This article introduces a p-stage step-stress accelerated life test on n system products, where each system contains m s-independent non-identical components connected in series, and it fails if any component has broken down. Due to cost considerations or environmental restrictions, masked causes of system failures and type-I censored observations might occur in the collected data. The time to failure under a pre-specified stress environment is described by a Weibull-distributed cumulative exposure model. A computationally feasible procedure based on the hybrid EM-NR algorithm is developed for maximum likelihood estimation of the model. Further, the reliability of the system and components are estimated at a specified time under usual operating conditions. The proposed method is illustrated through a numerical example and a simulation study under various masking levels.