[en] The paper deals with the topical issue of quality assurance of technical products according to precise geometrical specifications. The aim of this work is to develop proposals for improving the system of tolerances and fits for linear sizes in the international standard ISO 286-1. The objective of this work is to increase the level of adequacy of the linear size tolerance model to the real dimensional elements of the parts. Two sizes of dimensional element - maximum material size and minimum material size are basic concepts of F. W. Taylor principles. The difference between the size of the maximum material holes (the minimum size) and maximum material size of shaft (maximum size) determines the type of the pair fit. In the ISO system of tolerances the ideal model of a dimensional element without form deviations of the surfaces is applied to linear dimensions. The ideal model is inadequate to the real dimensional element. The rejection of the form deviations resulted in the loss of the dimensional element minimum material size. The tolerance interval limits the upper and lower limits and the deviations of only the maximum material size. Validity inspection of the maximum material size by the upper and lower limit dimensions shall be provided by complete through and no-go gauges. Such monitoring will provide a fit with the required limiting values of clearances and tightness. Form tolerances in the diameter expression that is joined to the dimension tolerance for maximum material size increase the tolerance interval and make the minimum material limit that should be monitored by the no-go two-point gauge. Inconsistencies of the international tolerances system can be eliminated if to move from an inappropriate ideal model of a dimensional element to to the adequate real model considering the form deviation. (paper)