This paper develops a competing risk model to simultaneously analyze censored catastrophic failures and nonlinear degradation data of the NAND-based solid-state drives for space application. Two dominant failure modes are the hard failure of the controller due to single-event latch-up (SEL) and the soft failure of the NAND Flash manifesting as random write current degradation. As hard failure probability increases with radiation intensity and particle number, we establish the inverse power law-Weibull model for SEL cross section to model the accelerated censored data. The hard failure model is presented based on the invariance principle of total environmental particles' energy. On the other hand, soft degradation is described by the nonlinear Wiener-process-based accelerated degradation test model. Specifically, the temporal variability concerning the inherent variability of the degradation process over time and the unit-to-unit variability in degradation rates are both taken into account. Then, we derive the reliability functions and other quantities of interest under normal conditions with the assumption of independence of failure modes. Furthermore, to estimate the unknown parameters in the competing risk model, the transformed extreme value regression analysis other than the least square fitting method is adapted to issue the problem of data uncertainty of hard failures, whereas the maximum likelihood estimation method is developed for soft failures. Finally, a detailed simulation example is given to illustrate the procedure of the proposed reliability model with a sensitivity analysis.