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

Abstract

Moment and compositional approaches to solving the measurement problem of calibration are considered. The use of the moment approach to solving a standard example of thermometer calibration is considered. In this work, this example is solved within the framework of the compositional approach and more accurate and complete results are obtained compared to using the moment approach. This fact is consistent with the assessment of the accuracy of solutions to measurement problems carried out back in 2001 using a more rigorous compositional approach than the moment one: in the problem of calibrating measuring instruments, the moment approach does not fully take into account the inadequacy of functional models, overestimates the accuracy estimates and does not allow obtaining nonlinear models of optimal complexity. To solve the measurement problem within the framework of the compositional approach, this work uses the “MMI-Calibration 3.0” program, which allows taking into account the errors of inadequacy of mathematical models of calibration functions and obtaining tolerance intervals for a given confidence probability. Among polynomials up to the ninth degree inclusive, a three-parameter model of optimal complexity was obtained, the average module of the inadequacy error is 0.002745 °C and the tolerance interval [–0.00828; 0.00761] with a confidence probability of 0.95. Within the framework of the compositional approach, the average module of the error of inadequacy and the kappa criterion used to find a model of optimal complexity are compared. It is shown that the compositional approach fully and strictly describes the solution to the calibration problem without simplifications, allows one to avoid inflated estimates of accuracy, and therefore can serve as an exemplary approach provided that the “MMI-Calibration 3.0” program is used. The simultaneous use of the criteria of the minimum average module of the error of inadequacy and the maximum of the kappa criterion is a necessary and sufficient condition for identifying a model of optimal complexity in the class of polynomials of degree n.