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, errors cannot be avoided. Metrology experts are of course aware of it, and able to identify the different sources that contribute to making errors. In this paper, the probability density function of measurement errors is assumed to be given as an input. Very little research has been made in metrology to develop methods that take into account such data. This work deals with a batch of measures and its statistical properties. A first method is proposed to correct the effects of the measurement errors on the distribution that characterizes the entire batch. Then a second method is proposed to estimate the true value that is hidden behind each single measure, 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.