Some life tests result in few or no failures. In such cases, it is difficult to assess reliability with traditional life tests that record only time to failure. For some devices, it is possible to obtain degradation measurements over time, and these measurements may contain useful information about product reliability. Even with little or no censoring, there may be important practical advantages to analyzing degradation data. If failure is defined in terms of a specified level of degradation, a degradation model defines a particular time-to-failure distribution. Generally it is not possible to obtain a closed-form expression for this distribution. The purpose of this work is to develop statistical methods for using degradation measures to estimate a time-to-failure distribution for a broad class of degradation models. We use a nonlinear mixed-effects model and develop methods based on Monte Carlo simulation to obtain point estimates and confidence intervals for reliability assessment.