Six Sigma SPC - Statistical Process Control

Six Sigma SPC's Quality Control Dictionary and Glossary
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R & R Repeatability and Reproducibility

R&R, GR&R, or gauge R & R is a concept to insure stabile measurements where a single person gets the exact same results each and every time they measure and/or collect data measurements. This can be necessary to ensure data consistency and stability. There are different ways to perform this. The following is an abbreviated explanation using the method recommended by the AIAG, (Automotive Industry Action Group). It is used in most quality plans including six sigma and ISO9000.

This will give you an approximation of the variation and percent of process variation for the total measurement system and its component's repeatability, reproducibility and part to part variations. The formulas to do this analysis and the proper sequence to follow is below.


Repeatability Formula

EV = Equipment Variation
r = 4.56 for 2 trials, 3.05 for 3 trials


Reproducibility Formula

AV = Appraiser Variation
k = 3.65 for 2 appraisers, 2.7 for 3 appraisers

Repeatability and Reproducibility

Repeatability and Reproducibility Formula

Part Variation

Part Variation Formula

PV = Part Variation
Rp = Range of part averages
j= Depends on number of parts

Part 2 3 4 5 6 7 8 9 10
j 3.65 2.7 2.3 2.08 1.93 1.82 1.74 1.67 1.62

Total Variation

Total Variation Formula

TV = Total Variation

Percentage of total variation is calculated using the formulas below

%EV = 100(EV/TV)
%AV = 100(AV/TV)
%R&R = 100(R&R/TV)
%PV = 100(PV/TV)

Guidelines for acceptable results are...

< 10% Satisfactory
10%-30% May be satisfactory. Depends on the magnitude of the use, cost of new gauges, cost of repairs, etc.
> 30% Unsatisfactory. Take corrective action.

For additional information see Quantifying uncertainties from a gauge study

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Last Updated: Monday, 22-May-06 01:23:52 PDT