A Bayesian Approach to the Analysis of Gauge R&R Data

ABSTRACT

Gauge repeatability and reproducibility (R&R) studies are used to assess precision of measurement systems. In particular, they are used to quantify the importance of various sources of variability in a measurement system. We take a Bayesian approach to data analysis and show how to estimate variance components associated with the sources of variability and relevant functions of these using the gauge R&R data together with prior information. We then provide worked examples of gauge R&R data analysis for types of studies common in industrial applications. With each example we provide WinBUGS code to illustrate how easy it is to implement a Bayesian analysis of gauge R&R data.

KEYWORDS:

• gauge studies
• random effects
• repeatability
• reproducibility
• variance components

ACKNOWLEDGMENTS

We thank C. C. Essix for her support and encouragement, Teresa Cremers for her assistance with one of the examples, and the editor and the reviewer for their helpful comments.

Additional information

Notes on contributors

Michael S. Hamada

Michael S. Hamada is a Scientist and holds a Ph.D. in Statistics from the University of Wisconsin–Madison. He is a Fellow of the American Statistical Association. His research interests include design and analysis of experiments, measurement system assessment, quality control, and reliability.

Stephen B. Vardeman

Stephen B. Vardeman is a University Professor in Statistics and Industrial Engineering. He holds a Ph.D. from Michigan State University in Statistics and is a Fellow of the American Statistical Association and (elected) Ordinary Member of the International Statistical Institute. His research interests include statistics and metrology, statistical methods for physical and engineering sciences, machine learning and data mining, and business analytics.

Alyson G. Wilson

Alyson G. Wilson is a Research Staff Member and holds a Ph.D. from Duke University. She is a Fellow of the American Statistical Association. Her research interests include reliability, Bayesian methods, and the application of statistics to problems in defense and national security.