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This paper compares two different approaches to estimate the reliability of mechanical components subject to degradation (wear, fatigue, etc.). This estimate is realized by considering the degradation drift (periodic or continuous measurement of the degradation level) from tests or exploitation. Two approaches are presented in this article. The first approach is based on a deterministic mechanical model given by the study of physical facts coupled with a Monte Carlo simulation to propagate the uncertainties of input parameters on the degradation. The second approach, based on the stochastic process, uses the Wiener process to model the evolution of degradation over time. A nonlinear formulation is developed in this paper. We compare these two approaches on an industrial case: the wear in rolling contact. The drift of degradation is estimated by the two approaches. We then calculate the failure distribution and associated reliability. Analysis of the results obtained with both approaches is made to discuss the advantages and disadvantages of each.