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Cg & Cgk – A Measurement System Capability Index from a customer.
Formula is basically the same as for Cp & Cpk, but it uses 20 Sigma & 10 Sigma respectively instead!
If anyone out there came across these index, I will appreciate your comments/ inputs.
This method examines the equipment-related variation behaviour of the measuring system at the location of application. 50 measurements (a minimum of 20) are effected under identical conditions (measurements carried out by the same operator on the same part*) or standard and feature at a precisely defined point) and then the deviations of the indications from the nominal indication are recorded.
If the value is > 1.33, the capability index Cgk can thus be calculated. That value must also be > 1.33.
Why not 50 or 1000 sgma? Where is the statistical significance of this measure?
It really is a meaningless number Stick with the Cp and Cpk
I, also, question the wisdom of this measure. One reply seems to suggest that 20-50 test-retest iterations are done. In a 10-20 Sigma process, I have worries that a quantity that small might not be sensitive enough unless the Discrimination is incredibly well done. Even with that, the value of 1.33 is nowhere near 10 or 20 Sigma.
The idea is, obviously, that the customer doesn’t want the measurement system contributing at all to the variation of the product. Multiple measures allow us to reduce our Beta risks at the rate of the square root of N. That means that 50(49 really) measures are about 7 times less risky than 1. That won’t, by itself, take you to 10 sigma from 6 sigma. The task at hand, then, would be 1.) Increase the sensitivity of the measurement gages, and 2.) Increase the spec width.
So it looks like it is not an industry standard, but something that the customer developed to ensure variation contributed by the measurement system is controlled.
Cg & Cgk is Tolerance related. Like JP pointed out, they consider the gage to be capable as long as both index are >1.33.
Thanks for all your posts.
a Cp of 1.33 has been the standard for many years when computed using the accepted Capability equation. In six sigma the goal is a Cpk of 2.0
If you play with the denominator by increasing the number of standard deviation utilized such as you described you are placing an unrealistic burden on your process to perform.
I would be interested to know who the customer is if you can give that information out.
I’ll try to avoid them in the future.
Tell your customer they are idiots. I expect to see them in Dilbert any day now. There are useful measures of Gauge Capability already in place. Most measurements are not yet capable, go use what is in place.
There are relatively new thoughts in the area of capability analysis, such as Cpm. This is not one of them.
I have heard about Cg/Cgk which are Instrument Capability Indexes.
The idea for Cg is the same than for Cp, the “conceptual” formula for Cp and Cg is:
Cg=(allowable variation)/(actual variation).
The differences are what we take for allowable and actual variation. For Cp, the actual variation is the process variation, and the allowed variation is the specification range.
For Cg, the actual variation is the INSTRUMENT ALONE variation (6 x Sinst). No between parts, within part, between operators or along time variation is included. As said in a previous post, about 50 measurements are made consecutively on a master or “best available” part, and allways on the same point of the part, and by the same person, and in a controlled enviroment (ussually the metrology room).
The allowable variation is taken as 1/5 of the process variation (6 x Sproc) or 1/5 of the product specification range, deppending on whether you want the instrument to controll the process or to check conformance of the parts, then:
Cg=(0.2 x 6 x Sproc)/(6 x Sinst)=Sproc/5Sinst, or
Cg=(0.2 x Tol))/(6 x Sinst)=Tol/30Sinst
If you think that the 30 Sigma in the denominator here is ridicously excessive, you are just wrong. Imagine an instrument that has a Cg of 1.33, that means that the Sinst is 0.025 x Tol. Now, no measurement system that uses this instrument will have a Sigma due to r&R lower that this, because you have to add all the other variations to the instrument alone. Then, at best, S(r&R)=0.025 x Tol, and the value of r&R=5.15 x S(r&R)=0.13 x Tol. Then, the r&R using this instrument will never be better that 13% of the tolerance (in fact, it will allways be worse). Not such a crazy number!
Cgk, as Cpk, takes into account the possition (which would be the bias): Cgk=(0.5 of the allowable variation – |bias|) / (0.5 of the actual variation)
The idea of Cg/Cgk is to have this information in advance to use it for the dessition about if the instrument would be “selectable” for a given measurement. If you decide to include the instrument in a measurement system that you will include in the control plan, only then you make the r&R with the full system, the real process parts and the full measurement variation. But you don’t want to develope a measuring system, design and build a measurement device, and write the measuring instructions only to find that the instrument itself could have never been capable of such a measurement.
Thanks for the detailed post.
The formula you stated for Tolerance related is same as the one my customer provided. The reason I had 20-Sigma is that for repeated measurements, they use 4*Sinst as denominator instead. (Valid only if nomal distribution exists).
The one for Process related differs a little. I have:
Cg = 0.15*Sproc / Sinst, which gives a denominator of 6.67.
Thanks again for your great post.
I’m searching for literature about Cg/Cgk calculation. Could you give me a hint where to find more information about Cgk or Cg?
Thanks in advance.
Not a big hint, sorry. What I posted comes from an internal manual about measurement system evaluation, which has no much more about Cg/Cgk than what I posted. However, in the “References” sections it list several sources and has a note saying that it is generally based on the AIAG’s MSA February 1995, Ford’s “Measurement System and Equipment Capability – Guidelines” December 1989, and Opel/Vauxhall/GM “Acceptance of Measurement Systems” B-01 amendment May 1996.
I think that the MSA does not mention it, so you have two sources left. Good luck.
Maybe Stan can lead you to the Dilbert’s issue that covers this subject too.
Dear Forum readers,
I have to employ Cg and Cgk in my current project.
However, I am dealing with a Single-sided tolerance; in my case, I only have a LSL.
Can I modify Cg formula like Cp for single-sided tolerance?
(i.e. denominator of 15 sigma, instead of 30 sigma).
Will this be an acceptable practice? Any inputs will be appreciated.
Thanks in advance.
You said Cg = (0.2 x Tol)/(6 x Sinst)
I want to know what this 6 is.
Because I’ve seen same formula but using 4 instead of 6.
Although I am not familiar with the concept of Cg & Cgk, the 6 in the formula for Cp comes from the properties of a normal distribution where approximately 99.7% of all data points in a stable process will fall within a range of +/-3 standard deviations around the mean (6 standard deviations total).
Hi Wally, I have the same problem with the Tolerances.
If you find a solution, I would appreciate if you can give me information.Regards,
Thanks Claudio. As you can see, I have been waiting since 2003 for someone to respond. Glad you have the same problem with tolerances as well as with intelligence. I have provided you the appropriate information consistent with the tardiness of your response.
the cg and cgk are mentioned in fiat norm 7G8101
Why on earth are you responding to a 7 year old post? WOW…
This is the 4th sign of the coming apocolypse…
I found this in MinitabCg
Capability indices are calculated only when the gage tolerance is specified.The capability of the gage is given by:Cg =
(K/100 * Tolerance)
whereK = percent of the tolerance for calculating Cg specified in the Options subdialog box, default = 20.SV = study variation
Capability indices are calculated only when the gage tolerance is specified.The capability of the gage, considering both the gage variation and the bias is given by:CgK =
(K/200 * Tolerance) – | X – Xm |
whereK = percent of the tolerance for calculating Cg specified in the Options subdialog box, default = 20.X = mean of n measurementsXm = reference measurementSV = study variation I hope that this serve! :)
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