The Gage R&R is a tool used in the Measure phase of a Six Sigma project. The R's represent Repeatability and Reproducibility.
Before the data analysis phase begins, the Six Sigma GB/BB should understand the variation caused by the measurement system (devices) and be able to quantify this variation.
The remaining variation is due to the process and the is the variation that the team originally intended to resolve.
To exaggerate in an effort to make a point, it is possible that a Six Sigma project was originally scoped due to high variation and out of control performance. However, early on in the Measure phase the Six Sigma GB/BB finds out that most of the variation is from the measurement system and not the process!
There are cases when the measurement system creates too much variation (based on subjective decision of the company) and fixing the measurement system alone becomes a Six Sigma project or a Kaizen Event.
If the measurement system is negatively impacting the Voice of the Customer, then it is every bit as important to fix and control as the process variation itself.
There is a third analysis that is involved and that is the appraiser assessments compared to a master known value when there are known master values. In summary there are three evaluations:
The first two can be very tight where each appraiser mirrors each others' results (reproducibility) and each appraiser repeats his/her own assessment (repeatability) but both situations may not match the master known or correct value.
Therefore, it's necessary to have them accurate and precise where all three of the above are met to a certain criteria. The first two bullets have to do with "precision" but the last bullet has to do with "accuracy".
Repeatability is the capability of the gage (a.k.a. the measurement system which could be a gage, an appraiser, inspector, or measurer) generating the same exact result every time measuring the same thing more than one time.
How well does the appraiser repeat their own measurement?
Perhaps that appraiser get the exact same result but that results if off the true actual value the same amount each time. This indicates that the gage itself has a calibration problem that first needs to be resolved.
Reproducibility compares the measurement of one appraiser to other appraiser(s) measuring the same object using the same gage.
The term "among" is used when explaining reproducibility since it relays information about the measurements among all the appraisers.
What is the capability of each appraiser getting the same exact measurement on the same part using the same gage?
How well do they reproduce each others' resulting measurements on each part?
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