Real-time profile monitoring schemes considering covariates using Gaussian process via sensor data

Profile monitoring faces great challenges on account of the rapid development of advanced sensor technology. Massive sensor data are highly correlated and change in a complex way over time, which are difficult to describe with parametric models. Furthermore, quality characteristics are often affected by covariates. In this paper, nonparametric monitoring schemes considering covariates are proposed to monitor the correlated profiles in real-time. A profile model considering covariates based on Gaussian process is developed to predict the expected profile. Two control charts are then constructed based on the differences between the observed and expected profiles, which are calculated by Euclidean distance and definite integral, respectively. The effectiveness of the proposed monitoring schemes is validated by simulations. The proposed schemes are applied to a real case of busbar state monitoring in an automotive manufacturing plant.