A case study: Comparing testers for means and variances in a balanced incomplete block design

Abstract

In this article, we present a gauge R & R study that is different from the standard setup in several ways. A balanced incomplete block design (BIBD) was used to collect the data because the measurement is destructive. Besides addressing reproducibility, differences in repeatability (i.e., tester variances) were also of interest. Here we use Bayesian methods to analyze the study data to address whether the three tester means and variances are similar. We also consider what happens if the BIBD structure of the data and possibly different tester variances are ignored in analyzing the study data.

Keywords:

• BIBD
• Bayesian
• gauge R & R study
• measurement system assessment
• repeatability
• reproducibility

Acknowledgment

We thank C. C. Essix for her encouragement and support. We also thank an anonymous reviewer for insightful comments that helped improve an earlier version of this article.

Additional information

Notes on contributors

M. S. Hamada

M. S. Hamada is a Scientist and holds a PhD in Statistics from the University of Wisconsin–Madison. He is a Fellow of the American Society for Quality, American Statistical Association, and Los Alamos National Laboratory. His research interests include design and analysis of experiments, measurement system assessment, quality control, and reliability.

K. A. Yeamans

K. A. Yeamans is a Research & Development Engineer with an MS in Structural Engineering with specialization in Health Monitoring and Nondestructive Evaluation. She currently supports projects related to mechanics of materials, production and quality controls, process improvements, and model-based systems engineering; she also volunteers her time with various organizations for STEM education in northern New Mexico.

C. P. Harris

C. P. Harris is a Lead Mechanical Engineer for Honeywell FM&T with an MS in Mechanical Engineering. He currently supports projects related to the production and acceptance of Gas Transfer Systems and cellular silicone/room temperature vulcanized rubber products.