Cgk - The Kolmogoroff (Kolmogorov-Smirnov) Method




Hello to all, this is my first post.

I am about to get involved in a GR&R study using the Gomanoroff (?) theory, whereby, an object is measured 5 times, the results are taken and a 'Cgk' value is calculated.
This Cgk value ranges between 0 and 1, where 1 is the maximum confidence of the measurement device.

Does anyone have any experience of such a technique?
If so, can you throw some light on it for me?

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Kolmogoroff method

Sorry Paul, can't help with this method but I was just wondering why you wouldn't use the 3 operator - 3 repetition method.

There are lots of good gage R&Rs offered here at the Cove, all free for downloading. Unless a customer specifically asked for another method, I would worry they wouldn't understand what they are looking at and ask for the common R&R anyway.

I would be interested to learn if this is a "special" method applied to particular circumstances where the "normal" R&R is impractical. Never too old to learn.


Atul Khandekar

Quite Involved in Discussions
I have heard of Kolmogorov-Smirnoff (K-S) Test for Normality. Never come across it being used in R&R studies.

Apart from Range-Average and ANOVA methods of R&R given in MSA manual, there is Shainin's ISOPLOT for measurement systems analysis.

Would certainly like to learn if there are any new methods available / recommended.



Hi guys, sorry, I posted the link on the previous message to show that Kolmogoroff existed, not to demonstrate any solution to my repeatability problems.
I now have a very basic understanding of this approach;
The theory is called the Kolmogoroff-Smirnoff (sounds like a drink, I know) theory.
Basically it involves applying a formula (which at this stage I am still trying to work out - ****ed SPC software package!) to a series of data collected by the measurement system.
The ouptput of this formula is a coefficient, Cgk.
The logic goes as follows;
If Cgk > 0.15 then you have a normal (Gaussean) distribution, and therefore your measurement system is behaving as it should.
However, if Cgk < 0.15 then you have an abnormal (non-Gaussean) distribution and your measurement system is behaving erratically.
This is my (very limited) understanding of the Kolmogoroff theory.
The more I know, the more I'll tell.


Atul Khandekar

Quite Involved in Discussions
The K-S test is a goodness-of-fit test used to determine if your data comes from any specific distribution (such as Normal). I believe your SPC package is testing data for normality.

There are tables of critical value available and if the Test Statistic (D Statistic - the Cgk in your case?) is greater than the critical value, the test is said to have failed.

If you want to know more:

Kolmogorov-Smirnov Goodness-of-Fit Test
Kolmogorov-Smirnov Test

Martin S

Re: Cgk - The Kolmogoroff Method

Hi all
Got a request from one of our customers to perform an "analyse of measurement equipment Cgk >1,33". Since I never heard about Cgk analysis I tried google it and found your conversation. But since last reply was in 2002 I hope that someone still is "alive" on this thread and are able to help me understand this problem. Reading prior posts it says that Cgk runs from 0 to 1. If that's true exceeding 1,33 will be a tough one...

In a normal situation I would have used either GR&R or MSA studies but in this case I don't know what to do.

Thanks in advance!


Super Moderator
Re: Cgk - The Kolmogoroff Method

Welcome, Martin.

I think this post by 'Miner' should answer your query well.

There is not much information available on this topic, which means that it never really took off.

The short story is:

Cg = 0.2 * StDev(Process) / StDev(Gage)


Cgk = [3 * StDev(Process) - |Bias|] / [3 * StDev(Gage)]

Cg is really rendundant if you have %GRR. It adds no new information, just packages it differently. Cgk is only of use if you did not establish credible calibration acceptance limits. If that was done, Cgk adds little value.
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