpretation in relation to the unit of measure, but the variance components are additive. Determining whether a gauge is appropriate and useful is always up to the user.  Statistics must always be interpreted. 

There are multiple ways to do measurement system studies, including control chart method.  All methods require interpretation by the user.

[#5]

Hi Statman,

Thanks for your reply.

The two GR&R numbers I mentioned referred to the %GR&R under the standard deviation section of the Anova table and the separate GR&R % of total variation under the Variance Components section of the table... For example here is a GR&R study with the standard deviations and variances> The %GR&R by standard deviation is 7.35%. By Variances it is 0.54%. And the criteria to decide whether a gauge is acceptable for use is <10% in either case. That does not make sense...

If the total variation for std deviation is 100.00% adding up the individual components of variation total more than 100% as Wheeler mentioned. For this reason the Std Deviation method does not make sense. It does not matter to me that the variances are in the same units as the original data. We are taking relative ratios of two factors and are taking about % variation, not % units. - just my thoughts.

Thanks, Jens

	Std Dev	Variance	% of Total (Std Dev)	% of Total (Variances)
EV	0.005914978	0.000034987	4.69%	0.22%
AV	0.007133345	0.000050885	5.66%	0.32%
RR	0.009266692	0.000085872	7.35%	0.54%
PV	0.125669222	0.015792753	99.73%	99.46%
TV	0.126010417	0.015878625	100.00%	100.00%

[#6]

I'm sorry you completely miss my point, but no worries.  All analyses need interpretation.

[#7]

Hey @Jens_Riege ,

Glad the explanation helped some and I understand your concern with using Stdevs.  Wheeler was so miffed about it that he came up with the EMP method!  I like using the total GR&R with standard deviations as this can be used to get a % tolerance and that is the main metric we report out on in Aerospace.  If I'm concerned about which portion is driving the GR&R results I'll look at the variance results.  I also like looking at the 6xStdevs of the Gauge as a gut check on if I would expect that much variation from the gauge and how much could a measurement be off if the true part was right at a spec limit.  I think this can be more informative for the use of the Gauge then just thinking in percentages. If you're looking for a % GR&R then using the variance components would be the way to go as they are additive and easier to understand from that point.

Hope this helps, like you and Statman said there are a lot of different ways of looking at Gauge performances.

Steve