Bayesian learning of structures of ordered block graphical models with an application on multistage manufacturing processes

The Ordered Block Model (OBM) is a special form of directed graphical models and is widely used in various fields. In this article, we focus on learning of structures of OBM based on prior knowledge obtained from historical data. The proposed learning method is applied to a multistage car body assembly process to validate the learning efficiency. In this approach, Bayesian score is used to learn the graph structure and a novel informative structure prior distribution is constructed to help the learning process. Specifically, the graphical structure is represented by a categorical random variable and its distribution is treated as the informative prior. In this way, the informative prior distribution construction is equivalent to the parameter estimation of the graph random variable distribution using historical data. Since the historical OBMs may not contain the same nodes as those in the new OBM, the sample space of the graphical structure of the historical OBMs and the new OBM may be inconsistent. We deal with this issue by adding pseudo nodes with probability normalization, then removing extra nodes through marginalization to align the sample space between historical OBMs and the new OBM. The performance of the proposed method is illustrated and compared to conventional methods through numerical studies and a real car assembly process. The results show the proposed informative structure prior can effectively boost the performance of the graph structure learning procedure, especially when the data from the new OBM is small.