Analytically determining of the absolute inaccuracy (error) of indirectly measurable variable and dimensionless scale characterising the quality of the experiment

摘要

In the following paper we present an easily applicable new method for the analytical representation of the maximum absolute inaccuracy (error) of an indirectly measurable variable f(velence)f(x_(1), x_(2), ..., x_(n)) as a function of the maximum absolute inaccuracies (errors) of the directly measurable variables x_(1), x_(2), ..., x_(n). Our new approach is more adequate for the objective reality. The gist of it is that in order to find the analytical form of the maximum absolute inaccuracy of the variable f we take for being fixed variables the statistical mean values |(partial deriv)f/(partial deriv)x_(1)|, |(partial deriv)f/(partial deriv)x_(2)|, ..., |(partial deriv)f/(partial deriv)x_(n)| of the modules of the moment velocities of alteration of f in respect of the variables x_(1), x_(2), ..., x_(n) and the numerical value of the maximum absolute inaccuracy of the variable f is found using the statistical mean values of the absolute values of the absolute inaccuracies |(DELTA)x_(1)|, |(DELTA)x_(2)|, ..., |(DELTA)x_(n)|. Having this in mind we develop the theory of errors, which we will call with what we feel is a more precise term - theory of inaccuracies. We introduce some new terms - space of the absolute inaccuracy and stochastic plane of the absolute inaccuracy of f. We also define a sample plane of the ideal absolutely accurate experiment and using it we define a universal numerical characteristic - a dimensionless scale for evaluation of the quality (accuracy) of the experiment.