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Multistage Manufacturing Process (MMP) that comprises multiple manufacturing stages has been deployed to fabricate complex products through stage-wise sequential processing. Due to its sequential dependency and interconnectivity, MMP can induce a shutdown when all machines allocated at a specific stage break down regardless of Remaining Useful Life (RUL) of residual machines involved in the subsequent stages. Previous studies have contributed to deriving RUL predictive models for a single machine or process in the preventive maintenance realm; however, they rarely accommodate multiple machines and multi-stages in their modeling, considering the dependency and interconnectivity in MMP. This article proposes a method that predicts stage-level RULs for individual stages based on statistics and reliability approaches and finds optimal replacement time in terms of economic efficiency. The proposed method comprises: (1) the generation of RUL predictive models for individual machines using statistical process control, (2) the generation of RUL predictive models for individual stages using Weibull distribution, and (3) the finding of optimal replacement time for the individual stages based on an age replacement policy. This article includes a case study to validate the feasibility of the proposed method using an open dataset. The proposed method enables the prevention of a shutdown in MMP, wherein unintended breakdowns can occur at the stage-level, through exploring the stage where degradation becomes the most severe.