Analysis of compositional and moment approaches to solving the calibration problem using a standard example

The article examines the moment and compositional approaches to solving the measurement problem of calibration. The use of the moment approach in solving a standard example problem of thermometer calibration is considered. In this work, this problem is solved under the compositional approach, yielding more accurate and better results as compared to the moment approach. This fact is consistent with the accuracy assessment of solutions to measurement problems performed back in 2001 using the compositional approach (more rigorous than the moment approach): in the problem of measuring instrument calibration, the moment approach fails to fully take into account the inadequacy of functional models, overestimates the accuracy, and fails to obtain nonlinear models of optimal complexity. In order to solve the measurement problem under the compositional approach, the present work used the MMI-calibration 3.0 program, which provides a means to factor in the inadequacy errors of mathematical models of calibration functions and to obtain tolerance intervals for a given confidence level. Among polynomials up to and including degree nine, a three-parameter model of optimal complexity was obtained, with an average modulus of inadequacy error of 0.002745℃ and a tolerance interval of [−0.00828; 0.00761] at a confidence level of 0.95. Under the compositional approach, the average modulus of inadequacy error and kappa test used to find the optimal complexity model were compared. The compositional approach is shown to be rigorous in describing the solution of the calibration problem without simplifications and to avoid overestimation of accuracy; therefore, it can serve as an exemplary approach provided the MMI-calibration 3.0 program is applied. The combined use of the criteria of minimum average modulus of inadequacy error and maximum kappa test constitutes a necessary and sufficient condition for identifying a model of optimal complexity in the class of polynomials of degree n.