# Non-normal Data in Gage RR

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• #31452

alghanmi
Member

Hello,
The B-bar and R method for Gage R&R assumes a normal distribution of the measurements. It is evident from the constants it uses (K1,K2, etc.), and the range is multiplied by 5.15 assuming a normal distribution. My question is what happens if the readings I get are non-normal? Can we still use these formulae?

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#82929

alghanmi
Member

Correction to my message. The first line should read X-bar and R method.Thanks Sameer

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#82930

Hemanth
Participant

Hi Sameer,
You have asked a tricky question. Theoretically you cannot use the formulae without fulfilling the assumptions. But, practically no one has asked me so far to check my GR&R data for normality. So practically there is no harm in using them as long as you have either very good or very bad measurement system. Only in cases of marginal ones that your judgement could be wrong. You can also try the ANOVA method which is not as dependent on normality assumption as X bar and R method.
Hope this helped.

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#82939

Chip Hewette
Participant

Why would the data from a gage be abnormally distributed?  Only if there were special causes of variation!  One can choose to ignore data containing special causes, but this needlessly confuses the situation.
How do you know the data is not normal?  Can you state with high confidence that one or more of the measurements are unusual?  Can you identify a cause for this unusual nature?  If so, should this cause not be eliminated prior to using the gage?
Consider the sources of variation within your measurement system.  How the part is secured?  How the gage is zeroed prior to use?  The temperature of the room?  How the operator interprets the numbers?  A difficult dimension to acquire using the gage?  Are any of these reasons likely to be the cause of abnormal data?
Classic GR&R methods require that the data be acquired and evaluated against the specification.  If the variation exceeds a percentage of that specification width, the gage must be improved.  This is a preliminary DMAIC project within the “M” of the original project that will likely identify the special causes to be eliminated.

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#82945

Gabriel
Participant

Do not confuse “normal distribution” with a normal or abnormal situation.
“Normally distributed” refers to the sape of the distribution (the bell shaped Gauss distribution). Other shapes are log-normal, folded normal, triangular, rectangular, Weibul, etc.
Clearly, the data can be normally distributed or not, regardless of the existence of special causes of variation. If a process (including a measurement process) delivers all the time values that variate randomly within the same distributrion (normal or not) then the process is stable and it is free of special causes of variation.
Indeed, if the process was not stable (affected by special causes) it would be hard to talk about a “process distribution”, because that distribution would be changing along the time.

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#82952

Chip Hewette
Participant

I am not confused.  Especially with any facts!;)
Your last paragraph mirrors what I tried to say.  Distribution type was immaterial to my thinking.  The original question about use of non-normal data points to a real need to understand what is going on, not the distribution type, as the measurements are clearly at risk.

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#82960

alghanmi
Member

Non-normally distributed data doesn’t mean that it is bad. What I am getting out of this discussion is that I can’t get any other distribution than normal unless I have special cause influence. Is this correct? Is there any possiblility that I will get something other than normal distribution. MSA doesn’t talk about this situation nor any software.My understanding was that as we use X-bar and R method we always use averages and ranges which follow normal distribution (or close approximation). As Dr. Wheeler explains in his textbook on SPC. The assumption in gage R&R about normality lies in multiplying sigma with 5.15. Maybe this value will not change much even if I have some other distribution? Otherwise using ANOVA method looks more logical approach.

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#83036

Gabriel
Participant

From now on I will assume that with “normal” you refer to the shape of the distribution: Normal = Gauss’s bell.
“I can’t get any other distribution than normal unless I have special cause influence. Is this correct?”
Not correct. A process can have any distribution and, in fact, almost never will it be normal. The normal distribution is a mathematical model that can be, at best, a very good approximation to the real process distribution. Usually, when you don’t have enough data to prove that the shape is not normal you will accept that the normal fits Ok and you will say that the process is normally distributed (which is a simplification of the reality). We didn’t mention special causes. If the process is affected by special causes then it is unstable then it is changing its behavior. In that case, you could hardly say that it fits ANY distribution at all, because the distribution itself is changing due to the special causes.
“Is there any possiblility that I will get something other than normal distribution?”
Absolutely yes. Try throwing a die. You will get a value from 1 to 6, and all the values have the same probability (1/6). This is far from the normal distribution.
“as we use X-bar and R method we always use averages and ranges which follow normal distribution (or close approximation)”
As you said, this is an approximation which works better for the Xbar where, because yopu are averaging and then you can apply the central limit theorem. The approximation will be better the larger the sample size and the closer from normal the is individuals distribution.
“The assumption in gage R&R about normality lies in multiplying sigma with 5.15. Maybe this value will not change much even if I have some other distribution?”
The r&R% is “measurement variation” / “total variation”. Toatal variation was defined as 6 times sigma of the readings of the process output (Stot). 6 times sigma contains about 99.7% of the individuals in a normal distribution. Measurement variation was defined as 5.15 times sigma of the measurement sigma due to repeatability and reproducibility S(r&R). 5.15 sigmas contain about 99% of the indivifuals in a normal distribution. So r&R%=100x[5.15xS(r&R)]/[6xStot]. Why 99.7% was used for “total” and 99% for measurement, I don’t know. The new issue of the AIAGs MSA (third edition) defines r&R% just as 100xS(r&R)/Stot, so it is just a comparison of sigmas. If you agree that “sigma” is a good way to measure variation, then you don’t care about the shape of the distribution. If you prefer to measure variation as the span that contains a given % of individuals, then shape matters.
However, in a typical r&R study you get 10 parts measured by 3 operators 3 times each. So you have 9 readings per part. That is usually not enough data to draw an histogram for each part and see if the distributions of the readings for each part is normal or not. I.E. you won’t be able to rejet that the distribution is normal and you will say hey! it’s normal!. I wonder how you arrived to the conclusion that the distribution was not normal.
Anyway, it is ussual to omit the shape of the distribution in the measurement analysis. An example is the standard about Measurement Uncertainty, that state that you just find the standard deviation in the measurement result and apply a cover factor: 2 for 95 of confidence and 3 for 99% of confidence. The satndard says that about any practical measurement distribution will cover close to 95% of the individuals within ±2sigmas and 99% within ±3sigmas. And it is true. For example, the rectangular distribution and the triangular distribution has 100% of the individuals within ±3sigmas.

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