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One of the reasons for the large number of road accidents on highways in Ukraine [1] is the instability of the braking properties due to the unstable characteristics of the brake mechanisms’ friction pairs. The manufacturer produces new automobiles with installed brake pairs (brake pads and their counter bodies), which have passed long-term tests for the stability of the friction coefficient and braking forces distribution of between the axles. This ensures the compatibility of the friction pairs characteristics for front and rear brake mechanisms according to the criteria of heat resistance. During operation, instead of worn-out brake pads, brake discs and drums, drivers can purchase new ones, manufactured as spare parts. However, in the well-known literature there are no methods that allow to check the compatibility of the friction pairs characteristics for front and rear brake mechanisms according to the criteria of heat resistance.

The solution to the problem of stability of a multi-axle vehicle during braking is connected with the determination of the dynamic distribution of normal road reactions between the axles. To assess the stability of the vehicle is used as an indicator of the stability factor representing the ratio of the stabilizing moment to moment, the perturbing skid. When the values of the stability coefficient is greater than or equal to unity, the movement is stable, and otherwise it is unstable. For a multi-axle vehicle, determining the dynamic normal road reactions on the axles is possible after disclosing the static uncertainty of the physical model of the car, which is a multi-support beam. The solution to this problem involves the use of the "three sigma" rule.