Estimation of non-statistical uncertainty in precision measurement using grey system theory

A new uncertainty assessment method is proposed to characterize non-statistical uncertainties in precision measurement. The proposed method is based on grey system theory to address the problem involved in uncertainty assessment where the sampling size is small and the distribution of the data is unknown. The advantage of the proposed approach is that the requirements of the statistics based methods are removed. In the proposed method, an accumulated true size vector and an accumulated measurement data vector are established to reduce the effects of the errors in the measurement and in the numerical calculation. The uncertainty assessment is based on the l∞ norm of the difference between the accumulation of the sorted measurement data vector and that of the true size vector. A number of computational and experimental tests were carried out. The results demonstrated the effectiveness and consistency of the proposed method in non-statistical uncertainty assessment, compared with the existing methods.