In the presented work, a methodical approach was developed for determining rational operation modes of tribosystems, taking into account their design. This approach makes it possible in the designing stage, according to the predicted operating modes, to calculate the limits and margins of stable work in operation. The definition of the robustness of the tribosystem and the criteria for assessing the robustness are formulated based on the theory of stability of technical systems. It is shown that such a methodical approach allows for determining the modes of the rational operation of the designed structures without damaging the friction surfaces. Experimental studies have proven that not all designs of tribosystems lose stability due to the appearance of friction surface burrs. There are designs where the loss of stability occurs upon the appearance of accelerated wear. The developed criteria take into account two options for the loss of stability. An experimental verification of the modes of loss of stability of tribosystems was performed by the appearance of a burr or the beginning of accelerated wear with the calculated values of the robustness criteria. The obtained results allow us to conclude that the modeling error is within 8.3–18.7%, which is a satisfactory result in the study of friction and wear processes. Robustness criteria is based on the coefficient of friction RRf and wear rate RRI, and must be used when designing new constructions of tribosystems. Theoretical calculations of such criteria and the dependence of their change on changing the predicted operating modes will allow for justifying rational operating modes within their stability.