In this paper, we investigate the problem of mining multivariate time series data generated from sensors mounted on manufacturing stations for early product quality prediction. In addition to accurate quality prediction, another crucial requirement for industrial production scenarios is model interpretability, i.e., to understand the significance of an individual time series with respect to the final quality. Aiming at the goals, this paper proposes a multi-task learning model with an encoder-decoder architecture augmented by the matrix factorization technique and the attention mechanism. Our model design brings two major advantages. First, by jointly considering the input multivariate time series reconstruction task and the quality prediction in a multi-task learning model, the performance of the quality prediction task is boosted. Second, by incorporating the matrix factorization technique, we enable the proposed model to pay/learn attentions on the component of the multivariate time series rather than on the time axis. With the attention on components, the correlation between a sensor reading and a final quality measure can be quantized to improve the model interpretability. Comprehensive performance evaluation on real data sets is conducted. The experimental results validate that strengths of the proposed model on quality prediction and model interpretability.