Estimation of the best measurement result and its standard uncertainty by input observations processing using the method of reference samples based on order statistics

In the paper the new method of the measurement observations processing, based on their comparison (after sorting) with several reference samples, which are corresponded to the models of the general population density distributions (so called reference distributions), is investigated and analyzed. The elements of reference samples are equal to the mathematical expectations of order statistics corresponding to the reference distribution. The mathematical models of the determination of the best result and its standard uncertainty are presented. The effectiveness of proposed method is investigated by the Monte Carlo method for 5 models of general population (Laplace, normal, triangular, uniform and arcsine) with the number of observations equal 9, 19, 29, 39 and 49. The proposed method can be used if the observations number is small. If the observations distribution significantly differs from normal distribution then the proposed method guarantees considerable decreases of the uncertainty result in comparison with the uncertainty of average value.