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

In the following paper we present an easily applicable new method for analytical representation of the maximum relative inaccuracy (error) of an indirectly measurable variable f = f(x1, x2, ..., xn) as a function of the maximum relative inaccuracies (errors) of the directly measurable variables x1, x2, ..., xn. 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 relative inaccuracy of the variable f we take for being fixed variables statistical mean values ∣∣∣∣ x1 f · ∂f ∂x1 ∣∣∣∣, ∣∣∣∣ x2 f · ∂f ∂x2 ∣∣∣∣, ..., ∣∣∣∣ xn f · ∂f ∂xn ∣∣∣∣ of the modules of the coefficients of influence of relative inaccuracies ∆x1 x1 , ∆x2 x2 , ..., ∆xn xn in f . The numerical value of the maximum relative inaccuracy of the variable f is found using the statistical mean values of the absolute values of the relative inaccuracies ∣∣∣∣ ∆x1 x1 ∣∣∣∣, ∣∣∣∣ ∆x2 x2 ∣∣∣∣, ..., ∣∣∣∣ ∆xn xn ∣∣∣∣. Moreover, we look into functions which are continuous but are not differentiable in respect to certain arguments in some points. 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 relative c ©2012 by K. Kolikov, G. Krastev†, Y. Epitropov, A. Corlat ∗This work was supported by the Fund ”Scientific Studies” of the Bulgarian Ministry of Education, Youth and Science as part of the contract DTK 02/35