Method of estimation the result and its accuracy indicators for indirect measurements in the form of a quotient

The theoretical foundations of mathematical processing of indirect measurement results in the form of a quotient are considered. In practice, the results and accuracy indicators are represented by approximate formulas obtained by the linearization method. The correct presentation of the results with this method provides for the determination of the systematic error of the result by an additional assessment of the degree of approximation of the formulas. It is shown that the systematic error of an indirect measurement result can be determined with known arithmetic means and standard deviations of the measurement results necessary to obtain the desired value. It is almost impossible to clarify the value of the variance without considering the distribution laws of random errors in measurement results. It is established that the analytical formula for the quotient of random variables, derived within the framework of the necessary and suffi cient conditions for the Taylor series expansion of the quotient of random variables, can be represented as a linear function of random errors of the measurement results required to obtain the desired value. For the specifi ed linear function, based on theorems on the numerical characteristics of functions of random arguments, exact formulas are obtained that describe the mathematical expectation and variance and coincide with the formulas used in practice as approximate ones. Formulas representing the result of indirect measurements as a quotient are obtained by a method different from the linearization method, which allows these formulas to be considered exact, i.e. there is no need to evaluate the accuracy of their approximation. The results of the conducted studies are intended for use by a wide range of people involved in measurements in various fi elds of science and technology, and may be useful to instrument makers, metrologists, students of relevant specialties at universities and postgraduates.

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