The lumen degradation of light emitting diodes subject to increasing stress loading is investigated by using a cumulative damage model. The cumulative damage process is taken as a Wiener diffusion process with a drift which depends on two stress loadings. General statistical inferences on the parameters and percentiles of the light emitting diode lifetime distribution are presented based on the cumulative damage measurements, collected from a two-variable constant-stress loading accelerated degradation test. Approximate lower s-confidence bounds of the light emitting diode lighting lifetime percentiles are given using the Fisher information of the maximum-likelihood estimators, and Bonferroni's inequality. The application of the proposed method is illustrated by a lumen cumulative damage data set of high power light emitting diodes.