Question: Cg/Cgk formula

[Ranma]

Hi everyone, I’m performing Type one Gage on some control we have in the machine.
The first part of the machine has two control that do the same type of control so I will be performing the Gage R&R with the two controls as appraiser.
All the product that comes from the first part is controlled in the second part of the machine in which there is only one control. So, I’m thinking to do the type one Gage on this control (as suggested here).

I’m studying this type of gage (very thank to the cove!) and there is one thing I cannot understand well:

Why, as guidelines, we should calculate Cg/Cgk using 20% of the tolerance? Because to me it seems very narrow, but I don’t know if I’m missing some important concepts that don’t let me understand well.

Here an example of our process:

The control I’m studying is on the total length of the product. We have 10mm +/- 0,5 as specification limits. In the machine we set narrower limit +/- 0,45. Our range is basically 0,90 à 90% of the real tolerance.
Using 90% of the tolerance seems extreme but, to me, also the 20%.

So, I would like some more detailed explanation to “customize”, the better I can, this parameter to our case, please.
Thank you for the support in advance and sorry for my English, hope it is clear.

Edit: cannot really understand what add the two %Var. Since they are calculated as K/Cg or K/Cgk i don't know what they can possible add (K from the Cg formula ((K/100)*toll)/6Sd)

 

[Ranma]

Up.
Anyone?
Thanks in advance

 

[Bromus]

I don't fully understand your measurement process, but I can explain where the 20% came from in the formula for Cg. The idea is to be able to compare the obtained Cg result with the expected process capability (Cp or Pp depending on the client). For example, if you expect the process to have a capability of 1.33, then when you get a Cg of 1.33, then you can say that the observed repeatability of the measurement is no more than 20% of the total process variation (which, again, is used for Cp/Pp calculation).

This means that this statistical assumption (20% of tolerance) cannot be compared with the narrowed specification limits (also 20%) that you apply to product qualification. These are 2 different things.

 

[MOester]

There's a trend to take the Cp/Cpk and Pp/Ppk for process production and use it for everything. Capability metrics for a process already leave a bit to be desired as useful metrics - my question is: why reinvent the wheel when you are looking for a Gage R&R study?

 

[Semoi]

Your aim is to machine parts within the tolerance (10 +/- 0.5)mm.Thus, you have to be able to measure with a precision (much) smaller than +/-0.5mm. The question is how much smaller should you be? Simple answer: Your measurement uncertainty should not exceed 20% of the tolerance -- often 10% is recommended.
However, usually, we also want to use a machining process, which consistently generates parts within specification. In order to develop this machining process we have to measure the parts and study the machining input parameters. Thus, we have to resolve the process variations. Hence, the more accurate answer: To optimise the machining process your measurement device should be approx. 5-10 times more precise than the machining capability you are aiming for. If you achieve this precision in the gage, you are able to concentrate your attention to the machining process and assume that the measurement error is negligible.
Of course there is no mathematical argument behind this "magic numbers" 10%-20%. You could as well take 25% or maybe even 30%. However, if the measurement uncertainty becomes "too large" the machining optimisation process will become inefficient, because you will need larger sample sizes to analyse the machining process.