Statistical Approaches for the Reduction of Measurement Errors in Metrology

Abstract

Metrology is extensively used in the manufacturing industry to determine whether the dimensions of parts are within their tolerance interval. However, measurement errors cannot be avoided. Metrology experts are of course aware of it and they are able to identify the different sources that contribute to making errors. In this paper, the probability density function of the measurement error is considered as a given input. As it is rare to have access to this distribution, there are very few methods in the literature that aim to use this knowledge directly to improve the measurements obtained in metrology. A first method is proposed to correct the effects of the measurement errors on the distribution that characterizes a set of measurements. Then a second method is proposed to estimate the true value that is hidden behind each single measurement, by removing the measurement error statistically. The second method is based on the output knowledge of the first, which is integrated with Bayesian statistics. The relevance of these two methods is shown through two examples applied on simulated data.