Open AccessReduction of the bias of measurement uncertainty estimates with significant non-linearity of a model equation
Author(s) -
Ігор Захаров,
Pavel Neyezhmakov,
Олеся Боцюра
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1379/1/012013
Subject(s) - mathematics , nonlinear system , kurtosis , monte carlo method , taylor series , propagation of uncertainty , calibration , series (stratigraphy) , method of moments (probability theory) , measurement uncertainty , statistics , mathematical analysis , physics , estimator , paleontology , quantum mechanics , biology
The analysis of the nonlinear model equation is carried out. The nonlinear model equation in a Taylor series is expanded. It is shown that the bias in the estimation of the combined standard uncertainty by using the Law of Propagation of Uncertainty is due to the terms of the expansion of the second degree. To eliminate this bias, it is necessary to take into account the kurtosis of the input quantities distributions. A finite increments method for obtaining reliable estimates of the uncertainties contributions for nonlinear model equations is proposed. A practical example of calculation of comparison loss in microwave power meter calibration by various methods was considered. Estimate of the measurement uncertainty obtained with Law of Propagation of Uncertainty in this case has a bias. The result obtained with the finite increments method coincides with the results obtained using the Monte Carlo method.