The most important characteristics of many engineering objects are their strength and reliability. To determine the probability of an object failure according to the strength criterion, it is necessary to know the laws of distribution of the actual and ultimate stresses. However the processing of actual data on the acting and ultimate stresses indicates that these data cannot be described by the known laws of the parametric statistical theory. This paper proposes a new approach to the solution of the problem, which is based on the application of the mathematical apparatus of nonparametric statistics. The considered approach of calculating the probability of a failure and the quantile estimates of the safety factor of machine parts are universal. They allow estimation of the strength reliability of items regardless of the complexity of the laws of distribution of random values of the actual and ultimate stresses.