Causation-based process monitoring and diagnosis for multivariate categorical processes

As many manufacturing and service processes nowadays involve multiple categorical quality characteristics, statistical surveillance for multivariate categorical processes has attracted increasing attention recently. However, in the literature there are only a few research papers that focus on the monitoring and diagnosis of such processes. This may be partly due to the challenges and limitations in describing the correlation relationships among categorical variables. In many applications, causal relationships may exist among categorical variables, in which the shifts at upstream, or cause, variables will propagate to their downstream, or effect, variables based on the causal structure. In such cases, a causation-based rather than correlation-based description would better account for the relationship among multiple categorical variables. This provides a new opportunity to establish improved monitoring and diagnosis schemes. In this article, we employ a Bayesian network to characterize such causal relationships and integrate it with a statistical process control technique. We propose two control charts for detecting shifts in the conditional probabilities of the multiple categorical variables that are embedded in the Bayesian network. The first chart provides a general tool, and the second chart integrates directional information, which also leads to a diagnostic prescription of shift locations. Both simulation and real case studies are used to demonstrate the effectiveness of the proposed monitoring and diagnostic schemes.