Fault detection and isolation (FDI) has become a critical issue for increasing availability, reliability, and production safety in industrial process monitoring. While model-based FDI methods rely on the mathematical model and input-output data of a process to perform detection, the local approach is a new model-based FDI method that aims to detect slight changes of parametric properties of a system. Robustness with respect to model uncertainties is an important issue for the local approach. To reduce false alarms caused by the estimation error of process parameters, a new algorithm is proposed to recalculate the threshold based on the original threshold and covariance matrix of the estimated parameters. A similar algorithm is also provided to recalculate the threshold to reduce false alarms due to regular parameter fluctuations. The effectiveness of the proposed algorithms is shown by simulation studies on a papermaking cross-direction control system.