Error Estimation of Indirect Measurement Results for Certain Quantities

Abstract

The basic mathematical provisions that determine the necessary and sufficient conditions for the application of the method of linearization of nonlinear functions of random arguments in estimating the errors of indirect measurements are considered. The necessity of assessing the emerging systematic component of the error and the degree of approximate representation of functions is noted. Within the framework of necessary and sufficient conditions for expanding an arbitrary function into a Taylor series, a new analytical formula is obtained for approximating a nonlinear function in the form of a quotient of independent random arguments. When using this formula for estimating the errors of the results of the indicated indirect measurements, it is possible not to refine the results obtained by adding terms to the Taylor series and not to evaluate the degree of approximation of the nonlinear function from the values of the corresponding remainder terms. The proposed formula allows one to determine practical conditions under which, for estimating the errors of the corresponding results, one can use well-known and fairly simple formulas for estimating the absolute and relative errors without preliminary processing of the results of direct measurements.