The purpose of this paper is to introduce a method for evaluating the production tolerances influence on the practically realized optimal solution of electrotechnical devices. The influence is estimated by the optimal solution range defined with a given probability.
Because of the tolerances nature, the paper is in probabilistic categories. The accent is put on the cases when the mathematical description of the cost function is analytical, for example polynomial found on the basis of the design of experiments and response surface methodology. The optimal solution range is defined with a given probability. The governing equation is Chebychev's inequality. In some cases, Chebychev's inequality would be rather weak but the advantage is that it is valid for all kinds of probabilistic distributions.
A numerical example – an electrical machine – is considered with respect to variances in the magnetic characteristics of the stator and rotor core electrotechnical steel and tolerances in the geometrical dimensions of the machine. An analytical expression for the variance of the optimal solution is obtained in the case of a second order polynomial cost function. It is found that the energetic characteristic of the realized optimal design is expected to be negligibly different from its value in the proposed optimal project.
Although the example concerns the field of electrical machines, the methodology can be of interest for other domains and for different electrotechnical devices.
