Gauge R&R Analysis for Two-Dimensional Data with Circular Tolerances

Abstract

We consider gauge repeatability and reproducibility (R&R) analyses for two-dimensional data when the engineering tolerance associated with measurements is a circle. We develop summaries for repeatability, reproducibility, and R&R by employing the diameters of circles that provide 99% capture rates. We derive an inequality between the results of a one-dimensional gauge R&R method and this two-dimensional method. We also show that the additivity-of-variance in the one-dimensional gauge R&R case becomes a sub-additivity-of-variance in the two-dimensional case under certain conditions. We use measurements of unbalance of rotating devices, where the tolerance must be a circle, to motivate the ideas and to illustrate the technique. Our results apply to corresponding coordinate-measuring-machine data when the engineering tolerance is a circle. The method can be extended to other problems, including square and spherical tolerances. We recommend that this method be used in conjunction with graphical, other univariate, and multivariate analyses.

• Measurement Systems Analysis
• Tolerances
• Two-Dimensional Data

Additional information

Notes on contributors

Joseph G. Voelkel

Dr. Voelkel is Associate Professor and Graduate Chair. He is a Fellow of ASQ. His e-mail address is [email protected].