# Gage R&R Standard Deviations

#### stm08007

##### Starting to get Involved
Hello,
Hopefully my screenshot is visible! Studying for the CQE and looking through the primer, and I am getting hung up on a few parts of this page.

1) the total observed variation is found to be 0.881 based on the 0.701 sigma_proc and 0.534 sigma_meas. Fine that makes sense. But then it says "the measurement error constitutes a substantial portion of the total observed variation- about 37%". Where does that come from? Sigma_observed=0.881, and 0.534 is not 37% of that figure...

2) for the final sentence where it says "obviously the 49% consumed by the measuring system is too large" - what would be acceptable, 30%?

MODERATOR NOTE: Clip of copyrighted test document removed.

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#### stm08007

##### Starting to get Involved
One more question on this section:

The same data is plotted on a control chart for each technician (after using ANOVA to find that process variation accounted for about 59% of the total variation). I dont understand the point that over half of the data points would be expected to fall outside of the control limits. Anyone have any idea on that too?

MODERATOR NOTE: Clip of copyrighted test document removed.

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#### Ninja

##### Looking for Reality
Trusted Information Resource
Howdy,

Since you posted screenshots which were then (correctly) deleted, your questions are not complete and thus hard to understand.

#### stm08007

##### Starting to get Involved
Howdy,

Since you posted screenshots which were then (correctly) deleted, your questions are not complete and thus hard to understand.

Ugh I was afraid that'd happen.. Difficult to do all the formula subscripting, etc myself.
1) sigma_process was found to be 0.701 and sigma_measurement was found to be 0.534. Plugging these into formula sigma_observed = sqrt[ (sigma_process)^2 + (sigma_measurement)^2] gives us a sigma_observed of 0.881. The book then says "the measurement error constitutes a substantial portion of the total observed variation (37%)". If sigma_measurement is 0.534, and sigma_observed is 0.881, that's not 37%. Is "measurement error" not the same as "sigma_measurement"? (if so, "measurement error" was not clearly defined in the text before this.

2) it then uses the formula [(5.15)(sigma_meas)/tolerance] to find the percentage of tolerance consumed by the measuring system. The resulting value is 49% and it says this is obviously too large--- what is acceptable, 30%?

3) This one will be more difficult to explain without looking at the actual page, but it shows a control chart of each appraiser (with 2 measurements each per part of 5 parts)-- so it's an X-bar chart with 5 values per appraiser. all but 1 value is within the control limits.
The text goes on to explain that the area within the control limits represents the measurement sensitivity. Since the group of parts being measured represents part variation, approximately 50% or more of the averages should fall OUTSIDE the control limits.. I don't understand why that would be so.
It says since the chart doesnt show this pattern either the measurement system lacks effective resolution or the samples do not represent the expected process variation.

#### Miner

##### Forum Moderator
Staff member
1) Standard deviations are not additive, but variances are additive, so they obtain 37% using the variances.
2) It depends. < 10% is definitely acceptable, but 10% - 30% may be acceptable depending on the application. > 30 % is not acceptable.
3) On an gage R&R the control limits represent the zone in which a gage cannot distinguish between parts. Therefore, it can see and distinguish between parts that are outside of these limits. The limits represent the gages effective resolution or ability to discriminate between parts.

#### stm08007

##### Starting to get Involved
1) Standard deviations are not additive, but variances are additive, so they obtain 37% using the variances.
2) It depends. < 10% is definitely acceptable, but 10% - 30% may be acceptable depending on the application. > 30 % is not acceptable.
3) On an gage R&R the control limits represent the zone in which a gage cannot distinguish between parts. Therefore, it can see and distinguish between parts that are outside of these limits. The limits represent the gages effective resolution or ability to discriminate between parts.
3) so the standard assumption is that half the points being looked at fall outside the limits?

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