The grey relational approach for evaluating measurement uncertainty with poor information

The Guide to the Expression of Uncertainty in Measurement (GUM) is the master document for measurement uncertainty evaluation. However, the GUM may encounter problems and does not work well when the measurement data have poor information. In most cases, poor information means a small data sample and an unknown probability distribution. In these cases, the evaluation of measurement uncertainty has become a bottleneck in practical measurement. To solve this problem, a novel method called the grey relational approach (GRA), different from the statistical theory, is proposed in this paper. The GRA does not require a large sample size or probability distribution information of the measurement data. Mathematically, the GRA can be divided into three parts. Firstly, according to grey relational analysis, the grey relational coefficients between the ideal and the practical measurement output series are obtained. Secondly, the weighted coefficients and the measurement expectation function will be acquired based on the grey relational coefficients. Finally, the measurement uncertainty is evaluated based on grey modeling. In order to validate the performance of this method, simulation experiments were performed and the evaluation results show that the GRA can keep the average error around 5%. Besides, the GRA was also compared with the grey method, the Bessel method, and the Monte Carlo method by a real stress measurement. Both the simulation experiments and real measurement show that the GRA is appropriate and effective to evaluate the measurement uncertainty with poor information.