Recursive principal component analysis (RPCA) has gained significant attention as a monitoring tool for time-varying systems in recent years. The contribution of this article is the development of numerically efficient and memory-saving recursive fault detection and isolation (FDI) approaches for time-varying processes. The proposed approaches incorporate a recursive PCA based on a first-order perturbation (RPCA-FOP) analysis procedure and two recursive fault isolation methods. The proposed recursive fault isolation methods are the (i) recursive partial decomposition contribution (RPDC) and (ii) recursive diagonal contribution (RDC) methods. Four types of sensor faults, including bias, drifting, precision degradation, and complete failure, are simulated to test the proposed approaches. The utility of the proposed FDI approaches is demonstrated using a nonisothermal continuous stirred tank reactor (CSTR) system.