Integrated Variable Importance Assessment in Multi-Stage Processes

We introduce integrated multi-stage importance assessment (IMSIA), a method for the assessment of stage importance in multi-stage processes (MSPs) characterized by a hierarchy of relationships between stages. The importance measured by IMSIA may be used as a basis to strategize intervention actions on key stages directed at influencing the process outcome. The method deconstructs the overall MSP into its local building blocks, each composed by a specific individual stage and all of its direct inputs. Within each building block, a random forest regression model and a novel conditional permutation metric are then employed to quantify the local contribution of every input to the stage in question. Global contributions are finally measured by integrating the local contribution assessments, based on the overall structure of indirect and direct relationships in the process. After a theoretical characterization of the procedure, we illustrate IMSIA on two simulated MSP, as well as on a real-world multi-stage process of industrial semiconductor manufacturing.