A novel copula subspace division strategy is proposed for fault detection and diagnosis. High-dimensional industrial data are analyzed in two elemental subspaces: margin distribution subspace (MDS) modeled by joint margin distribution, and dependence structure subspace (DSS) modeled by copula. The highest density regions of two submodels are introduced and quantified using probability indices. To improve the robustness of the monitoring index, a hyperrectangular control boundary in MDS is designed, and the equivalent univariate control limits are estimated. Two associated contribution indices are also constructed for fault diagnosis. The interactive relationships among the root-cause variables are investigated via a proposed state chart. The effectiveness and superiority of the proposed approaches (double-subspace and multisubspace) are validated using a numerical example and the Tennessee Eastman chemical process. Better monitoring performance is achieved compared with some conventional approaches such as principal component analysis, independent component analysis, kernel principal component analysis and vine copula-based dependence description. The proposed multisubspace approach fully utilizes univariate-based alarm data with a dependences restriction modulus, which is promising for industrial application.