# Cgk - The Kolmogoroff (Kolmogorov-Smirnov) Method

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#### paulf

Hi,

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?

Cheers,

D

#### D.Scott

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.

Dave

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#### Atul Khandekar

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.

-Atul.

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#### paulf

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.

Cheers,

A

#### Atul Khandekar

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
-Atul.

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#### 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.

/M

#### harry

Super Moderator
Re: Cgk - The Kolmogoroff Method

Welcome, Martin.

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)

and

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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