Optimal Placement of Programmable Tooling Machines Considering Hierarchical Structure via Sparse Learning for Multistage Assembly Processes

End-of-line product dimensional quality assurance is crucial in multistage assembly processes (MAPs). Active control strategies involve the deployment of controllable, programmable tooling machines (PTs) to adjust part positions for in-process dimensional error compensation. In MAPs, multiple PTs may be deployed within a single stage or across various stages. To enable the normal operation of deployed PTs within a specific stage, an associated supporting platform (SP) is necessary. Consequently, the lower PT-level and the upper platform-level define a two-level hierarchical structure in MAPs. This paper aims to propose an optimal placement strategy of PTs, focusing on the final dimensional quality of the product and the total cost related to the number of accommodated PTs and required SPs. Based on the stream-of-variation (SOV) model of MAPs, we develop a novel sparse learning framework along with the corresponding parameter estimation algorithm to achieve the optimal placement. The case study demonstrates the effectiveness of our proposed method for the optimal placement of PTs in reducing dimensional variation in MAPs. Note to Practitioners—This paper was motivated by the widespread use of programmable tooling machines (PTs) in multistage assembly processes (MAPs), such as controllable fixtures and computer numerical control (CNC) machines. These PTs automatically compensate for in-process dimensional errors and enhance the final assembly quality. Multiple PTs can be allocated within the same stage or across various stages, but an associated supporting platform (SP) is needed to install, maintain, and manage the PTs at a specific stage. Given the high costs of PTs and SPs, it is crucial to find an optimal placement of PTs that minimizes the number of PTs and required SPs while ensuring assembly products acceptable by industrial quality standards. To address this issue, we propose a novel methodology that formulates the problem into a sparse learning framework, which can be efficiently solved using our developed algorithm. This research provides valuable insights for practitioners working on the dimensional quality control of final products in MAPs and similar manufacturing processes. By implementing our proposed optimal placement strategy of PTs, practitioners can assure product quality while minimizing the associated total cost.