In industrial scenarios, data augmentation is an effective approach to improve model performance. However, its benefits are not unidirectionally beneficial. There is no theoretical research or established estimation for the optimal sample size (OSS) in augmentation, nor is there an established metric to evaluate the accuracy of OSS or its deviation from the ground truth. To address these issues, we propose an information-theoretic optimal sample size estimation (IT-OSE) to provide reliable OSS estimation for industrial data augmentation. An interval coverage and deviation (ICD) score is proposed to evaluate the estimated OSS intuitively. The relationship between OSS and dominant factors is theoretically analyzed and formulated, thereby enhancing the interpretability. Experiments show that, compared to empirical estimation, the IT-OSE increases accuracy in classification tasks across baseline models by an average of 4.38%, and reduces MAPE in regression tasks across baseline models by an average of 18.80%. The improvements in downstream model performance are more stable. ICDdev in the ICD score is also reduced by an average of 49.30%. The determinism of OSS is enhanced. Compared to exhaustive search, the IT-OSE achieves the same OSS while reducing computational and data costs by an average of 83.97% and 93.46%. Furthermore, practicality experiments demonstrate that the IT-OSE exhibits generality across representative sensor-based industrial scenarios.