Confidence Intervals for a Discrimination Ratio in a Gauge R&R Study with Three Random Factors

Abstract

In this paper, we extend results of the typical two-factor gauge repeatability and reproducibility (R&R) study to a situation with three random factors. The objective of this study is to form a confidence interval on a discrimination ratio used to determine the adequacy of the measurement system. Two confidence intervals are proposed and evaluated for effectiveness with regard to confidence coefficient and interval length using computer simulation. The basic conclusions are that: i) a closed-form interval that is easily computable performs well in a variety of conditions, ii) a more intensive computational method performs slightly better than the closed-form interval, and iii) increased replications do not have much affect on interval length.

Keywords:

• Measurement study
• Repeatability
• Reproducibility
• Variance components

Acknowledgment

The authors wish to thank the referee for suggestions that led to significant improvements in the paper.