In the manufacturing industry, the process capability index (Cpk) measures the level and capability required to improve the processes. However, the Cpk is not enough to represent the process capability and performance of the manufacturing processes. In other words, considering that the smart manufacturing environment can accommodate the big data collected from various facilities, we need to understand the state of the process by comprehensively considering diverse factors contained in the manufacturing. In this paper, a two-stage method is proposed to analyze the process quality performance (PQP) and predict future process quality. First, we propose the PQP as a new measure for representing process capability and performance, which is defined by a composite statistical process analysis of such factors as manufacturing cycle time analysis, process trajectory of abnormal detection, statistical process control analysis, and process capability control analysis. Second, PQP analysis results are used to predict and estimate the stability of the production process using a long short-term memory (LSTM) neural network, which is a deep learning algorithm-based method. The present work compares the LSTM prediction model with the random forest, autoregressive integrated moving average, and artificial neural network models to convincingly demonstrate the effectiveness of our proposed approach. Notably, the LSTM model achieved higher accuracy than the other models.