In this paper, lumen degradation is described by using a modified Brownian motion process for mid-power white-light LED packages, which were aged under step stress accelerated degradation test (SSADT). First, a SSADT model has been established based on the theory of equivalent accumulative damage. Then, a method was proposed to improve the accuracy of the parameter estimation by carefully modifying the estimator, which was proposed in the previous research. Experimental data show that parameters estimated by using SSADT model are very close to those estimated by using constant stress accelerated degradation test (CSADT) model, indicating the feasibility of the SSADT model. The experiment also indicates that SSADT can be used as an alternative to CSADT, as it enables comparable estimation accuracy, while using less testing time, a smaller sample size and less test capacity. Index Terms-accelerated test; Brownian motion; degradation test; light-emitting diodes; step stress; Wiener process I. INTRODUCTION ID-POWER white-light LEDs (MP-LEDs) have been widely considered as the new generation of luminaires due to their advantages of higher efficiency, longer lifetime, and more environment protections as compared to currently widely used lighting solutions (incandescence, fluorescence). Recently, due to fast evolution of the technologies, the lifetime of LED packages has been claimed to be as high as 50,000 hours. For such kind of products, failed units would be seldom observed during life tests, even though they are subjected to accelerated conditions. Therefore, it is unreasonable to collect Manuscript received