A Bayesian approach to the evaluation of comparisons of individually value-assigned reference materials |
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Authors: | Toman Blaza Duewer David L Aragon Hugo Gasca Guenther Franklin R Rhoderick George C |
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Institution: | (1) Statistical Engineering Division, National Institute of Science and Technology, Gaithersburg, MD 20899-8980, USA;(2) Analytical Chemistry Division, National Institute of Science and Technology, Gaithersburg, MD 20899-8390, USA;(3) Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305, USA |
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Abstract: | Several recent international comparison studies used a relatively novel experimental design to evaluate the measurement capabilities
of participating organizations. These studies compared the values assigned by each participant to one or more qualitatively
similar materials with measurements made on all of the materials by one laboratory under repeatability conditions. A statistical
model was then established relating the values to the repeatability measurements; the extent of agreement between the assigned
value(s) and the consensus model reflected the participants’ measurement capabilities. Since each participant used their own
supplies, equipment, and methods to produce and value-assign their material(s), the agreement between the assigned value(s)
and the model was a fairer reflection of their intrinsic capabilities than provided by studies that directly compared time-
and material-constrained measurements on unknown samples prepared elsewhere. A new statistical procedure is presented for
the analysis of such data. The procedure incorporates several novel concepts, most importantly a leave-one-out strategy for
the estimation of the consensus value of the measurand, model fitting via Bayesian posterior probabilities, and posterior
coverage probability calculation for the assigned 95% uncertainty intervals. The benefits of the new procedure are illustrated
using data from the CCQM-K54 comparison of eight cylinders of n-hexane in methane. |
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