For failure modes that are caused by a degradation mechanism, almost all of the existing models assume that degradation starts once a product begins operation. However, under some situations, there is a degradation free period where degradation starts only after an initiation time. Both the initiation period and the degradation growth period affect the product reliability. The lengths of these two periods are usually governed by different failure mechanisms. In this paper, a two-step strategy for modeling degradation with an initiation period is proposed. Individual models are first built for the degradation free and the degradation growth periods. These two models are then integrated to obtain the final reliability model of the system. The relative importance values of the degradation free period and the degradation growth period with respect to product reliability are also studied. The importance values can help engineers allocate resources to improve the reliability of a product more effectively.