Appropriate sensor deployment is the key to the efficient diagnosis of product variation. Yet, optimizing sensor placement in complex manufacturing systems remains challenging. We propose a variation propagation analysis (VPA)-based sensor deployment strategy for variation diagnosis in multistation assembly processes. A state-space model is employed to analyze the influences of fixture faults and workpiece dimensional deviations on assembly variation. Based on matrix transformation, the assembly variation propagation characteristics are quantified and a VPN-based causal graph is constructed to represent the causality between assembly variation and sensor measurement. To ensure the diagnosability of over-tolerance of assembly variation (OAV) and the economics of the sensor system, an optimal sensor deployment scheme is presented. It uses the enhanced shuffled frog-leaping algorithm to minimize the OAV unobservability per unit cost and the sensor cost under the constraint of detectability. Finally, the effectiveness of the proposed approach is illustrated by a case study of sensor deployment for variation diagnosis in a multistation automobile differential assembly process.

Accurately and efficiently determining a system’s physical variables is crucial for precise product-quality control. This study proposes a novel method for optimal sensor deployment to increase the accuracy of sensing data for physical variables and ensure the timely detection of the product’s particle size in a wet-grinding system. This approach involves three steps. First, a Bayesian network (BN) is designed to model the cause–effect relationship between the physical variables by applying the path model. The detectability is determined to confirm that the mean shifts of all the physical variables are identifiable using sensor sets in the wet-grinding system. Second, the sensing location of accelerometers mounted on the chamber shell is determined according to the coupled computational fluid dynamics–discrete element method simulations. Third, the shuffled frog leaping algorithm is developed by combining the BN to minimize the maximum data output deviation index among all sensor sets and sensory costs; this is achieved under the constraints of the mean shift detectability, achieving optimum sensor allocation. Subsequently, a case study is performed on a zirconia powder production process to demonstrate that the proposed approach minimizes the requirements of the data output deviation index, sensory costs, and detectability. The proposed approach is systematic and universal; it can be integrated into monitor architecture for parameter estimation in other complex production systems.