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The purpose of this paper is to evaluate the rate of discrepancy between the group of expected project results and the group of corresponding results realized preliminarily at the design stage.

The authors formulate and solve the problem to determine the values of two assemblies of independent variables guaranteeing the project with the best (X→^*) and as well this one with the worst (X→^**) tolerance field of the expected Z_x realization. The problem is formulated as an optimization one in nonlinear mathematical programming and it is solved by applying the flexible tolerance method.

By the use of basic relations in statistical science an expression of standard deviation σ_Zx of Z_x is found and proposed. The limits in which are expected to be change in the deviations between the main project results and the corresponding ones of the implemented design, mathematically defined previous to its realization.

The accent is put on the cases when the device characteristics are presented as polynomials, obtained on the bases of the design of experiments (DOE) and the response surface methodology. An arbitrary technical characteristic Z_x=Z(x→) is presented.

A researcher could confine numerically the tolerance field between project results and expected realized ones in the whole investigated region.

The paper is characterized by an original approach and a new expression of standard deviation is proposed which will be of interest to designers.