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A multistage manufacturing process (MMP) is a sequential manufacturing process where products enter a machine in each stage and go through multiple stages for their production. In MMP, the machines even with possessing remaining useful life (RUL) at the current stage have to stop production when all the machines in their previous stage fail to operate. A majority of the relevant studies focus on predicting RUL without considering the characteristics of MMP; thus, hardly provide predictive RUL and optimum replacement time for stage-level maintenance. The proposed method aims to predict RUL and optimize replacement time for stage-level maintenance under the MMP structure. It consists of three steps: (1) detection and prediction models for caution and breakdown alarms are generated from historical data, (2) RUL of currently running machines and the probability distribution of RUL at stage level is estimated by analyzing current data with the detection and prediction models, and (3) an optimal replacement time at the stage level is derived based on the probability function of RUL. The proposed method is demonstrated in a hypothetical case study to derive the optimal machine replacement time and validated in a real case study.