This paper presents a method for uncertainty analysis of prognostics with a focus on electronics subject to random vibration. First we identify uncertainty sources and types: measurement uncertainty, parameter uncertainty, failure criteria uncertainty, and future usage uncertainty. Next, we present an approach to determine the uncertainty in a prognostic analysis. Our approach utilizes a sensitivity analysis to identify the dominant input variables that influence the model output. With information of the input parameter variable distributions, a Monte Carlo simulation provides a distribution of accumulated damage. From the accumulated damage distributions, the remaining life can then be predicted with confidence intervals. A case study is presented whereby prognostics with uncertainty is applied to an electronic circuit board subject to random vibration. The results show that the experimentally measured failure time is within the bounds of the uncertainty analysis prediction.