Profile monitoring based on transfer learning of multiple profiles with incomplete samples

Profile monitoring is an important tool for quality control. Most existing profile monitoring approaches focus on monitoring a single profile. In practice, multiple profiles also widely exist and these profiles contain rich correlation information that can benefit the monitoring of interested/target profile. In this article, we propose a transfer learning framework to extract profile-to-profile inter-relationship to improve the monitoring performance. In this framework, profiles are modeled as a multi-output Gaussian process (MGP), and a specially designed covariance structure is proposed to reduce the computational load in optimizing the MGP parameters. More importantly, the proposed framework contains features for dealing with incomplete samples in each profile, which facilitates the information sharing among profiles with different data collection costs/availability. The proposed method is validated and compared with various benchmarks in extensive numerical studies and a case study of monitoring ice machine temperature profiles. The results show the proposed method can successfully transfer knowledge from related profiles to benefit the monitoring performance in the target profile. The R code of this paper would be available as on-line supplementary materials.