Statistics and Metrology

Abstract

Metrology is the science of measurement, whose scope includes measurements made in all fields of science and technology, of properties that may be quantitative or qualitative. A measurement result comprises an estimate of the value of the property being measured and an evaluation of the associated measurement uncertainty. The concepts and tools of probability and statistics are used in metrology because measurement uncertainty typically is interpreted probabilistically, and statistical methods are used to estimate the true value of the property under measurement, and to evaluate the associated uncertainty. Measurement models represent the relationship between inputs (measurement data) and an output (value of the property being measured) and may be either measurement equations or observation equations (statistical models). Estimating the value of the property under measurement, and evaluating the associated uncertainty, depends on the measurement model, whose definition also may be surrounded by uncertainty. Many different probabilistic and statistical models and methods are used in metrology. This article includes applications of the Delta Method, the parametric statistical bootstrap, and random effects models in the context of measurement science.