Average lifetime, or mean time to failure (MTTF), of a product is an important metric to measure the product reliability. Current methods of evaluating MTTF are mainly statistics or data based. They need lifetime testing on a number of products to get the lifetime samples, which are then used to estimate MTTF. The lifetime testing, however, is expensive in terms of both time and cost. The efficiency is also low because it cannot be effectively incorporated in the early design stage where many physics-based models are available. We propose to predict MTTF in the design stage by means of physics-based models. The advantage is that the design can be continually improved by changing design variables until reliability measures, including MTTF, are satisfied. Since the physics-based models are usually computationally demanding, we face a problem with both big data (on the model input side) and small data (on the model output side). We develop an adaptive supervised training method based on Gaussian process regression, and the method can then quickly predict MTTF with minimized number of calling the physics-based models. The effectiveness of the method is demonstrated by two examples.