Analysis of CMM measurements of hole plates in interlaboratory comparisons (English)

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Interlaboratory comparisons are a key activity in monitoring and improving the state of art in all measurement disciplines, and they have assumed increased importance in the metrological community now that the Mutual Recognition Arrangement provides a framework for users of metrological services to assess the competence of laboratories. While the evaluation of an ensemble of measured values derived from an artefact that provides a single reference quantity, such as a kilogram mass or a gauge block length standard, still poses problems, the analysis of measured values for an artefact, such as a hole or ball plate, that provides multiple references represents a new set of challenges. Even a 5 x 5 hole plate presents 47 independent reference quantities (three degrees of freedom are removed by fixing a frame of reference). The measurement of such a hole plate will normally reflect correlated effects and a full account of these correlations requires up to 1128 ((47 x 48)/2) variances and covariances, the elements of a 47 x 47 uncertainty matrix. In fact, if all the participants were able to provide an uncertainty matrix, we show that an evaluation approach can be developed, taking into account frames of reference, within the general framework provided by multivariate statistics. However, uncertainties in coordinate metrology are usually expressed in terms of an A + L/B statement where L/B represents the dependence on the length L of the artefact. Such uncertainty statements provide only a partial description of the uncertainty information and limit the analysis that can be performed. While an aim of the paper is to help those involved in interlaboratory comparisons, the same issues arise whenever an artefact is measured by two CMMs, e.g., by a component supplier and a manufacturer, and an assessment is required concerning whether or not the two sets of measured values are consistent with each other.

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