Case study: Using all the available data to assess a measurement system via a Bayesian analysis of unbalanced data

ABSTRACT

This article considers a real application where all the data available to assess a new measurement system do not follow a planned protocol. Instead of analyzing only the sample averages of the planned protocol data, we show how a hierarchical model allows all the available data to be used to assess a measurement system. We show the advantages of using all the available data from the application.

Keywords:

• Bayesian inference
• credible interval
• normal distribution
• posterior distribution
• prior distribution
• relative standard deviation

Acknowledgment

We thank two anonymous referees whose insightful comments helped improve the exposition of this article.

Additional information

Notes on contributors

M. S. Hamada

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

A. C. Olson

Angela C. Olson earned a PhD in Chemistry from the University of California, Irvine. She is a Scientist whose work focuses on chemical and radiochemical analysis of materials where actinide elements are a significant component of the sample.

L. Tandon

Lav Tandon is a Senior Scientist and obtained a PhD in radioanalytical chemistry from the University of Kentucky, Lexington followed by a postdoc at the National Institute of Standards and Technology (NIST). His current research includes improvements and validation of actinide analytical chemistry techniques, standards production and characterization, study of pyrochemical processes and analytical measurement data quality assessments.