Abstract
Quality monitoring and control in design and manufacturing pose humongous challenges in the case when multivariate non-normal processes involved. For quality monitoring in manufacturing, statistical process control (SPC) control chart is a widely used SPC tool in real-world applications. Two main groups of methods for the construction of a multivariate control chart existed: 1) parametric or distribution (normal distribution) required methods. This given assumption is not usually satisfied, especially in the modern industrial manufacturing process; 2) nonparametric or distribution-free techniques, such as the construction of a multivariate control chart based on machine learning or classification algorithm. However, this type of method is complicated to determine unknown “out-of-control” state, or need large learning samples to determine it. In some cases, the task is impossible or lacks efficiency. In this study, a model-free method for multivariate process control (MSPC) is initially proposed and developed. Kernel Density Estimation directly learns the density distribution from data, and the Metropolis-Hastings algorithm generates large samples for control chart construction. The MSPC method is designed for both monitoring and diagnosis when the out-of-control signal is trigged. Simulation studies are performed through the proposed algorithm via the fixed bandwidth KDE and adaptive bandwidth KDE, and through the conventional Hotelling T² algorithm, and the comparations of the performance based on the introduced benchmark ARL₀ are listed and summarized. Geometric Dimensioning and Tolerancing (GD&T) is an essential part of design and manufacturing. Its verification involves complex geometric feature variation’s representing, modeling and analysis. A mode-based method for geometric feature variation modeling is introduced prior to the verification. Then a modal-based statistical GD&T tolerance verification method based on predictive confidence region concept is proposed. The effectiveness of the novel method is verified through cases and simulation studies. The proposed MSPC method avoids inevitable difficulties in generic parametric model estimation with an automatic and adaptive model learning algorithm and in small initial sample case. The GD&T verification method creates a platform for analyzing variation propagation among random surfaces in assembly and verification of GD&T tolerances with statistical inferences that are impossible with conventional deterministic models.