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Smart manufacturing, which integrates a multi-sensing system with physical manufacturing processes, has been widely adopted in the industry to support online and real-time decision making to improve manufacturing quality. A multi-sensing system for each specific manufacturing process can efficiently collect the in situ process variables from different sensor modalities to reflect the process variations in real-time. However, in practice, we usually do not have enough budget to equip too many sensors in each manufacturing process due to the cost consideration. Moreover, it is also important to better interpret the relationship between the sensing modalities and the quality variables based on the model. Therefore, it is necessary to model the quality-process relationship by selecting the most relevant sensor modalities with the specific quality measurement from the multi-modal sensing system in smart manufacturing. In this research, we adopted the concept of best subset variable selection and proposed a new model called Multi-mOdal beSt Subset modeling (MOSS). The proposed MOSS can effectively select the important sensor modalities and improve the modeling accuracy in quality-process modeling via functional norms that characterize the overall effects of individual modalities. The significance of sensor modalities can be used to determine the sensor placement strategy in smart manufacturing. Moreover, the selected modalities can better interpret the quality-process model by identifying the most correlated root cause of quality variations. The merits of the proposed model are illustrated by both simulations and a real case study in an additive manufacturing (i.e., fused deposition modeling) process.