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Fault isolation and identification are necessary components for system reconfiguration and fault adaptive control in complex systems. However, accurate and timely on-line fault identification in nonlinear systems can be difficult and computationally expensive. In this paper, we improve the quantitative fault identification scheme in the TRANSCEND diagnosis approach. First, we propose to use possible conflicts (PCs) to find the set of minimally redundant subsystems that can be used for parameter estimation. Second, we introduce new algorithms for computing PCs from the temporal causal graph model used in TRANSCEND. Third, we use the minimal estimators to decompose the system model into smaller, independent subsystems for the parameter estimation task. We demonstrate the feasibility of this method by running experiments on a simulated model of the reverse osmosis subsystem of the advanced water recovery system developed at the NASA Johnson Space Center. Our results show a considerable reduction in parameter estimation time without loss of accuracy and robustness in the estimation.