An Introduction to Statistical Issues and Methods in Metrology for Physical Science and Engineering

Statistical science and metrology are intertwined. Measurement quality affects what can be learned from data collected and processed using statistical methods, and appropriate data collection and analysis quantifies the quality of measurements. Metrologists have long understood this and have often developed their own statistical methodologies and emphases. Some statisticians, notably those working in standards organizations such as the National Institute of Standards and Technology (NIST), at national laboratories, and in quality assurance and statistical organizations in manufacturing concerns have contributed to good measurement practice through the development of statistical methodologies appropriate to the use of ever-more-complicated measurement devices and to the quantification of measurement quality. In this regard, contributions such as the NIST e-Handbook (National Institute of Standards and Technology, 2003), the AIAG MSA Manual (Automotive Industry Action Group, 2010), and the text of Gertsbakh (2002) are meant to provide guidance in statistical practice to measurement practitioners, and the review of Croarkin (2001) is a nice survey of metrology work done by statisticians at NIST. Our purpose here is to provide an overview of the interplay between statistics and measurement for readers with roughly a first year graduate level background in statistics. We believe that most parts of this will also be accessible and useful to many scientists and engineers with somewhat less technical background in statistics, providing introduction to the best existing technology for the assessment and expression of measurement uncertainty. Our experience is that while important, this material is not commonly known to even very experienced statisticians. Although we don’t claim originality (and do not provide a comprehensive summary of all that has been done on the interface between statistics and metrology), our main goal here is to bring many important issues to the attention of a broader statistical community than that traditionally working with metrologists. We will refer to both frequentist and Bayesian methodologies (the latter implemented in WinBUGS (see Lunn et al. (2000))). Our rationale is that while some simple situations in statistical metrology can be handled by well-established and completely standard frequentist methods, many others call for analyses based on nonstandard