This paper presents an approach to analyze accelerated life testing (ALT) data involving two failure modes. The approach first transforms the ALT dataset into two new datasets that correspond to individual failure modes. Each transformed dataset is modeled using a two-step procedure, and the resulted models associated with individual failure modes are combined into a competing risk model. The approach is illustrated using the ALT data of industrial heaters from the literature. The analysis shows that the shape parameter of the life distribution can change with stress level.