The cumulative exposure model (CEM) is often used to express the failure probability model in step-stress accelerated life tests (SSALT). This probability model is widely accepted because accumulation of fatigue is considered to be reasonable. Contrary to this assumption, the memoryless model (MM) is also used in electrical engineering because accumulation of fatigue is not observed in some cases. We propose here a new model, the extended cumulative exposure model (ECEM), which includes features of both the described models. A simulation study and applications to the actual experimental cases support the applicability of the proposed model. The independence model (IM) is also discussed.