Total Monitoring of Causation‐Based Multivariate Processes

We consider monitoring multiple quality characteristics with causal relationships among them, and shifts occurring in cause variables may propagate to effect ones. Usually, a Bayesian network (BN) can describe causation, where, through directed arcs, a variable depends on its direct cause variables. In the literature, some monitoring methods have been proposed based on BNs, but these approaches focus merely on the means of each variable. By fully exploiting the BN structure, we propose for each quality characteristic to monitor shifts in its mean and variance, as well as in the functional dependency on its direct cause variables, and therefore achieve total monitoring of causation‐based multivariate processes. Specifically, we propose two causation‐based control charts. The first chart serves as a general tool for process monitoring, while the second one incorporates directional information, enabling the identification of shift locations through a diagnostic prescription. Simulations have validated the effectiveness of the proposed monitoring and diagnostic schemes.