# Influence of the Coverage Factor - Worksheets based on the Average and Range Method

D

#### Depo74

Good morning everyone

I dicovered this forum two weeks ago and it helped me a lot to understand this manual.

But, since I try to make my own worksheets based on the Average and Range Method, I need need some help. Indeed, I don't see clearly how the coverage coefficient k (5.15 or 6 for instance) affects the results of the %GRR.

According to the formulas p191, %GRR based on Process variation is given by (k * sigma_measure)/(6 * sigma_observed)*100%
So, i would like to know if the number 6 is always constant or if it depends on the value of this k
I assume the formulas given in %GRR report p.114 are already simplified with a k=6 and this is why %GRR is equal to sigma_meausre/sigma_observed but i would like someone to confirme that

And at last, are these observations true for the Anova Method ?

Thanks for your help ( and sorry for my English)

Last edited by a moderator:

#### Hershal

##### Metrologist-Auditor
Staff member
Super Moderator
Re: Influence of the coverage factor

I suspect someone with more knowledge in this application will answer soon.

#### Miner

##### Forum Moderator
Staff member
Re: Influence of the coverage factor

i would like to know if the number 6 is always constant or if it depends on the value of this k
I assume the formulas given in %GRR report p.114 are already simplified with a k=6 and this is why %GRR is equal to sigma_meausre/sigma_observed but i would like someone to confirm that

And at last, are these observations true for the Anova Method ?
The value of k depends on the number (5.15 or 6). 5.15 represents 99% of the measurement variation and is older usage. The current usage is 6, and you are correct, the formulae have been update to take 6 into account.

The ANOVA method does not use the k factors. It calculates sigma directly rather than estimating it from the Ranges.

D

#### Depo74

Re: Influence of the coverage factor

And thanks fot the information on the Anova. Actually, I made a confusion between the Variance estimated and the spread of the standard deviation (where k is used to evaluate this spread it seems to me)

#### Miner

##### Forum Moderator
Staff member
Re: Influence of the Coverage Factor - Worksheets based on the Average and Range Meth

For the AIAG MSA manual 2nd edition: The k in the numerator is tied to the 6 (or 5.15) used in the denominator

In the 3rd edition, they simplified the formula by removing the 6 in the denominator. The k factors were adjusted to result in the same answer.

D

#### Depo74

Re: Influence of the Coverage Factor - Worksheets based on the Average and Range Meth

Ok, so does it mean the %GRR for process variation will stay the same regardless the K choosen.
It will only affect the %GRR based on the tolerance ?

#### Miner

##### Forum Moderator
Staff member
Re: Influence of the Coverage Factor - Worksheets based on the Average and Range Meth

Correct. The formula for %GGR (% Study Variation) is a straight ratio of standard deviations. Any multipliers such as 6 would appear in both numerator and denominator and would cancel out.

D

#### Depo74

Re: Influence of the Coverage Factor - Worksheets based on the Average and Range Meth

Thanks to you, i managed to put the right formulae in my worksheet (I suppose)

I let my work here so, if you mind, you can check it, and since this worksheet has been done be able to do the study with any number of appraisers, parts and tests (even if there is a max), i think it could be useful for some people here

I just hope you understand French

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