Gage Repeatability and Reproducibility
Gage repeatability and reproducibility (GR&R) is defined as the process used to evaluate a gauging instrument’s accuracy by ensuring its measurements are repeatable and reproducible. The process includes taking a series of measurements to certify that the output is the same value as the input, and that the same measurements are obtained under the same operating conditions over a set duration.
Factors that affect measurement system variation can be studied using the GR&R technique. When using the GR&R system, measurement system variation can be characterized by location (stability, bias, linearity) and width or spread (repeatability and reproducibility).
The GR&R technique can be applied in most manufacturing-related measurement systems. It may be used as:
- A criterion for judging new measuring equipment
- A comparison among measuring devices
- A means for improving performance of measuring instruments
- A comparison for measuring equipment before and after repair
- A required component for calculating process variation and the acceptability level for a production process
- A measure of the need for training in how to use measuring instruments
Estimating Total Measurement Variation
The "repeatability" aspect of the GR&R technique is defined as the variation in measurement obtained:
- With one measuring instrument
- When used several times by the same operator
- When measuring an identical characteristic on the same part
The standard deviation for repeatability (σe) is estimated using the formula displayed below, where R is the average range of repeated measurements:
The "reproducibility" aspect of the GR&R technique is the variation in the average of measurements made by different operators:
- Who are using the same measuring instrument
- When measuring the identical characteristic on the same part
Operator variation, or reproducibility, is estimated by determining the overall average for each appraiser and then finding the range (R0) by subtracting the smallest operator average from the largest.
The standard deviation for reproducibility (σ0) is estimated by:
The measurement system variation (R&R) or gage R&R is represented by σR&R.
Part-to-Part Variations in Measurement
Part-to-part variation also makes a contribution to the total variation in a measurement and can be determined from the measurement system data or an independent process capability study.
- If the measurement system study is used, the part standard deviation σp (PV) is estimated by Rp /d2*. Rp can be estimated as the average range of part measurements.
Total Measurement Variation
Total variation (TV or σTV) for the study is calculated by summing the square of both the repeatability and reproducibility (R&R) variation and the part-to-part variation PV, and taking the square root, as follows:
The contribution of the equipment variation contribution EV is calculated as 100(EV/TV). The contribution of other factors to the total variation TV can be similarly calculated, as follows:
Gage Repeatability and Reproducibility resources
A Study In Measurement (Quality Progress) This article details how gage repeatability and reproducibility studies can determine whether a measurement system is acceptable.
Gauge R&R Studies for Destructive Measurements (PDF) Alternatives to standard GR&R studies are necessary when objects cannot be measured more than once.
Attribute Gage R&R (PDF) This case study details the measurement phase of a Six Sigma project and shows how attribute GR&R saved one company $400,000 a year.
Adapted from The Certified Quality Technician Handbook, ASQ Quality Press.