<p>Sophisticated machine learning (ML) and deep learning (DL) methodologies have been widely applied in predictive maintenance. However, such applications focus on optimizing overall prediction (or classification) accuracy across all learned examples, making it difficult to determine whether the prediction result for a single case is trustworthy. To fill this gap, a neutrosophic reasoning approach is proposed in this study for trustworthy predictive maintenance in smart manufacturing. In the proposed neutrosophic reasoning approach, a deep neutrosophic neural network (DNNN) is constructed and trained to predict the next time to failure of a machine, so as to arrange preventive maintenance in advance. By considering the overall prediction accuracy and the local prediction accuracy and learning sufficiency of each case, the three memberships of the neutrosophic time-to-failure forecast are derived. If the indeterminacy of the neutrosophic time-to-failure forecast exceeds a threshold, the prediction result is considered not trustworthy, because similar cases were either mis-predicted or rarely predicted before. The methodology proposed in this study has been applied to a case of a computer numeric control (CNC) tool in the literature to validate its applicability. According to the experimental results, the prediction results of about 6% of unlearned cases were not sufficiently trustworthy and should not be casually communicated to maintenance engineers. In addition, the trustworthiness can be economically enhanced by collecting the data of three more similar examples for each case. Furthermore, improving local prediction accuracy by 40% appeared to be a cost-effective approach to increasing the effectiveness of predictive maintenance in smart manufacturing.</p>