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The problem of large amounts of carbon emissions causes wide concern across the world, and it has become a serious threat to the sustainable development of the manufacturing industry. The intensive research into technologies and methodologies for green product design has significant theoretical meaning and practical value in reducing the emissions of the manufacturing industry. Therefore, a low carbon-oriented product reliability optimal design model is proposed in this paper: (1) The related expert evaluation information was prepared in interval numbers; (2) An improved product failure analysis considering the uncertain carbon emissions of the subsystem was performed to obtain the subsystem weight taking the carbon emissions into consideration. The interval grey correlation analysis was conducted to obtain the subsystem weight taking the uncertain correlations inside the product into consideration. Using the above two kinds of subsystem weights and different caution indicators of the decision maker, a series of product reliability design schemes is available; (3) The interval-valued intuitionistic fuzzy sets (IVIFSs) were employed to select the optimal reliability and optimal design scheme based on three attributes, namely, low carbon, correlation and functions, and economic cost. The case study of a vertical CNC lathe proves the superiority and rationality of the proposed method.